Kenichi Ishikawa (石川顕一) ...ishiken.free.fr/english/lectures/ARE20191023.pdf · Advanced...

高次高調波発生とアト秒科学 High harmonic generation & Attosecond science

Advanced Radiation Engineering放射線応用工学E

Kenichi Ishikawa (石川顕一) http://ishiken.free.fr/english/lecture.html

http://www.atto.t.u-tokyo.ac.jp [email protected]

2019/10/23

Advanced Radiation Application (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo)

2

東京大学原子力国際専攻

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Optical tweezers

method of generating high-intensity, ultra-short optical pulses


3


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Grating pair,pulse stretcher

Grating pair,pulse compressor

Amplifier

CPA - chirped pulse amplification

1 2 3Short light pulse from a laser.

The pulse is stretched,which reducesits peak power.

The stretchedpulse is amplified.

4 The pulse is compressed and its intensity increases dramatically.

©Johan Jarnestad/The Royal Swedish Academy of Sciences

https://6702d.https.cdn.softlayer.net/2019/10/pop_fy_en_18.pdf


4


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ELI


Focu

sed

inte

nsity

(W/c

m2)

CPA

Towards ever higher intensities

Several methods were developed for emitting extremely powerful short laser pulses, but then development stopped – it was not possible to amplify the light pulses further without damaging the amplifying material.

The world’s first functioning laser was built by the American physicist Theodore Maiman.

Extreme Light Infrastructure (ELI) is a European project with three sites that will be completed in a few years.

history of pulsed laser technology in terms of peak intensity


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“Scientific Background on the Nobel Prize in Physics 2018” lists applications of CPA technology

https://www.nobelprize.org/uploads/2018/10/advanced-physicsprize2018.pdf

• Strong-field physics and attosecond science

• Laser-plasma acceleration• High-intensity lasers in industry and

medicine

today’s topic


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High-harmonic generation (= one of the strong-field phenomena)

高次高調波発生

Quantum Beam Generation Engineering (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo)


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References 参考文献

7

The lecture material is downloadable from:　　　http://ishiken.free.fr/english/lecture.html M. Protopapas, C.H. Keitel and P.L. Knight, “Atomic physics with super-high intensity lasers”, Rep. Prog. Phys. 60, 389–486 (1997)F. Krausz and M. Ivanov, “Attosecond Physics”, Rev. Mod. Phys. 81, 163-234 (2009)K. L. Ishikawa, High-harmonic generation, in Advances in Solid-State Lasers, ed. by M. Grishin (INTEH, 2010), pp. 439-464大森賢治編「アト秒科学: 1京分の1秒スケールの超高速現象を光で観測・制御する」（化学同人、2015/8/10）


高調波発生 (Harmonic generation)

8


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線形光学効果（弱い光）

非線形光学効果（強い光）€

ω

€

ω

€

ω

€

ω,3ω,5ω,!

結晶、ガス等(crystal, gas)

Material response is linear in light intensity 物質の応答が、入射光強度に比例

物質の応答が、入射光強度に非線形に依存

€

3ω

€

5ω

：３次高調波(3rd harmonic)

：５次高調波(5th harmonic)

波長変換 (frequency conversion)

€

D = ε0E +P

€

P = ε0 χ(1)E + χ (2)E2 + χ (3)E 3 +![ ]

反転対称な媒質では、

€

χ (2) = 0線形分極 linear polarization

非線形分極 (nonlinear)

€

∇×∇×E = −µ0∂2D∂t2

Linear optical effect

Nonlinear optical effect

for a medium with inversion symmetry

Nonlinear material response


摂動論的高調波発生 (perturbative harmonic generation)

基底状態

電離

€

!ω

€

!ω

€

!ω仮想準位

€

3!ω

基底状態

電離

€

!ω

€

!ω

€

!ω

仮想準位

€

5!ω

€

!ω

€

!ω

３次高調波５次高調波

次数が高くなるほど、発生効率は減少。

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Harmonic order ↑ Efficiency ↓

3rd harmonic 5th harmonic

Ionization Ionization

Virtual levelVirtual level

Ground state Ground state


10


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高次高調波発生 High-harmonic generation (HHG)

新しい極端紫外・軟エックス線光源として注目される。 New extreme ultraviolet (XUV) and soft X-ray source

discovered in 1987

Highly nonlinear optical process in which the frequency of laser light is converted into its integer multiples. Harmonics of very high orders are generated.

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-2 -1 0 1 2Fundamental optical cycle

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2

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er s

hift

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d)

-10 -5 0 5 10

Pulse width (fs)

Intense femtosecond laser pulse�

High-order short-wavelength pulse�

gas jet�


Plateau（プラトー）- remarkable feature of high-harmonic generation

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Wahlström et al., Phys. Rev. A 48, 4709 (1993)

1015 W/cm2 Simulation

プラトー(plateau)：Efficiency does NOT decrease with increasing harmonic order. 次数が上がっても強度が落ちない。

カットオフ(cutoff)：Maximum energy of harmonic photons

•摂動論的には解釈できない(non-perturbative)

plateau

cutoff

plateau

cutoff

ponderomotive energyEc � Ip + 3Up Up(eV) =

e2E20

4m�2= 9.3� 10�14I(W/cm2)�2(µm)

800 nm, 1.6×1014 W/cm2

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

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rmo

nic

in

ten

sity (

arb

. u

nit)

50403020100

Harmonic order

= strong-field phenomena


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高次高調波発生のメカニズム = 3 step model Mechanism of HHG = 3 step model

-3

-2

-1

0

1

2

3

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4

Paul B. Corkum, Phys. Rev. Lett. 71, 1994 (1993)

K. C. Kulander et al., in Super-Intense Laser-Atom Physics, NATO ASI Ser. B, Vol. 316, p. 95 (1993)

Paul B. Corkum


Even up to 1.6 keV, > 5000 orders

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(almost) x-ray!

a new type of laser-based radiation sourceレーザーをベースにした新しいタイプの放射線源

Popmintchev et al., Science 336, 1287 (2012)

-600 -400 -200 0 200

time / as

0

0.2

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0.6

0.8

1

|Exu

v|2

/ a

rb. units

→ ←

τSXR

=

(43±1) as

(C) reconstructed SXR pulse

-6

-3

0

3

6

9

arg

(Exu

v)

/ ra

d

reconstructed

FTL pulse

phase

-20 -10 0 10 20

tau / fs

-4

-2

0

2

4

EIR

/ (

V/n

m)

→ ←

τmid-IR

=

(11.1±0.7) fs

(D) reconstructed mid-IR pulse

A(t)

FTL pulse

TG FROG

(A) mesured spectrogram

-10 -5 0 5 10

tau / fs

40

60

80

100

120

140

160

kinetic

energ

y / eV

(B) reconstructed spectrogram

-10 -5 0 5 10

tau / fs

40

60

80

100

120

140

160

kinetic

energ

y / eV

vector potential

50 100 150

photon energy / eV

0

0.5

1

-π

0

π

rec.

meas.

phase

Fig. 7. Analysis of streaking spectrogram and reconstructed attosecond pulse. A)Measured attosecond streaking trace obtained in xenon and B) Retrieved spectrogram withscaled mid-IR vector potential obtained using the ML-VTGPA algorithm. C) Temporalamplitude (blue) and phase (black) of the isolated attosecond pulse. The reconstruction by ourML-VTGPA algorithm provides an SXR pulse duration of ⌧SXR = (43 ± 1) as and a mid-IRpulse duration of ⌧mid�IR = (11.1±0.7) fs. The merit was found to be 4.3 ·10�3. The Fourier-transform-limited pulse (dashed red) calculated from the SXR photon spectrum measured inparallel to the streaking experiment. Measured (red) and reconstructed (blue) spectra with thereconstructed spectral phase (black) of the attosecond pulse are presented in the inset. D) Thevector potential of the mid-IR pulse obtained from the VTGPA reconstruction in comparisonwith the Fourier-transform-limited pulse (dashed red) calculated from the measured spectrumshown in Fig. 1(a) and the pulse measured with our home-built TG-FROG (dotted green).

line), although the detailed shapes of the two pulses di�er somewhat. The Fourier-transformedmid-IR spectrum (red dash-dotted line) demonstrates that the mid-IR pulse (black) is reasonablyclose to the Fourier limit.

We have verified the stability of the reconstruction by changing the initial guess for the mid-IRpulse in carrier frequency, absolute phase and vector-potential envelope A(t), as well as theinitial pulse duration of the SXR pulse. A total of three independent streaking spectrograms wereanalyzed. In each case, multiple sets of input parameters were used and all obtrained results enteredthe statistical analysis. The quoted pulse duration refers to the average of eight reconstructionsobtained in this way and the error interval corresponds to the standard deviation of the pulse

Vol. 25, No. 22 | 30 Oct 2017 | OPTICS EXPRESS 27516


What happens if the fundamental laser pulse is very short? では、超短パルスレーザーによる高次高調波はどんな感じ？

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Light emission takes place only once.

光の放出は１回だけ Attosecond (10-18 sec) pulseアト秒パルス

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Hentschel et al. (2001)

Gaumnitz et al. (2017)

Light propagates only 16 nm within 53 attoseconds.

attosecond


Attosecond pulses アト秒パルス

15


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As we successfully obtained the AC trace of the TC-HH in themid-plateau, we furthermore explored the temporal characteriza-tion for the HH cutoff. In this experiment, we switched thefocusing mirror from the SiC mirror to the Sc/Si multilayermirror. The signal is scanned every 148 as from ! 8.5 to 8.5 fswith 1" 103 laser shot accumulation at each delay point. Theresultant signal points versus delay are shown in the top panel inFig. 3. Three distinct signal points around 0 delay seem to be acorrelation peak and there are no noticeable side peaks in thisfigure, although our simulation result (see Discussion section)exhibits side peaks at ±6.7 fs with B0.2 relative AC amplitudecompared with the maximum peak at 0 delay. To confirm that thesignal around 0 delay is certainly the correlation signal and thatthere are no significant side peaks at ±6.7 fs, we performed ahigh-resolution AC measurement in the delay scanning rangesaround 0 fs and ±6.7 fs, as shown in the bottom panels in Fig. 3.We accumulated 1" 103 laser shots at each delay point and set thescanning delay step Dt to be 28 as. We can demonstrate a clearpeak at 0 delay as an AC in the middle-bottom panel in Fig. 3. TheAC duration was evaluated to be tAC¼ (700±90) as by fitting theexperimental trace to a Gaussian function; hence, the pulseduration is estimated to be tHHB500 as. We also find that thereare no noticeable side peaks in the measured AC traces in the left-bottom and right-bottom panels in Fig. 3. This is owing to the factthat the background noise amplitude (see Methods section) iscomparable to the amplitude of the side peaks expected from oursimulation. The noise magnitude against the peak AC amplitude isestimated to be B0.24; thus, we cannot clearly find side peakswith amplitudes o0.24. In other words, we can safely concludethat the side-peak ratio should be o0.24. As discussed below, wecan find both pre- and post-pulse in the calculated temporal pro-file at any CEP and relative phase. By assuming that the HH pulseconsists of three (pre-, main and post-) pulses and the upper limitof the side peaks in the AC trace should be 0.24, we can estimatethe possible largest peak height ratio of the pre- and post-pulses tobe B0.14. Further detailed analysis of the pre-/post-pulse issue ispresented in the next section with the help of our numerical modelof the TC-HH and statistical analysis of the relative phase.

From the measured pulse energy and pulse duration, the peakpower of the IAP nonlinearly interacting with the target medium

is evaluated to be 2.6 GW with weak satellite pulses (seeDiscussion section). This ultrahigh power from our tabletoplight source even surpasses that from a compact XUV FEL16,17.The peak brightness is also estimated to be B2" 1030 photonsper s! 1 mm! 2 mrad! 2, assuming a 60-mm beam diameter atthe exit of the gas cell.

DiscussionFinally, we examine attosecond pulse generation in our TC-HHscheme by numerical simulations. In these simulations, thesingle-atom response is calculated within the strong-fieldapproximation. The propagation of the TC laser pulse and thehigh harmonics are computed separately in cylindrical coordi-nates14,18. All the parameters, such as laser intensity, target gaspressure and medium length, are determined by the experimentalconditions. Here we assume that the CEP fCE fluctuatesrandomly during the AC measurement, whereas the statisticalfluctuations of the relative phase f0 are characterized by themeasured histogram of the relative phase in the TC inter-ferometer. To evaluate the relative phase variation with time inthe TC interferometer, we injected a continuous-wave (CW) laserbeam with a wavelength of 547 nm into the TC interferometer inthis measurement. We recorded spatial interference fringes on thesuperposed beam profile of the CW laser with a charge-coupleddevice camera (exposure time: B10 ms with 10 Hz repetition rate,which is synchronized with the pump laser) during B35 min,which is equivalent to the data acquisition time of one AC trace inour measurements. The phase of the spatial fringes at eachrecorded profile was converted to the relative delay and relativephase corresponding to the 1,300-nm field. The measured timeevolution of the relative phase, f0, is shown in Fig. 4a. We canthen evaluate the s.d. of f0 fluctuations, s, to be 0.23p from thismeasurement, whereas the offset of f0 is arbitrary. We adjust theoffset in Fig. 4a such that the average of f0 is equal to 0. Toimprove the S/N ratio of the AC trace, we overlapped ten ACtraces in Figs 2 and 3. The s-value with a typical normaldistribution of the ten AC traces’f0 fluctuations was almost thesame during the experiment, even though the phase profile as afunction of time was different.

–1.0 0.0 1.0

–70

–60

–50

–40

–7.98 –5.32 –2.66 0.00 2.66 5.32 7.98

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(×1

0–3 a

.u.)

(×1

0–3 a

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!t (fs)

Figure 3 | Measured AC traces of an IAP obtained from the side peak of Nþ ion signals. The time resolutions of the top and bottom panels correspondto 148 and 28 as, respectively. The error bars show the s.d. of each data point. The grey solid profiles are AC traces obtained using the simulated HH fields.

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3691

4 NATURE COMMUNICATIONS | 4:2691 | DOI: 10.1038/ncomms3691 | www.nature.com/naturecommunications

& 2013 Macmillan Publishers Limited. All rights reserved.

500アト秒 2.3 GW

highest powerTakahashi et al., Nat. Commun. 4, 2691 (2013)

highest photon energy

Xe29 eV

1.6 keV (> 5000 orders!)

�0 = 3.9µm

1.3 micro joule, 500 as

shortest pulse

Gaumnitz et al., Opt. Express 25, 27506 (2017)

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K. L. Ishikawa

How to generate an isolated attosecond pulse

(IAP)

18

K. L. Ishikawa

AMPLITUDE GATING

Light emission takes place only once.

Attosecond (10-18 sec) pulse

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© 2001 Macmillan Magazines Ltd

Hentschel et al. Nature 414, 509 (2001)

19

Baltuska et al. Nature 421, 611 (2003)530 as


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40

60

80

100

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< 2 cycles

Ne

K. L. Ishikawa

AMPLITUDE GATING

20


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43 as

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modified as compared to the attosecond pulse, which has to be taken into account in any reliablereconstruction method.

Fig. 5. CEP dependence of SXR supercontinua and attosecond streaking trace. A)CEP scan of SXR continua generated in argon and transmitted through a 100-nm Zr filter.A controlled variation of the CEP and pulse duration is achieved by scanning a pair offused-silica wedges, which translates to a modulation of the shape and cut-o� of the SXRcontinuum. B) Photoelectron streaking spectrogram obtained by ionizing xenon with anattosecond pulse generated in argon by varying the delay between the SXR and mid-IRpulses. The data consists of 350 spectra recorded with a step size of 100 as.

Recently, the Volkov-transform generalized projection algorithm (VTGPA, [35]) has beenproposed, which avoids the use of Fourier transformations, circumvents the CMA and thereforeenables the incorporation of the target-atom PMEs. The VTGPA has been tested with experimentaldata in the regime of attosecond pulse trains and with numerical simulations of isolated attosecondpulses. It has been shown to faithfully retrieve attosecond pulses with complex temporal structuresand broad spectral bandwidths. VTGPA has been shown to systematically retrieve the correctattosecond pulse duration, in contrast to the tendency of LSGPA to underestimate this quantity. Inits original formulation, the VTGPA is limited to spectrograms consisting of a single photoelectronband. Here, we adapt this formulation to include multiple overlapping photoelectron bands.Due to the very large bandwidths of our SXR pulses, photoelectrons measured at a givenenergy may originate from di�erent initial electronic shells, which have been ionized to the


K. L. Ishikawa

IONIZATION SHUTTER

21

HHG is suppressed when neutral atoms are depleted

tional two-photon ionization10. When a nonlinear optical process isobserved, it becomes possible to characterize the pulses bythe intensity autocorrelation, which is the standard diagnostictechnique in the visible region14. In the autocorrelation measure-ment, the intensity of nonlinear optical signal is recorded as afunction of the delay time between two replicas of a laser pulse. Theautocorrelation measurement is therefore the simplest type ofpump-probe experiments immediately extendable to femtosecondand attosecond nonlinear optical spectroscopy. In comparison withsynchrotron radiation (SR), which also covers the XUV and softX-ray regions, high harmonic pulses have temporal coherence andshort pulse duration—that is, high peak intensity. Thus, highharmonics are expected to open the new field of XUV nonlinearoptics.Previous work motivated us to generate and characterize high

harmonic pulses experimentally in the expectation of generatingintense attosecond pulses (Fig. 1). We focus on the ninth harmonicgenerated by the sub-10-fs blue laser pulse (photon energy 3.1 eV)in a multi-cycle regime, in contrast with previously reportedattosecond pulse generation in a few-cycle regime from the coher-ently superimposed broadband continuum in the cut-off region4,5.From nonadiabatic viewpoints, in which the slowly varying envel-ope approximation is not valid, Christov et al. simulated the 51sthigh harmonic generation of a 25-fs Ti:sapphire laser15. The 51stpulse lasts for about three optical cycles with ionization of theinteracting gas medium. A driving laser with a shorter pulseduration and shorter wavelength is expected to generate a shorterpulse. Together with the nonadiabatic effect, the dipole moment oflower order induced by the blue laser is larger than that induced by aTi:sapphire laser7. An enhancement of the pulse energy is thereforeexpected. From the adiabatic viewpoints16, a ninth-harmonic pulseof a 3.1-eV laser pulse was simulated by using a zero-range potentialmodel17. The ninth-harmonic pulse driven by an 8-fs pulse evolvessteeply with the highly nonlinear response of the dipole moment inthe rising edge of a driving pulse. When the optical electric fieldbecomes high enough to ionize the interacting atoms18, highharmonic generation is shut off because of the small dipole momentof the ions. In this case, a driving laser with a shorter pulse durationis also preferred.With the foregoing as a basis, modifications could be made by

taking account of the spatial intensity distribution in the drivinglaser beam and the propagation of harmonics. For example,harmonic pulses would be generated at different times at differentpositions, but the phase-matching effect would not preserve thedifference19. However, two-dimensional or three-dimensionalsimulations of high harmonic generation indicate that the harmo-nic pulses still retain the features of the single atom in the cut-off

region8,15. The autocorrelationmeasurement will make it possible toinvestigate these effects experimentally.

Blue laser pulses lasting 8.3 fs and 12 fs were generated by thefrequency conversion of a Ti:sapphire laser (photon energy 1.55 eV)as driving laser pulses20,21. Figure 2 shows the experimental setup forthe autocorrelation measurement. Two optically delayed replicas ofa blue laser pulse were focused into an argon gas jet to generate theninth high harmonic. The gas jet operating at 1 kHz was placed4mm after the focus and there was no spatial overlap between twobeams at high harmonic generation, where the peak intensity was3.9 £ 1014W cm22. The fundamental and lower-order harmonicswere eliminated by an aluminium filter. The ninth-harmonic pulseswere focused into helium gas by an Sc/Si multilayer spherical mirrorwith a focal length of 5 cm. The total pulse energy on the target was2 nJ. The ejected photoelectrons were collected and energy-resolvedby a magnetic bottle photoelectron spectrometer, ensuring a highcollection efficiency of 50%. Figure 2b is the photoelectron spec-trum of two-photon ATI. The observed highest photoelectronsejected by a one-photon process were from the 11th harmonicabsorption of Ar atoms and the peak by two-photon ATI was wellseparated from the other peaks, ensuring the assignment and thetwo-photon process. An autocorrelation trace was recorded bymeasuring the electron number at each optical delay.

The autocorrelation traces obtained by using 8.3-fs and 12-fs laserpulses are shown in Fig. 3a and Fig. 3b, respectively. Two electricfields superimpose coherently at a delay time of 0 fs, leading to theenhancement of two-photon ATI. The ratio of the peak to the

Figure 1 High harmonic pulse generation in the adiabatic picture. The red line is the ninthharmonic pulse of the 8-fs driving pulse with a peak intensity of 5.5 £ 1014W cm22

(dashed line). The blue line is the density of the neutral Ar atoms radiating high harmonics

calculated by using a tunnelling ionization theory18. The generation of high harmonics

ceases with the ionization of neutral atoms.

Figure 2 Two-photon above-threshold-ionization (ATI) autocorrelator. a, Experimentalsetup for the autocorrelation measurement of the ninth harmonic (9q) of the blue laser. To

improve the spectral resolution of the photoelectron spectrometer, an electrostatic field

was applied to the time-of-flight (TOF) tube and the photoelectrons were decelerated

inside the tube. b, The photoelectron spectrum. c, Diagram of the two-photon ATI

process. The area in red in b indicates the photoelectrons ejected from He atoms by the

process shown in c.

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NATURE |VOL 432 | 2 DECEMBER 2004 | www.nature.com/nature606 © 2004 Nature Publishing Group

density of neutral Ar atoms fundamental field envelope (400 nm)

9th harmonic (of 400 nm) = 27.9 eV

backgroundwas almost 3:1, in good agreement with the ideal case ofthe autocorrelation measurement, indicating that the peak is notthe coherent spike. To estimate the pulse durations of the ninthharmonics, the autocorrelation traces were fitted to gaussianfunctions; the results are shown by the red lines in Figs 3a and 3b.The corresponding full widths at half maximum of the autocorrela-tion traces were 1.3 ^ 0.1 and 1.8 ^ 0.1 fs, resulting in pulsedurations of 950 ^ 90 as and 1.3 ^ 0.1 fs, respectively.

In the 950-as pulse, however, bumps appeared around the mainpeak and the gaussian function does not seem to be appropriate todescribe the pulse shape. To check the validity of the experimentalresults, the spectra of the ninth harmonic (Fig. 3c) were Fourier-transformed with an assumption of a flat phase in the frequencydomain, and the autocorrelation functions were then calculated.The results are shown by the blue lines in Fig 3a, b. Both theautocorrelation trace of the 1.3-fs pulse and that of 8.3-fs pulse arereproduced well. The bumps are therefore attributable to thespectrum shape. Consequently, no other pulses were observedwithin the scanned time range of 20 fs, showing the isolated single

pulses. This is an advantage of the autocorrelation measurementover electron streaking, in which the measurable time range islimited by one-half of the optical cycle22. In future this method willbe extended to frequency-resolved optical gating (FROG)23 byimproving the spectral resolution to characterize the harmonicpulses completely.The spectra of the ninth harmonic reflect the spectra of the

Ti:sapphire and blue lasers. To increase the spectrumwidth, the gainaround 800 nmwas reduced by inserting an etalon in a regenerativeamplifier of the Ti:sapphire laser system, resulting in a spectrumwith two peaks24. This type of spectrum gives a relatively short pulseduration, although side bumps appear. Two peaks in the harmonicspectra are made prominent by the nonlinear process.For further pulse shortening to the attosecond timescale with the

use of a multi-cycle driving laser, one experimental approach is togenerate higher-order harmonics; the lower-order harmonics riseearlier than the higher-order harmonics, resulting in a longer pulseduration. Higher-order harmonics would therefore be adequate forattosecond pulse generation, and a driving laser with shorter pulseduration is also required. However, it would be difficult to shortenthe temporal duration below the half cycle of the driving laser(650 as). The feature of this scheme is a peak intensity high enoughto induce nonlinear phenomena.Finally, we estimate the photoelectron numbers created by the

two-photon ATI. The photoelectron yield Y from the interactionvolume V ( ¼ 3.1 £ 1029 cm3) with an atomic density n( ¼ 1011 cm23) is given by Y ¼ j (2)F2t n V, where j (2) is thecross-section of two-photon ATI, F is the photon flux, and t isthe pulse duration. In the present experimental conditions, F and twere 7.8 £ 1030 photons s21 cm22 and 1 fs, respectively, and j (2)

was set to 10252 cm2 from ref. 10. Consequently, Y is estimated to be1.6 £ 1023 electrons per pulse. The observed yield was 1.0 £ 1023

electrons per pulse, taking account of the collection and quantumefficiencies, which is consistent with the estimation. A

MethodsDriving laserBlue laser pulses were generated by broadband frequency doubling of the Ti:sapphire laserpulses to obtain shorter pulses than originally generated21. To broaden the bandwidth ofthe laser pulse, broadband frequency conversion was realized by spatial dispersion of eachspectrum component of the Ti:sapphire laser pulse so that it was phase-matched20. Thepulse energies of the blue laser pulses were 1.3mJ at a repetition rate of 1 kHz. The pulsedurations were controlled by changing the spectral bandwidth of the Ti:sapphire lasersystem. The optical system for spectrum dispersion was modified to employ a telescopeconfiguration for a large beam diameter of 2 cm. If this was not done, spatial pulse-fronttilt and phase mismatch were so large that high harmonics were not generated. Spatialcoherence of the driving laser is also important for generating two identical harmonicpulses. The pulses were characterized by self-diffraction frequency-resolved optical gatingand were found to be Fourier-transform limited.

Autocorrelation measurementIn the present experiment, two harmonic pulses were generated from two beamsproduced by spatially dividing a blue laser beam into two. This is different fromconventional autocorrelation measurements in the visible range, in which a beamsplitter is used. However, the original driving laser beam had high spatialcoherence, ensured by interfering the inverted image with the original one, so thetwo harmonic pulses naturally retained coherence. There still remained thepossibility of generating different pulses because of inequality in beam division.However, because the energy difference was less than a few per cent, the harmonicpulses generated were almost identical.

Anothermethod of producing two identical harmonic pulses has been shown6, involvingthe division of a harmonic beam spatially into two by a split XUV mirror after harmonicgeneration. However, in this case too the two pulses are not always identical. Because of theintensity distributionwithin a driving laser beam, harmonic pulses are generated at differenttimes. So, unequal spatial division of the harmonic beam leads to the production of twodifferent harmonic pulses even when a split XUV mirror is used.

Received 4 June; accepted 11 October 2004; doi:10.1038/nature03108.

1. McPherson, A. et al. Studies of multiphoton production of vacuum-ultraviolet radiation in the rare

gases. J. Opt. Soc. Am. B 4, 595–601 (1987).

2. Corkum, P. B. Plasma perspective on strong-field multiphoton ionization. Phys. Rev. Lett. 71,

1994–1997 (1993).

3. Paul, P. M. et al. Observation of a train of attosecond pulses from high harmonic generation. Science

292, 1689–1692 (2001).

Figure 3 Autocorrelation traces and the spectra of the ninth harmonic of the blue laser.a, b, Autocorrelation traces of the ninth harmonic pulses generated by using 8.3-fs (a)and 12-fs (b) blue lasers. The error bars show the standard deviation of each data point.

The full widths at half maximum of the autocorrelation traces obtained by the least-

squared fit to the gaussian functions were 1.3 ^ 0.1 and 1.8 ^ 0.1 fs, resulting in pulse

durations of 950 ^ 90 as and 1.3 ^ 0.1 fs, respectively. The lines in red show the fitting

results. The lines in blue are the calculated autocorrelation traces from the spectra (c) ofthe ninth harmonic. c, The spectra of the ninth harmonic pulses generated by using 12-fsand 8.3-fs pulses are shown by the blue and red lines, respectively.

letters to nature

NATURE |VOL 432 | 2 DECEMBER 2004 | www.nature.com/nature 607© 2004 Nature Publishing Group

950 as from 8.3 fs

1.3 fs from 12 fs

Ar

Isolated sub-fs pulse generation from a ~10 fs pulseSekikawa et al., Nature 432, 605 (2004)

K. L. Ishikawa

POLARIZATION GATING (PG)

22

NATURE PHOTONICS | VOL 4 | DECEMBER 2010 | www.nature.com/naturephotonics 827

plasma cannot be eliminated, even by using very short driving laser pulses. As higher harmonics are generated at higher levels of ioniza-tion, the phase-matching cut-off is always less than the single-atom cut-off given by equation (1), and is <150 eV even for helium driven by Ti:Sapphire lasers35. For harmonics generated at ionization lev-els of >ηcr, the finite phase mismatch due to uncompensated plasma

dispersion reduces the coherent build-up length to the microme-tre range, which reduces the yield by several orders of magnitude. Overcoming this phase-matching limit to generate bright harmon-ics in the soft- and hard-X-ray regions (required for many appli-cations in spectroscopy and imaging) has therefore been a grand challenge in extreme nonlinear optics.

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Figure 6 | Attosecond pulse generation. a, Isolated attosecond pulse generation driven by a few-cycle laser field. The cut-off photon energy varies significantly on a cycle-by-cycle basis, so that simple spectral filtering can isolate HHG emission from a single electron recollision at the peak of the laser field95. This approach has yielded isolated extreme-ultraviolet (EUV) pulses as short as 80 as (ref. 96). b, Isolated 130 as EUV pulse generation using polarization gating97,98. HHG emission is suppressed except during the most intense central cycle of the field, where the laser polarization is linear. c, If a second laser field of a different colour is added to this polarization gating method, even shorter EUV pulses can be generated99. d, Isolated attosecond pulse generation using gated phase-matching confined to a narrow temporal window near the critical ionization level. This approach results in isolated 210 as EUV pulses at photon energies around 50 eV, using multicycle driving lasers33. e, Isolated attosecond pulses through gated infrared phase-matching in the soft-X-ray region of the spectrum. Bandwidths sufficient to support 10 ± 1 as pulses are observed at around 400 eV. Figure reproduced with permission from: a (right), ref. 96, © 2008 AAAS; b (right), ref. 97, © 2006 AAAS; c (left), ref. 100, © 2010 NPG; c (right), ref. 99, © 2010 APS.

REVIEW ARTICLE | FOCUS NATURE PHOTONICS DOI: 10.1038/NPHOTON.2010.256 FOCUS | REVIEW ARTICLENATURE PHOTONICS DOI: 10.1038/NPHOTON.2010.256HHG is suppressed when circular polarization is used

Sansone et al., Science 314, 443 (2006)

counter-rotating circularly polarized pulses with a delay




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REVIEW ARTICLE | FOCUS NATURE PHOTONICS DOI: 10.1038/NPHOTON.2010.256 FOCUS | REVIEW ARTICLENATURE PHOTONICS DOI: 10.1038/NPHOTON.2010.256

Lin et al. (2017)

the turbo pumps. The decrease of cutoff photon energy at highgas pressure is likely caused by ionization-induced plasmadefocusing, which decreases the laser intensity at the interactionregion and shortens the extension of the plateau harmonics25.

53-attosecond pulses retrieved by PROOF method. Thestreaked photoelectron spectrum as a function of delay betweenthe soft X-ray pulse and the streaking IR pulse is measured anddepicted in Fig. 3a. Helium is used as the detection gas to avoidthe contribution of multiple valence orbitals to the photoelectronspectrum. Despite its low absorption cross section for the softX-ray pulse, the momentum shift of photoelectron is clearlyvisible across the whole photoelectron spectrum from 100 to 300eV, indicating the generation of an IAP into the water window.

To characterize such a broadband IAP, the phase retrieval byomega oscillation filtering (PROOF) technique is implemented11.In PROOF, the photoelectron spectrogram is broken down intoits primary Fourier components:

I ν; τð Þ # Io νð Þ þ Iω ν; τð Þ þ I2ω ν; τð Þ ð1Þ

where Io does not change with delay τ, Iω, and I2ω oscillate withthe streaking laser frequency ω and twice the frequency 2ω,respectively, and ν is the photoelectron momentum. While thesoft X-ray spectrum is directly measured by the TOF spectro-meter, the unknown spectral phase is encoded in Iω(ν,τ). Duringthe retrieval, the amplitude and phase of the soft X-ray pulses,depicted in Fig. 3c, d, are guessed iteratively in PROOF to match

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Fig. 4 Carbon dioxide K-shell photoabsorption spectrum. The twoabsorption peaks correspond to C1s → 2πu* and C1s → Rydberg 3s state26.Carbon dioxide gas with 25 torr·mm pressure-length product is used in thismeasurement

NATURE COMMUNICATIONS | DOI: 10.1038/s41467-017-00321-0 ARTICLE

NATURE COMMUNICATIONS |8: 186 |DOI: 10.1038/s41467-017-00321-0 |www.nature.com/naturecommunications 3

K. L. Ishikawa

DOUBLE OPTICAL GATING (DOG)

23

Polarization gating + two-color gating

of the cell, the energies of the fundamental and secondharmonic pulses were 150 and 30 !J, respectively. Theestimated effective intensities inside the gate were 2:8!1014 W=cm2 and 7! 1013 W=cm2, respectively. The gen-erated harmonics were measured with a gratingspectrometer.

The laser field can be expressed as the combination oftwo perpendicularly polarized fields ~E"t# $ Edrive"t#i %Egate"t#j. The driving field is

Edrive"t# $ E0&"e' 2 ln2&"t% Td=2#2="2!(

% e' 2 ln2&"t' Td=2#2="2!(# cos"!0t % ’CE#

% ae' 2 ln2"t2="22!# cos"2!0t % 2’CE % # !;2!#(

(1)

and the gating field is

Egate"t# $ E0"e' 2ln2&"t% Td=2' T0=4#2="2!(

' e' 2ln2&"t' Td=2' T0=4#2="2!(#sin"!0t % ’CE#; (2)

where E0 is the amplitude of the circularly polarizedfundamental laser field with carrier frequency !0 (periodT0), pulse duration "!, and CE phase ’CE. Td is the timedelay between the two circular pulses. The delay, T0=4,between the gating and the driving fields is introduced bythe quarter-wave plate. # !;2! is the relative phase betweenthe fundamental and second harmonic pulses. The durationof the SH pulse is "2!. Finally, a represents the strength ofthe second harmonic field relative to the fundamental field.

Figure 2(a) shows harmonic spectra of argon for one-color (linearly polarized fundamental field only, Td $ 0,a $ 0), two-color (a second harmonic field added to afundamental field polarized in the same direction, Td $0), conventional PG (a $ 0), and DOG fields. Notice that

FIG. 2 (color). Comparison of harmonic spectra and pulses.(a) The harmonic spectrum images obtained by various gatingmethods. The lineout plots in (b) compare the spectral profileand intensity obtained from DOG (blue line) with those from PGfor delays of 12 fs (red line) and 15 fs (green line). The resultsfrom numerical simulations are shown in (c). (d) Shows theFourier transform for the DOG and (e) shows the Fourier trans-forms for the PG and two-color spectra. These were doneassuming flat phase.

FIG. 1 (color). The driving filed components for PG corre-spond to (a) without and (b) with the second harmonic field,respectively. The driving field is shown as the red line. The twovertical lines represent the gate width. Here, the filled curves arethe attosecond pulses emitted when the driving fields alone areapplied. The background color shows the strength of the PG. Infigure (c) the ionization probability of an argon atom in the fieldof PG pulses is compared with that in the field of DOG. Thelongest pulses that can be used are those at which the probabilityreaches one.

PRL 100, 103906 (2008) P H Y S I C A L R E V I E W L E T T E R S week ending14 MARCH 2008

103906-2

�

� + 2�with second-harmonic field

Mashiko et al., PRL 2008, 103906 (2008)

IAP generation from a ~10 fs pulse

by a 300 mm focal length lens. The diameter of the centerspot of the focused Bessel streaking beam was 55 μm.The delay between the XUV and NIR pulses was con-trolled by a piezo-electric transducer (PZT). A 532 nm la-ser beam co-propagating through both arms was used tostabilize the Mach-Zehnder interferometer [12].The continuous XUV spectra generated with DOGmea-

sured by the MBES without streaking are shown in Fig. 2.By tuning the Ne pressure in the gas cell from 0.03 to0.33 bar, the cutoff photon energy was reduced from160 to 120 eV, which corresponds to Ip ! 2.6Up toIp ! 1.8Up. The calculated single-atom cutoff is 190 eV.The spectrum with pressure below 0.03 bar was not mea-sured due to the low count rate. The observed cutoff re-duction with increasing generation gas pressure isqualitatively consistent with previous experiments withXUV pulse trains [8,9]. Finally, the pressure of 0.2 bar inthe generation cell was chosen for the streaking experi-ment, where the entire spectrum, from 55 to 130 eV, wasconfined within the low-energy part of the Zr transmis-sion window where the filter GDD is negative.The attosecond pulses were retrieved from the streak-

ing trace shown in Fig. 3(a) using both the PROOF(phase retrieval by omega oscillation filtering) [13] andFROG-CRAB (frequency-resolved optical gating for com-plete reconstruction of attosecond bursts) [14,15] techni-ques. Whereas the FROG-CRAB technique requires thebandwidth of the photoelectron spectrum to be smallcompared to its central energy, PROOF is applicableto much broader spectra [13]. Here, we apply the princi-pal component generalized projections algorithm toPROOF [16], which is more robust than the methoddeveloped in [13]. In the limit of low streaking intensi-ties, Up < ωL, the streaking spectrogram is given byS"v; τ# ≈ I0"v# ! IωL

"v; τ# ! I2ωL"v; τ#, where IωL

and I2ωL

oscillate with the streaking laser frequency,ωL, and twicethe frequency, respectively [13], τ is the delay betweenthe XUV and laser pulses, and v is the photoelectronspeed. Since the spectrum and phase information ofthe attosecond pulses are completely encoded in IωL

,the amplitude and phase of the XUV pulse are guessed

in PROOF to match the modulation depth and phaseangle of IωL

.The streaking trace was obtained at a low streaking

intensity, 2.5 × 1011 W ∕cm2, to satisfy the requirementsof PROOF. Two methods are used to confirm the correct-ness of the phase retrieval. The first is to compare thephotoelectron spectrum obtained experimentally to theretrieved ones. This criterion was used in the past [17],and is a necessary condition of an accurate retrieval. An-other criterion is the agreement between the filtered IωL

trace from the measured spectrogram and the retrievedone. It is a much stricter requirement than the first one,because the modulation depth and phase angle of IωL

aredetermined by both the spectrum and phase, whereas thefirst method compares a quantity that is dominated byI0"v#, the unstreaked component of the spectrogram.Our retrieval meets both criteria very well, as shownin Figs. 3(c) and 3(b), respectively. Both the FROG-CRABand PROOF retrievals yield nearly identical temporalprofiles with a pulse duration of 67$ 2 as, as shownin Fig. 3(d), close to the transform-limited value of 62 as.The error bar was obtained following the treatment in [1],by taking each delay slice in the final guessed spectro-gram as a separate measurement of the pulse duration.The experiment was repeated at a higher streaking inten-sity (5 × 1011 W ∕cm2) and yielded the same result. Withthe intrinsic and Zr phase, we calculated a pulse durationof 68 as with the experimental spectrum, in agreementwith our retrieved result. At generation gas pressures sig-nificantly lower than 0.2 bar, the count rate was not suf-ficient for obtaining streaking traces with satisfactorysignal to noise ratio. Streaking was also performed athigher pressures, which yielded longer pulses due tothe reduced spectral bandwidth. For instance, at 0.36 bar,the retrieved pulse duration was 88 as.

Both PROOF and FROG-CRAB assume that onlyphotoelectrons emitted in a small angle in the streaking

Fig. 2. (Color online) XUV continuum generated by DOG inNe gas at six pressures. The length of the gas cell is 1 mm.The peak intensity at the center of the polarization gate is1 × 1015 W ∕cm2.

Fig. 3. (Color online) Characterization of a 67 as XUV pulse.(a) Streaked photoelectron spectrogram obtained experimen-tally. (b) Filtered IωL

trace (left) from the spectrogram in(a) and the retrieved IωL

trace (right). (c) Photoelectron spec-trum obtained experimentally (thick solid) and retrieved spec-tra and spectral phases from PROOF (solid) and FROG-CRAB(dashed). (d) Retrieved temporal profiles and phases fromPROOF (solid) and FROG-CRAB (dashed).

3892 OPTICS LETTERS / Vol. 37, No. 18 / September 15, 2012

Ne

Zhao et al., Opt. Lett. 37, 3891 (2012)

K. L. Ishikawa

GENERALIZED DOUBLE OPTICAL GATING (GDOG)

24

Elliptical instead of circular polarization

Gilbertson et al., PRL 105, 093902 (2010)

IAP generation from a > 20 fs pulse without need of carrier-envelope stabilization

Gilbertson et al., PRA 81, 043810 (2010)




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ctro

nen

ergy

(eV

)

Phot

oele

ctro

n en

ergy

(eV

)

Time delay (fs)


Time delay (fs)

1

0

20 as

Ne1

0

65 as

Ar1

0–100 1000

15 as

He1

0

30 as

Ne1

0

80 as

Ar1

0–100 10000.2

0.0

0.5

1.0

0.3 0.4 0.5 0.6

X-ra

y in

tens

ity (a

.u.)


X-ra

y in

tens

ity (a

.u.)

X-ra

y in

tens

ity1

0

X-ra

y in

tens

it

0

1

nten

sity

(a.u

.)tee

nnsi

1

1

cLaser field


HHG bursts

Single HHG burst

0–200 200 4000

0.84

0

–4

0.60.40.2

1.0

EUV

inte

nsity

Phas

e (r

ad)

Time (as)

Ar

163 as

L = 0.8 µm�

L = 0.8 µm�

L = 0.8 µm�

ELinitial

ELfinal

EX-rayinitial

EX-rayfinal

vX-ray = c

vL = c

L = 2.0 µm� L = 1.3 µm�


REVIEW ARTICLE | FOCUS NATURE PHOTONICS DOI: 10.1038/NPHOTON.2010.256 FOCUS | REVIEW ARTICLENATURE PHOTONICS DOI: 10.1038/NPHOTON.2010.256

K. L. Ishikawa

INFRARED TWO-COLOR SYNTHESIS

25

800 nm + 1300 nm two-color driving field

Infrared Two-ColorMulticycle Laser Field Synthesis for Generating an Intense Attosecond Pulse

Eiji J. Takahashi,1,* Pengfei Lan,1 Oliver D. Mucke,2 Yasuo Nabekawa,1 and Katsumi Midorikawa1

1Extreme Photonics Research Group, RIKEN Advanced Science Institute, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan2Photonics Institute, Vienna University of Technology, Gusshausstrasse 27-387, A-1040 Vienna, Austria

(Received 24 December 2009; published 7 June 2010)

We propose and demonstrate the generation of a continuum high-order harmonic spectrum by mixing

multicycle two-color (TC) laser fields with the aim of obtaining an intense isolated attosecond pulse. By

optimizing the wavelength of a supplementary infrared pulse in a TC field, a continuum harmonic

spectrum was created around the cutoff region without carrier-envelope phase stabilization. The obtained

harmonic spectra clearly show the possibility of generating isolated attosecond pulses from a multicycle

TC laser field, which is generated by an 800 nm, 30 fs pulse mixed with a 1300 nm, 40 fs pulse. Our

proposed method enables us not only to relax the requirements for the pump pulse duration but also to

reduce ionization of the harmonic medium. This concept opens the door to create an intense isolated

attosecond pulse using a conventional femtosecond laser system.

DOI: 10.1103/PhysRevLett.104.233901 PACS numbers: 42.65.Ky, 32.80.Rm, 42.65.Re

To achieve a breakthrough in attosecond science [1] fornonlinear optics and other applications, one of the mostimportant issues is the development of high-power atto-second pulse sources. The progress of high-order harmonicgeneration (HHG) techniques has resulted in the creationof isolated attosecond pulses (IAPs) [2– 6] and attosecondpulse trains (APTs) [7,8]. High-power APTs have beensuccessfully generated as a result of research on harmonicenergy scaling using a loosely focusing geometry [9].Meanwhile, various methods have been proposed for cre-ating an IAP, such as the use of a few-cycle infrared (IR)pulse as a driving laser [2– 4], polarization gating [6],double optical gating (DOG) [10], and so forth [5,11–14]. Although the shortest pulse duration of IAPs attainedis 80 as [15], the output energy is still not sufficient toinduce nonlinear phenomena because the pump pulse en-ergy is typically limited to a few mJ owing to the require-ments of sophisticated laser technology such as a few-cyclepulse duration and carrier-envelope phase (CEP; !CE)stabilization. The scalability of pump laser energy is ofparamount importance for the development of intense IAPsources. It is, however, still difficult to apply high-powerconventional femtosecond laser technology to increase thepower of IAPs.

In this Letter, we present the generation of a continuumhigh-order harmonic spectrum by mixing multicycle two-color (TC) laser fields with the aim of easily obtaining anintense IAP. We utilize a TC IR driver source to greatlyreduce the requirements for the pump laser system used forgenerating an IAP. A similar theoretical proposal has beenreported by other groups [16,17]; essentially, they assumedthat a CEP-stabilized pulse is used for the driving field. Asmentioned above, the requirement of CEP stabilization isone of the factors hindering the generation of an intenseIAP by a TW-class high-power laser system. To meet thisrequirement for laser technology, we optimize and demon-strate, for the first time, the creation of an IAP with non-

CEP-stabilized multicycle laser pulses. By adjusting thewavelength of the supplementary IR pulse, we suppress themultiple pulse burst and successfully generate an IAP.The synthesized TC electric field (Emix) is expressed

as EmixðtÞ ¼ E0 exp½%2 ln2ð t"0Þ2&cosð!0tþ!CEÞ þ

E1 exp½%2 ln2ðtþ!t"1

Þ2&cosðK!0tþ!CE þ!1Þ, where K

and !t are the frequency ratio and the delay time betweenthe main field (!0) and the supplementary IR field (!1 ¼K!0, K < 1), the subscripts 0 and 1 denote the two laserfield components, E0;1 is the electric field amplitude, and"0;1 and !1 denote the pulse duration and constant phaseoffset, respectively. When the TC field is generated by an800 nm, 30 fs pulse and a 1300 nm, 40 fs pulse, the fieldamplitude (E2

mix) of the near neighbors on both sides of thecentral peak is markedly suppressed [see Fig. 1(a)]. Here,the intensity ratio (# ¼ E2

1=E20) and the phases (!CE, !1)

are fixed at 0.15 and 0 rad, respectively. The intensity ratiobetween the central peak and the highest side peak is 0.8,which is almost the same as that of a 5 fs pulse at 800 nm(red line). Note that the second most intense peak appears

1.0

0.8

0.6

0.4

0.2

0.0

2 mix [

arb.

uni

ts]

151050

Time [fs]

10-2

2

4

10-1

2

4

100

Ioni

zatio

n pr

obab

ility

40302010

Pulse duration [fs]

(a) (b)

FIG. 1 (color). (a) Field amplitude (E2mix) of an 800 nm, 5 fs

pulse (red line) and a TC field (green line). The TC field isgenerated by an 800 nm, 30 fs pulse mixed with a 1300 nm, 40 fspulse. The intensity ratio (#) and the phases (!CE, !1) are fixedat 0.15 and 0 rad, respectively. (b) ADK ionization probability ofan argon atom calculated for the DOG (blue line), OC (red line),and TC (green line) methods as a function of the pulse durationof the main field.

PRL 104, 233901 (2010) P HY S I CA L R EV I EW LE T T E R Sweek ending11 JUNE 2010

0031-9007=10=104(23)=233901(4) 233901-1 ! 2010 The American Physical Society

800 nm 800 nm + 1300 nm

Takahashi et al., PRL 104, 233901 (2010)

As we successfully obtained the AC trace of the TC-HH in themid-plateau, we furthermore explored the temporal characteriza-tion for the HH cutoff. In this experiment, we switched thefocusing mirror from the SiC mirror to the Sc/Si multilayermirror. The signal is scanned every 148 as from ! 8.5 to 8.5 fswith 1" 103 laser shot accumulation at each delay point. Theresultant signal points versus delay are shown in the top panel inFig. 3. Three distinct signal points around 0 delay seem to be acorrelation peak and there are no noticeable side peaks in thisfigure, although our simulation result (see Discussion section)exhibits side peaks at ±6.7 fs with B0.2 relative AC amplitudecompared with the maximum peak at 0 delay. To confirm that thesignal around 0 delay is certainly the correlation signal and thatthere are no significant side peaks at ±6.7 fs, we performed ahigh-resolution AC measurement in the delay scanning rangesaround 0 fs and ±6.7 fs, as shown in the bottom panels in Fig. 3.We accumulated 1" 103 laser shots at each delay point and set thescanning delay step Dt to be 28 as. We can demonstrate a clearpeak at 0 delay as an AC in the middle-bottom panel in Fig. 3. TheAC duration was evaluated to be tAC¼ (700±90) as by fitting theexperimental trace to a Gaussian function; hence, the pulseduration is estimated to be tHHB500 as. We also find that thereare no noticeable side peaks in the measured AC traces in the left-bottom and right-bottom panels in Fig. 3. This is owing to the factthat the background noise amplitude (see Methods section) iscomparable to the amplitude of the side peaks expected from oursimulation. The noise magnitude against the peak AC amplitude isestimated to be B0.24; thus, we cannot clearly find side peakswith amplitudes o0.24. In other words, we can safely concludethat the side-peak ratio should be o0.24. As discussed below, wecan find both pre- and post-pulse in the calculated temporal pro-file at any CEP and relative phase. By assuming that the HH pulseconsists of three (pre-, main and post-) pulses and the upper limitof the side peaks in the AC trace should be 0.24, we can estimatethe possible largest peak height ratio of the pre- and post-pulses tobe B0.14. Further detailed analysis of the pre-/post-pulse issue ispresented in the next section with the help of our numerical modelof the TC-HH and statistical analysis of the relative phase.

From the measured pulse energy and pulse duration, the peakpower of the IAP nonlinearly interacting with the target medium

is evaluated to be 2.6 GW with weak satellite pulses (seeDiscussion section). This ultrahigh power from our tabletoplight source even surpasses that from a compact XUV FEL16,17.The peak brightness is also estimated to be B2" 1030 photonsper s! 1 mm! 2 mrad! 2, assuming a 60-mm beam diameter atthe exit of the gas cell.

DiscussionFinally, we examine attosecond pulse generation in our TC-HHscheme by numerical simulations. In these simulations, thesingle-atom response is calculated within the strong-fieldapproximation. The propagation of the TC laser pulse and thehigh harmonics are computed separately in cylindrical coordi-nates14,18. All the parameters, such as laser intensity, target gaspressure and medium length, are determined by the experimentalconditions. Here we assume that the CEP fCE fluctuatesrandomly during the AC measurement, whereas the statisticalfluctuations of the relative phase f0 are characterized by themeasured histogram of the relative phase in the TC inter-ferometer. To evaluate the relative phase variation with time inthe TC interferometer, we injected a continuous-wave (CW) laserbeam with a wavelength of 547 nm into the TC interferometer inthis measurement. We recorded spatial interference fringes on thesuperposed beam profile of the CW laser with a charge-coupleddevice camera (exposure time: B10 ms with 10 Hz repetition rate,which is synchronized with the pump laser) during B35 min,which is equivalent to the data acquisition time of one AC trace inour measurements. The phase of the spatial fringes at eachrecorded profile was converted to the relative delay and relativephase corresponding to the 1,300-nm field. The measured timeevolution of the relative phase, f0, is shown in Fig. 4a. We canthen evaluate the s.d. of f0 fluctuations, s, to be 0.23p from thismeasurement, whereas the offset of f0 is arbitrary. We adjust theoffset in Fig. 4a such that the average of f0 is equal to 0. Toimprove the S/N ratio of the AC trace, we overlapped ten ACtraces in Figs 2 and 3. The s-value with a typical normaldistribution of the ten AC traces’f0 fluctuations was almost thesame during the experiment, even though the phase profile as afunction of time was different.

–1.0 0.0 1.0

–70

–60

–50

–40

–7.98 –5.32 –2.66 0.00 2.66 5.32 7.98

–70

–60

–50

–40

–7.0 –6.0 7.06.0

(×1

0–3 a

.u.)

(×1

0–3 a

.u.)

!t (fs)

Figure 3 | Measured AC traces of an IAP obtained from the side peak of Nþ ion signals. The time resolutions of the top and bottom panels correspondto 148 and 28 as, respectively. The error bars show the s.d. of each data point. The grey solid profiles are AC traces obtained using the simulated HH fields.

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3691

4 NATURE COMMUNICATIONS | 4:2691 | DOI: 10.1038/ncomms3691 | www.nature.com/naturecommunications

& 2013 Macmillan Publishers Limited. All rights reserved.

autocorrelation traceXe 500 as

29 eV

Takahashi et al., Nat. Commun. 4, 2691 (2013)

High-energy (1.3 micro J), high-power (2.6 GW) IAPmore than 100 times more energetic than previously reported

K. L. Ishikawa

Quest for higher photon energy (shorter wavelength)

26

Ec = Ip + 3.17Upcutoff

Up(eV) =e2E2

0

4m�2= 9.3� 10�14I(W/cm2)�2(µm)

Longer fundamental wavelength is advantageous

Optical parametric chirped-pulse amplification (OPCPA)

K. L. Ishikawa

WATER-WINDOW HHG

27

spectral range between the K-absorption edges of C (284 eV) and O (543 eV)

absorbed by biological samples but not by water

attractive for high-contrast biological imaging

Figure 2 shows the measured Ne HH spectra driven by a1:55 !m laser pulse at a focusing intensity of 3:5!1014 W=cm2, at which the ionization rate was estimatedto be approximately 0.35% from the Ammosov-Delone-Krainov ionization theory [27]. The pump energy was setat 2.2 mJ. Note that the vertical axis of HH intensity isplotted with a linear scale. The measured harmonic spec-trum gradually increases up to 250 eV, which is in strongcontrast to the previously reported HH spectra in the waterwindow region [1,2,11–14,28]. To evaluate the intensitydistribution of the lower harmonics, we changed the spec-trometer’s grating from 2400 to 1200 grooves=mm. TheHH intensity (dotted blue profile in Fig. 2) with the1200 grooves=mm grating exhibits a broad plateau up to150 eV. In contrast, the HH intensity rapidly increasesabove 150 eV, which agrees with the spectrum obtainedfrom the grating with 2400 grooves=mm, then it starts todecrease at 170 eV because of the low diffraction effi-ciency of the 1200 grooves=mm grating above 170 eV.The HH yield is optimized by adjusting the focusing pointand by varying the backing pressure of the gas jet. The HHyield gradually increases as the gas pressure increases,which shows a quadratic dependence of the harmonic yieldas a function of gas backing pressure. The HH intensityabove the carbon K edge (284 eV) is found to be maximumat a backing pressure of approximately 20 atm with aGaussian-like spatial profile. By using the configurationparameter of supersonic gas get [29], the effective gaspressure at the interaction region is estimated to be ap-proximately 580 Torr. At the 250 eV photon energy, Gouyphase and gas dispersion are evaluated to be 360 cm"1

from the spot size of pump pulse and 615 cm"1 frombacking pressure, respectively. Also, plasma dispersion is

calculated to be 980 cm"1 at the 0.35% ionization. Tocompensate the total phase mismatch, the pump pulse isfocused after the gas jet, at which the Gouy phase has aminus sign. The coherence length and absorption lengthare estimated to be approximately 0.6 and 0.085 cm at the250 eV HH, respectively. Therefore, our condition almostsatisfies the optimized phase-matching condition. Thesolid red curve in Fig. 2 shows the evolution of ð1=f2Þ2as a function of HH photon energy. As expected, the HHintensity increases with increasing ð1=f2Þ2 up to 250 eV.Above 250 eV, the HH intensity decreases because thecutoff energy of 270 eV set by the interaction laser inten-sity prevents further extension of the plateau region. Thus,the HH intensity reaches a maximum at 250 eV. Themeasured HH spectrum is in sharp contrast to the conven-tional plateau of HH and clearly shows that the ALC isachieved by phase matching. The generation of the waterwindow wavelength HH from the neutral Ne medium hasbeen clearly demonstrated. The inset of Fig. 2 shows themeasured far-field spatial profile of the water window x ray(290–310 eV). We directly obtained the spatial profile ofthe water window HH beam using a two-dimensionaldetector. The beam divergence was measured and had a7 mrad full width at half maximumwith a Gaussian profile.This good beam quality also indicates that the phasematching is substantially satisfied along the propagationaxis of the pump pulse. Moreover, this 2D image ensuresthat our coherent water window source will be useful foracquiring 2D diffraction images.We further explored the generation of HH under a

neutral-medium condition by changing the nonlinear me-dium from Ne to He with the aim of obtaining a higherphoton energy. Figure 3 shows the measured He HH spec-tra driven by a 1:55 !m pulse with a focusing intensity of5:5! 1014 W=cm2, which is obtained with a2400 grooves=mm grating. The pump energy, beam di-

1.0

0.8

0.6

0.4

0.2

0.0

1.55

µm

He

HH

G [a

rb. u

nits

]

550500450400350300250200

Photon energy [eV]

0.8

0.6

0.4

0.2

0.0

Transm

ission of Mylar filter

Spa

ce

Photon energy

Carbon K edge

FIG. 3 (color). Measured harmonic spectra from neutral He.These spectra (left axis) are obtained with a 2400 grooves=mmgrating. The red line and the blue line, respectively, correspondto the spectra with and without a 1-!m-thick Mylar filter(C10H8O4). Both HH spectra are normalized to the peak inten-sity. The inset depicts a 2D HH spectrum image with a1-!m-thick Mylar filter on a microchannel plate. This imageis obtained by the accumulation of 1000 shots.

1.0

0.8

0.6

0.4

0.2

0.0

1.55

µm

Ne

HH

G [a

rb. u

nits

]

400350300250200150100

Photon energy [eV]

0.8

0.6

0.4

0.2

0.0

(1/f2 ) 2

Int.

Space

FIG. 2 (color). Measured harmonic spectra from neutral Neand evolution of the square of the reciprocal of imaginarycomponent f2. The solid blue line and the dashed blue line(left axis) correspond to the Ne spectrum obtained with a2400 grooves=mm grating and a 1200 grooves=mm grating,respectively. Both HH spectra are normalized to the peak inten-sity. The inset shows the far-field spatial profile of the waterwindow x ray (280–310 eV) obtained from neutral Ne gas. Sincea toroidal mirror is not set in front of the spectrometer, we candirectly observe the spatial profile of the HH beam (see inset ofFig. 3).

PRL 101, 253901 (2008) P HY S I CA L R EV I EW LE T T E R Sweek ending

19 DECEMBER 2008

253901-3

He�0 = 1.55µm

I = 5.5⇥ 1014 W/cm2

Takahashi et al., PRL 101, 253901 (2008)

K. L. Ishikawa

keV HHG

28

Even up to 1.6 keV, > 5000 ordersalmost x-ray!

a new type of laser-based radiation sourcePopmintchev et al., Science 336, 1287 (2012)

�0 = 3.9µm


Attosecond Science アト秒科学

29


シンボル


femtosecond, attosecondミリ m 10-3

マイクロ μ 10-6

ナノ n 10-9

ピコ p 10-12

フェムト f 10-15

アト a 10-18

30


シンボル


Electrons moving around the nucleus

Electron

Nucleus

Orbital period of the electron inside an atom

mω2r =1

4πϵ0

e2

r2

T =2π

ω= 2π

√4πϵ0mr3

e2= 152 × 10−18 s = 152 as

Need for attosecond shutter31


シンボル


Attosecond science studies electron motion in atoms, molecules, and solids.

32


シンボル

★ radiation-matter interaction　放射線と物質の相互作用

★ control of chemical reactions化学反応の制御

10-1810-1510-1210-910-610-31

Electron motionin atoms andmolecules

PhotosynthesisMolecularvibrations

Chemicalreactions

Fastest camerashutter

Stopwatch Fastelectronics

attosecondfemtosecondpicosecondnanosecondmicrosecondmillisecondsecond




Dynamics of the Auger effect

33


シンボル

オージェ効果のダイナミクス


Auger effect

光電子

光電子オージェ電子

オージェ効果Photoelectron

Auger electron

特性Ｘ線を放出するかわりに軌道電子を放出

内殻電子が電離（光電効果）

内殻励起状態のイオン

Instantaneous

~ a few fs

Observation of the ejection of Auger electrons→Ionizing X rays < a few fs→Attosecond pulse

Photoelectron

Ejection of a core electron

Core-excited ion

Ejection of a valence electron

34


シンボル


How to measure the electron ejection time?

Pump（イオン化を引き起こす）高調波(HHG)

Probe（電子の放出時刻を測る）レーザー光（laser）

35


シンボル


Attosecond streaking

高調波とレーザー光を遅延時間を持たせて照射

36


シンボル

Irradiate an atom with an attosecond pulse and laser pulse with delay

© 2002 Nature Publishing Group

instant t r is changed by DpðtrÞ ¼ ½eEaðtrÞ=qL% sinðqLtr þJÞ alongthe light electric field vector according to a simple classical analysis4

(Fig. 2a). E a is the amplitude envelope, and q L and J stand for thecarrier frequency and carrier-envelope phase of the laser pulse,respectively. The final energy is given by:

W f ðtrÞ ¼W i þ 2UpðtrÞ sin2ðqLtr þJÞ cos2v

þ ½8W iUpðtrÞ%1=2 sinðqLtr þJÞ cosv ð1ÞwhereUpðtÞ ¼ e2E2

aðtÞ=4meq2L is the electron’s cycle-averaged quiver

energy in the probe light field, e,m e andW i are the electron’s charge,mass and initial energy, and v is the angle between its finalmomentum vector and the light electric field vector. For v < 08(Fig. 2b) and W i .. !hqL; a moderate field strength ðUp < !hqLÞ isable to shift the electron energy by many electronvolts. The energyshift varies from zero to its maximum value within a quarter-wavecycle T0=4¼ p=2qL (<0.6 fs at lL ¼ 750 nm). This time-to-energymapping permits sampling of electron emission with attosecond

resolution. The final energy spectrum for an initial energy distri-bution dN=dW ¼ fWðW iÞ and time structure dN=dt ¼ f tðtr 2 tr0Þ;where t r0 represents the instant of the emission peak, can becalculated for any detection direction v and timing t r0 by usingequation (1). Experimentally, t r0 can be varied by varying the arrivaltime, that is, the delayDt (Fig. 2b), of the probe light pulse relative tothe X-ray pump pulse that triggers the electron emission. For largeinitial kinetic energy,W i .. !hqL; the validity of this simple classicaltreatment of the influence of a strong light field on electrons emittedwithin a fraction of the light wave cycle T0 has been corroborated byseveral photo-emission experiments5,8 as well as by quantummechanical analyses11,12.

We have generalized one (ref. 12) of these quantum theoriesaddressing photo-electron emission in the presence of a strong laserfield to describe the behaviour of Auger electrons emitted undersimilar conditions (for more details see Supplementary Infor-mation). Our theory yields the temporal evolution of hypotheticalsingle-line Auger electron spectra probed by strong few-cycle lightfor different decay times th as shown in Fig. 3. In our modelling weassumed tX ¼ 0.5 fs (at !hqX ¼ 100eV) and t L ¼ 5 fs (atlL ¼ 750 nm, !hqL < 1:6eV), corresponding to the current stateof the art. For th , T0=2 (Fig. 3a–c), the energy distribution of theAuger electrons exhibits pronounced variation as the delay Dt isvaried by as little as T0/4 (for th # T0=5 in close agreement with theresults of the above classical treatment). From the energy distri-butions recorded for different values of Dt, the temporal evolution

Figure 2 Attosecond two-colour sampling technique for probing electron emission fromatoms. An extreme ultraviolet or X-ray pulse excites the atomic target and induces

electron emission (see Fig. 1a). A delayed probe light pulse transfers a momentum Dp to

the ejected electron after its release. pi and pf represent the electron’s initial and final

momentum, respectively. a, The transferred momentum sensitively depends on the phase

and amplitude of the light field vector EL(t ) at the instant of release resulting in a time-to-

energy mapping on an attosecond timescale. For processes lasting less than the light

cycle the oscillating light field constitutes a sub-femtosecond probe, whereas processes

lasting longer than the light-wave cycle are sampled by the amplitude envelope of the

laser pulse. In both cases, a sequence of light-affected electron energy spectra are

recorded at different delays Dt, from which the time evolution of electron emission is

reconstructed. b, In our experiments, we used a 97-eV, sub-femtosecond soft-X-raypulse for excitation and a 750-nm (1.6 eV), sub-7-fs few-cycle light pulse for probing

electron emission. The two pulses are collinearly focused into a krypton gas target by a

two-component mirror similar to that used in ref. 5 but designed to reflect photons with

higher energies. The kinetic energy distribution of the ejected photo and Auger electrons

has been measured with a time-of-flight spectrometer aligned parallel to the polarization

direction of the light pulse and the X-ray pulse.

Figure 1 Schematic illustration of atomic excitation and relaxation processes followingexposure to an ultrashort X-ray pulse. a, In the absence of resonances, the atom instantly

responds by ejecting photo electrons (processes a, a 0 ) with jw photo(t )j2 following thetemporal intensity profile of the exciting X-ray pulse. The inner-shell vacancy (W h ) is

subsequently filled (process b) by an electron from an outer shell upon emission (process

c) of a secondary (Auger) electron with jw Auger(t )j2 tracing the decay of the inner-shellvacancy. b, Probing the emitted photo and Auger electrons reveals the excitation andrelaxation dynamics of core-excited atoms. W kin, kinetic energy; W bind, binding energy;

Wh,W1,2, binding energies of core and valence electrons, respectively; N, number of freed

electrons. tX, duration of X-ray pulse; th, decay time of core hole. The photo and Auger

electrons are represented here (as in Fig. 5) in violet and green, respectively.

articles

NATURE |VOL 419 | 24 OCTOBER 2002 | www.nature.com/nature804

Drescher et al., Nature 419, 803 (2002)

How to measure the electron ejection time? Itatani et al., Phys. Rev. Lett. 88, 173903 (2002)

-0.010-0.008-0.006-0.004-0.0020.0000.0020.0040.0060.0080.010

0 2 4 6 8 10

Elec

tric

Fiel

d(a.

u.)

Time(fs)

attosecond pulse

infrared laser


How to measure the electron ejection time?E(t) = E0(t) cos(ωt + φ)

dp

dt= m

dv

dt= −eE(t)

t = tr で電離初速度（運動量）

p0 =√

2m(hωX − Ip)

検出器での運動量 Momentum at the detector

37


シンボル

ionization at

Initial momentum

p = p0 �Z 1

t0

eE(t)dt = p0 + eA(t0)

electron ejection

time

momentum (energy) change

vector potential


Life time of the Auger decay～8 fs

光電子


Auger effect

Auger electron

PhotoelectronPump…HHG soft x rays13 nm

Probe…Laser750 nm

数フェムト秒程度の超高速過程が見える！

光電子


38


シンボル

Ultrafast process ~ a few fs


Delay in photoemission (How long does the photoelectric effect take?)

39


シンボル

光電効果には何アト秒かかるか？


When Does Photoemission Begin?

40


シンボル

The photoelectric effect is usually considered instantaneous.

Ne Ne

Ne

Ne Ne

time delay?

2s2p

from 2s orbital

h⌫ > 48.5 eV

Schultze et al., Science 328, 1658 (2010)

from 2p orbital


The 2s electron appears to come out 21 attoseconds earlier than the 2p electron!

41


シンボル

bars are reduced at higher intensities, primarilybecause of the increased spectral shift.

Theoretical discussion. First, we show thatthemeasured delay of ~20 as cannot be explainedby a delayed onset of streaking, which was thedominant effect in (17). The streaking NIRfield may be significantly screened by boundelectrons at small distances from the nucleus.After the absorption of an XUV photon, it takesthe positive-energy electron a finite time to leavethis screened volume, and this time interval maybe different for electrons originating from dif-ferent orbitals. However, for an atom, this dif-ference cannot exceed a few attoseconds. Thecharacteristic scales can be extracted from theclassical trajectories shown in Fig. 1B. If we as-sume that the 2s and 2p electrons are set inmotion at the same moment, their classical

trajectories would acquire a relative delay of 20as after traveling over 5 Å, whereas significantscreening from the streaking field is limited to adistance of less than 1Å from the nucleus. Further-more, if screening played a dominant role, thefaster 2p electrons would be exposed to thestreaking field earlier than the slower 2s ones,whereas measurements and quantum simulationsshow that the slower electron is emitted first.

Now we turn our attention to the quantum-mechanical description. First of all, we need adefinition for the photoemission delay. Considera photoelectron wave function jyðtÞ⟩ created byan XUV pulse centered at t ¼ 0. The motion ofthe wave packet after photoionization is conve-niently described in a basis of continuum statesje⟩, each of which has a well-defined energy eand describes a wave that propagates in the di-

rection of the detector. In this basis, each prob-ability amplitude has a simple time dependence:⟨ejyðtÞ⟩ ¼ cðeÞe−ieℏt , where the complex-valuedfunction cðeÞ fully describes the properties ofthe wave packet. In this representation, a delayDtin photoemission, shown as a shift of the elec-tron’s trajectory in Fig. 1B, adds e

ℏDt to the phaseof cðeÞ. It is therefore meaningful to define thegroup delay of the outgoing electron wave pack-et, in accordance with earlier work (4, 5, 25), asaðeÞ ¼ ℏ d

de arg½cðeÞ%. Analyzing our simula-tions, we average aðeÞover the bandwidth ofthe XUV pulse (29) and denote the result as a.

As the first and most important task, we val-idate the experimental methodology. Intuitively,one expects that a delay in the formation of awave packet causes a corresponding temporalshift of the streaking spectrogram. This holds true

Fig. 2. Attosecond streaking spectrograms (A and B), evaluated photoelectronwave packets (C), and streaked spectra (D). The spectrograms in (A) are com-posed of a series of photoelectron energy spectra recorded by releasing 2s and2p electrons from Ne with an attosecond XUV pulse in the presence of a strongNIR few-cycle laser field, as a function of the delay between the XUV and NIRfields. The spectrogram is processed with a FROG algorithm tailored for streakingmeasurements (30). (B) shows the spectrogram reconstructed by this algorithm.

The retrieved 2s and 2p spectra, together with the respective group delays, areplotted in (C) (black solid line and red dotted line, respectively). The reconstructedenergy spectra are in excellent agreement with the measured ones (gray dashedline). The average difference between the group delays corresponds to a 20-asretardation of the 2p emission with respect to the 2s emission. (D) comparesreconstructed and measured streaked spectra at two delays, which exhibit thelargest positive and negative shifts of the electron energy distribution.

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within the Coulomb-Volkov approximation (CVA)(29). To quantify the accuracy of the CVA, thesingle-electron time-dependent Schrödingerequation in three spatial dimensions was numer-ically solved with an effective potential that mod-eled Ne (29). The analysis of wave packetsyielded a spectrally averaged relative group delayof a2p − a2s ¼ 4:5 as. Although the CVAyieldsthe same value of the temporal shift betweenspectrograms, the numerical solution of theSchrödinger equation results in simulated spec-trograms that are shifted with respect to eachother by 6.8 as. The origin of this discrepancy liesin the fact that the photoelectron interacts withboth the streaking field and the ion, resulting in aquantum motion that is not exactly described byknown analytical approaches. Thus, for the cur-rent experimental parameters, the small devia-tions between the electron’s exact motion andthat modeled via the CVA give rise to a 2-asdiscrepancy in the relative delay.

Accepting this small discrepancy, many-electron models were applied to investigate theeffects of electron correlation. As a first attempt,the multiconfigurational Hartree-Fock method wasused to evaluate transition matrix elements fromthe ground state of Ne to states where the electronwave asymptotically propagated along the direc-tion of the streaking NIR electric field. These

matrix elements predict a relative delay ofa2p− a2s ¼ 4:0 as. The major drawback of thismodel is that it does not account for inter-channel coupling (6). This deficiency was over-come by modeling the interaction with the XUVpulse using the state-specific expansion approach(31, 32). This model accounts for electron corre-lations before and after photoionization and pre-dicts a relative group delay of a2p− a2s ¼ 6:4 as.Our modeling successfully predicts that the emis-sion of 2s electrons precedes that of 2p elec-trons, but the computed relative delay is ~15 as(3 SD) smaller than the measured value.

So far, the theoretical discussion has focusedon the relative delay between two photoemis-sion channels, which can be acquired experi-mentally. Precise determination of the zero oftime for allowing us to track the history ofmicroscopic phenomena accurately (Fig. 1A)calls for precise knowledge of the delay be-tween the XUV pulse and an outgoing electronwave packet (henceforth, absolute delay). Thiscan only be inferred from theory. For multi-electron systems, such as Ne, physical descrip-tion of the discrepancies revealed by this workproved to be a challenge. The sensitive exper-imental test to which time-dependent many-electronmodels can now be subjected will benefittheir development.

Meanwhile, it is possible to obtain reliableabsolute emission times for He, with which trulyab initio simulations (33) can be carried out withthe help of supercomputers. Such simulationswere performed for the He (1s2) ground state, andfor direct ionization with a 100-eV photon, a 5-astemporal shift of the spectrogram was found.Such modeling will allow precise timing calibra-tion of attosecond measurements, once suffi-ciently powerful attosecond sources will allowthe recording of spectrograms for He withsufficiently good statistics in spite of its smallphotoionization cross-section.

Conclusions and outlook. Establishing thezero of time in atomic chronoscopy is currentlytainted with an error of up to several tens ofattoseconds. Because attosecond streaking canmeasure only relative delays between differentphotoemission channels, the knowledge of abso-lute delays relies on the predictions of thoroughlytested time-dependent multielectron models.Presently, only two-electron ab initio simulationsprovide this degree of reliability, but the lowphotoionization cross-section of He limits (be-cause of low S/N) the timing accuracy. For morecomplex systems, phase-sensitive measurementsof the photoelectron wave packets via attosecondstreaking will put many-electron models ofatomic photoionization to comprehensive, highlysensitive tests, which is a prerequisite for grad-ually improving them and gaining trust in theirpredictions. These developments will improve ourunderstanding of subatomic electron correlationsand will make the absolute timing precision ofatomic chronoscopy approach the 1-as frontier.

References and Notes1. H. Hertz, Annalen Physik Chem. 267, 983 (1887).2. W. Hallwachs, Annalen Physik Chem. 269, 301 (1888).3. A. Einstein, Annalen Physik 17, 132 (1905).4. E. P. Wigner, Phys. Rev. 98, 145 (1955).5. C. A. A. de Carvalho, H. M. Nussenzveig, Phys. Rep. 364,

83 (2002).6. A. F. Starace, in Handbuch der Physik, W. Mehlhorn, Ed.

(Springer, Berlin, 1982), vol. 31.7. S. T. Manson, Radiat. Phys. Chem. 75, 2119 (2006).8. M. Y. Ivanov, J. P. Marangos, J. Mod. Opt. 54, 899

(2007).9. A. Baltuška et al., Nature 421, 611 (2003).

10. R. Kienberger et al., Nature 427, 817 (2004).11. M. Nisoli, G. Sansone, Prog. Quantum Electron. 33, 17

(2009).12. G. Sansone et al., Science 314, 443 (2006).13. M. Schultze et al., N. J. Phys. 9, 243 (2007).14. E. Goulielmakis et al., Science 320, 1614 (2008).15. M. Hentschel et al., Nature 414, 509 (2001).16. A. Borisov, D. Sánchez-Portal, R. Díez Muiño, P. M.

Echenique, Chem. Phys. Lett. 387, 95 (2004).17. A. L. Cavalieri et al., Nature 449, 1029 (2007).18. A. K. Kazansky, P. M. Echenique, Phys. Rev. Lett. 102,

177401 (2009).19. C. Lemell, B. Solleder, K. Tőkési, J. Burgdörfer, Phys. Rev.

A 79, 062901 (2009).20. J. C. Baggesen, L. B. Madsen, Phys. Rev. Lett. 104,

043602; and erratum, 209903 (2010).21. U. Becker, D. A. Shirley, in VUV and Soft X-Ray

Photoionization, U. Becker, D. A. Shirley, Eds.(Plenum, New York, 1997), chap. 5.

22. A. Rudenko et al., Phys. Rev. Lett. 101, 073003 (2008).23. J. Mauritsson et al., Phys. Rev. Lett. 100, 073003 (2008).

Fig. 3. The relative delay between photoemission from the 2p and 2s subshells of Ne atoms, induced bysub–200-as, near–100-eV XUV pulses. The depicted delays are extracted from measured attosecondstreaking spectrograms by fitting a spectrogram, within the strong-field approximation, with param-eterized NIR and XUV fields. Our optimization procedure matches the first derivatives along the time delaydimension of the measured and reconstructed spectrograms, thereby eliminating the influence of un-streaked background electrons [for details on the fitting algorithm, see (29)]. From the analysis of a set ofspectrograms, the measured delays and associated retrieval uncertainties are plotted against the amplitudeof the vector potential applied in the attosecond streak camera. Spectrograms measured in the presence ofa satellite attosecond pulse were found to exhibit a less accurate retrieval of the delay value. When a subsetof data (red diamonds) that represents scans with less than 3% satellite pulse content was evaluated, amean delay value of 21 as with a standard deviation of ~5 as was found. The green circles represent theresult of analyzing spectrograms recorded with an XUV pulse with narrower bandwidth in order to excludethe potential influence of shakeup states contributing to the electron kinetic energy spectrum.

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Ultrafast electron dynamics in phenylalanine initiated through ionization by attosecond pulsesCalegari et al., Science 346, 336-339 (2014)

radiation damage of biomolecules

ATTOSECOND DYNAMICS

Ultrafast electron dynamics inphenylalanine initiated byattosecond pulsesF. Calegari,1 D. Ayuso,2 A. Trabattoni,3 L. Belshaw,4 S. De Camillis,4 S. Anumula,3

F. Frassetto,5 L. Poletto,5 A. Palacios,2 P. Decleva,6 J. B. Greenwood,4

F. Martín,2,7* M. Nisoli1,3*

In the past decade, attosecond technology has opened up the investigation of ultrafastelectronic processes in atoms, simple molecules, and solids. Here, we report the applicationof isolated attosecond pulses to prompt ionization of the amino acid phenylalanine andthe subsequent detection of ultrafast dynamics on a sub–4.5-femtosecond temporal scale,which is shorter than the vibrational response of the molecule. The ability to initiate andobserve such electronic dynamics in polyatomicmolecules represents a crucial step forwardin attosecond science, which is progressively moving toward the investigation of moreand more complex systems.

The investigation of ultrafast processes inatoms received a major stimulus with theintroduction of attosecond pulses in theextreme ultraviolet (XUV) spectral region(1). Real-time observation of the femto-

second Auger decay in krypton was the first ap-plication of isolated attosecond pulses in 2002(2). This demonstration was then followed byother important experimental results in the fieldof ultrafast atomic physics, such as the real-timeobservation of electron tunneling (3) and themeasurement of temporal delays of the order ofa few tens of attoseconds in the photoemissionof electrons fromdifferent atomic orbitals of neon(4) and argon (5). The unprecedented time reso-lution offered by attosecond pulses has also al-lowed quantummechanical electronmotion andits degree of coherence to be measured in atomsby using attosecond transient absorption spec-troscopy (6). Attosecond techniques have beenapplied in the field of ultrafast solid-state phys-ics, with the measurement of delays in electronphotoemission from crystalline solids (7) andthe investigation of the ultrafast field-inducedinsulator-to-conductor state transition in a di-electric (8). In the past few years, attosecondpulses have also been used tomeasure ultrafastelectronic processes in simplemolecules (9). Sub-femtosecond electron localization after atto-second excitation has been observed inH2 andD2

molecules (10), and control of photo-ionizationof D2 and O2 molecules has been achieved byusing attosecond pulse trains (APTs) (11, 12).More recently, an APT, in combination with twonear-infrared fields, was used to coherently ex-cite and control the outcome of a simple chem-ical reaction in a D2 molecule (13). Although thestudy ofmore complexmolecules is challenging,a formative measurement of the amino acidphenylalanine has shown that ionization by ashort APT leads to dynamics on a temporal scaleof a few tens of femtoseconds. This has been in-terpreted as the possible signature of ultrafastelectron transfer inside the molecule (14).The application of attosecond techniques to

molecules offers the possibility of investigatingprimary relaxation processes, which involve elec-tronic and nuclear degrees of freedom and theircoupling. In the case of large molecules (e.g., bi-ologically relevant molecules), prompt ioniza-

tion by attosecond pulses may produce ultrafastcharge migration along the molecular skeleton,which can precede nuclear rearrangement. Thisbehavior has been predicted in theoretical calcu-lations by various authors (15–19), whose workwas stimulated by pioneering experiments per-formed byWeinkauf, Schlag, and co-workers onfragmentation of peptide chains (20, 21). Thiselectron dynamics, evolving on an attosecond orfew-femtosecond temporal scale, can determinethe subsequent relaxation pathways of the mole-cule (9). The process is induced by sudden gen-eration of an electronic wave packet, whichmovesacross the molecular chain and induces a site-selective reactivity, which is related to charge lo-calization in a particular site of themolecule (15).Although picosecond and femtosecond pulsesare suitable for the investigation of nuclear dy-namics, the study of electronic dynamics withthese pulses has been made possible by slowingdown the dynamics through the use of Rydbergelectron wave packets (22). However, in orderto study the electron wave-packet dynamics inthe outer-valence molecular orbitals relevant tomost chemical and biological systems, attosecondpulses are required.Here, we present experimental evidence of

ultrafast charge dynamics in the amino acidphenylalanine after prompt ionization inducedby isolated attosecond pulses. A probe pulse thenproduced a doubly charged molecular fragmentby ejection of a second electron, and charge mi-gration manifested itself as a sub-4.5-fs oscilla-tion in the yield of this fragment as a functionof pump-probe delay. Numerical simulations ofthe temporal evolution of the electronic wavepacket created by the attosecond pulse stronglysupport the interpretation of the experimentaldata in terms of charge migration resulting fromultrafast electron dynamics preceding nuclearrearrangement.The a-amino acids consist of a central carbon

atom (a carbon) linked to an amine (-NH2)group, a carboxylic group (-COOH), a hydrogen

336 17 OCTOBER 2014 • VOL 346 ISSUE 6207 sciencemag.org SCIENCE

1Institute of Photonics and Nanotechnologies (IFN)–ConsiglioNazionale delle Ricerche (CNR), Piazza Leonardo daVinci 32, 20133 Milano, Italy. 2Departamento de Química,Modulo 13, Universidad Autónoma de Madrid, Cantoblanco28049 Madrid, Spain. 3Department of Physics, Politecnico diMilano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy.4Centre for Plasma Physics, School of Maths and Physics,Queen’s University, Belfast BT7 1NN, UK. 5IFN-CNR, ViaTrasea 7, 35131 Padova, Italy. 6Dipartimento di ScienzeChimiche e Farmaceutiche, Università di Trieste andCNR–Istituto Officina dei Materiali, 34127 Trieste, Italy.7Instituto Madrileño de Estudios Avanzados en Nanociencia,Cantoblanco, 28049 Madrid, Spain.*Corresponding author. E-mail: [email protected] (F.M.);[email protected] (M.N.)

Fig. 1. Three-dimensionalstructure of phenylalanine.Molecular structure of the mostabundant conformer of thearomatic amino acid phenylalanine.Dark gray spheres representcarbon atoms; light gray spheres,hydrogen atoms; blue sphere,nitrogen; and red spheres, oxygen.The molecular geometry hasbeen optimized by using densityfunctional theory (DFT) with aB3LYP functional.

RESEARCH | REPORTS

N O

amino acidアミノ酸

フェニルアラニン

生体分子の放射線損傷


ATTOSECOND DYNAMICS

Ultrafast electron dynamics inphenylalanine initiated byattosecond pulsesF. Calegari,1 D. Ayuso,2 A. Trabattoni,3 L. Belshaw,4 S. De Camillis,4 S. Anumula,3

F. Frassetto,5 L. Poletto,5 A. Palacios,2 P. Decleva,6 J. B. Greenwood,4

F. Martín,2,7* M. Nisoli1,3*

In the past decade, attosecond technology has opened up the investigation of ultrafastelectronic processes in atoms, simple molecules, and solids. Here, we report the applicationof isolated attosecond pulses to prompt ionization of the amino acid phenylalanine andthe subsequent detection of ultrafast dynamics on a sub–4.5-femtosecond temporal scale,which is shorter than the vibrational response of the molecule. The ability to initiate andobserve such electronic dynamics in polyatomicmolecules represents a crucial step forwardin attosecond science, which is progressively moving toward the investigation of moreand more complex systems.

The investigation of ultrafast processes inatoms received a major stimulus with theintroduction of attosecond pulses in theextreme ultraviolet (XUV) spectral region(1). Real-time observation of the femto-

second Auger decay in krypton was the first ap-plication of isolated attosecond pulses in 2002(2). This demonstration was then followed byother important experimental results in the fieldof ultrafast atomic physics, such as the real-timeobservation of electron tunneling (3) and themeasurement of temporal delays of the order ofa few tens of attoseconds in the photoemissionof electrons fromdifferent atomic orbitals of neon(4) and argon (5). The unprecedented time reso-lution offered by attosecond pulses has also al-lowed quantummechanical electronmotion andits degree of coherence to be measured in atomsby using attosecond transient absorption spec-troscopy (6). Attosecond techniques have beenapplied in the field of ultrafast solid-state phys-ics, with the measurement of delays in electronphotoemission from crystalline solids (7) andthe investigation of the ultrafast field-inducedinsulator-to-conductor state transition in a di-electric (8). In the past few years, attosecondpulses have also been used tomeasure ultrafastelectronic processes in simplemolecules (9). Sub-femtosecond electron localization after atto-second excitation has been observed inH2 andD2

molecules (10), and control of photo-ionizationof D2 and O2 molecules has been achieved byusing attosecond pulse trains (APTs) (11, 12).More recently, an APT, in combination with twonear-infrared fields, was used to coherently ex-cite and control the outcome of a simple chem-ical reaction in a D2 molecule (13). Although thestudy ofmore complexmolecules is challenging,a formative measurement of the amino acidphenylalanine has shown that ionization by ashort APT leads to dynamics on a temporal scaleof a few tens of femtoseconds. This has been in-terpreted as the possible signature of ultrafastelectron transfer inside the molecule (14).The application of attosecond techniques to

molecules offers the possibility of investigatingprimary relaxation processes, which involve elec-tronic and nuclear degrees of freedom and theircoupling. In the case of large molecules (e.g., bi-ologically relevant molecules), prompt ioniza-

tion by attosecond pulses may produce ultrafastcharge migration along the molecular skeleton,which can precede nuclear rearrangement. Thisbehavior has been predicted in theoretical calcu-lations by various authors (15–19), whose workwas stimulated by pioneering experiments per-formed byWeinkauf, Schlag, and co-workers onfragmentation of peptide chains (20, 21). Thiselectron dynamics, evolving on an attosecond orfew-femtosecond temporal scale, can determinethe subsequent relaxation pathways of the mole-cule (9). The process is induced by sudden gen-eration of an electronic wave packet, whichmovesacross the molecular chain and induces a site-selective reactivity, which is related to charge lo-calization in a particular site of themolecule (15).Although picosecond and femtosecond pulsesare suitable for the investigation of nuclear dy-namics, the study of electronic dynamics withthese pulses has been made possible by slowingdown the dynamics through the use of Rydbergelectron wave packets (22). However, in orderto study the electron wave-packet dynamics inthe outer-valence molecular orbitals relevant tomost chemical and biological systems, attosecondpulses are required.Here, we present experimental evidence of

ultrafast charge dynamics in the amino acidphenylalanine after prompt ionization inducedby isolated attosecond pulses. A probe pulse thenproduced a doubly charged molecular fragmentby ejection of a second electron, and charge mi-gration manifested itself as a sub-4.5-fs oscilla-tion in the yield of this fragment as a functionof pump-probe delay. Numerical simulations ofthe temporal evolution of the electronic wavepacket created by the attosecond pulse stronglysupport the interpretation of the experimentaldata in terms of charge migration resulting fromultrafast electron dynamics preceding nuclearrearrangement.The a-amino acids consist of a central carbon

atom (a carbon) linked to an amine (-NH2)group, a carboxylic group (-COOH), a hydrogen


1Institute of Photonics and Nanotechnologies (IFN)–ConsiglioNazionale delle Ricerche (CNR), Piazza Leonardo daVinci 32, 20133 Milano, Italy. 2Departamento de Química,Modulo 13, Universidad Autónoma de Madrid, Cantoblanco28049 Madrid, Spain. 3Department of Physics, Politecnico diMilano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy.4Centre for Plasma Physics, School of Maths and Physics,Queen’s University, Belfast BT7 1NN, UK. 5IFN-CNR, ViaTrasea 7, 35131 Padova, Italy. 6Dipartimento di ScienzeChimiche e Farmaceutiche, Università di Trieste andCNR–Istituto Officina dei Materiali, 34127 Trieste, Italy.7Instituto Madrileño de Estudios Avanzados en Nanociencia,Cantoblanco, 28049 Madrid, Spain.*Corresponding author. E-mail: [email protected] (F.M.);[email protected] (M.N.)

Fig. 1. Three-dimensionalstructure of phenylalanine.Molecular structure of the mostabundant conformer of thearomatic amino acid phenylalanine.Dark gray spheres representcarbon atoms; light gray spheres,hydrogen atoms; blue sphere,nitrogen; and red spheres, oxygen.The molecular geometry hasbeen optimized by using densityfunctional theory (DFT) with aB3LYP functional.

RESEARCH | REPORTS

N Opump

sub-300 as XUV15-35 eV

probe

4 fs VIS/NIR1.77 eV / 700 nm

detect++NH2-CH-R dication


atom, and a side chain (R), which in the case ofphenylalanine is a benzyl group (Fig. 1). In ourexperiments, we used a two-color, pump-probetechnique. Charge dynamics were initiated by iso-lated XUV sub-300-as pulses, with photon energyin the spectral range between 15 and 35 eV andprobed by 4-fs, waveform-controlled visible/nearinfrared (VIS/NIR, central photon energy of1.77 eV) pulses (see supplementary materials).A clean plume of isolated and neutral moleculeswas generated by evaporation of the amino acidfrom a thin metallic foil heated by a continuouswave (CW) laser. The parent and fragmentions produced by the interaction of the mol-ecules with the pump and probe pulses werethen collected by a linear time-of-flight device formass analysis, where the metallic foil was in-tegrated into the repeller electrode (23). Ionizationinduced by the attosecond pulse occured in asufficiently short time interval to exclude sub-stantial electron rearrangement during the exci-tation process.We measured the yield for the production of

doubly charged immonium ions as a function ofthe time delay between the attosecond pumppulse and the VIS/NIR probe pulse (the struc-ture of the immonium dication is ++NH2−CH-R).Figure 2A shows the results on a 100-fs timescale. The experimental data display a rise time of10 T 2 fs and an exponential decay with timeconstant of 25 T 2 fs [this longer relaxation timeconstant is in agreement with earlier experi-

mental results reported in (14)]. Figure 2B showsa 25-fs-wide zoom of the pump-probe dynamics,obtained by reducing the delay step betweenpump and probe pulses from 3 to 0.5 fs. An os-cillation of the dication yield is clearly visible. Fora better visualization, Fig. 2C shows the sameyield after subtraction of an exponential fittingcurve. The data have been fitted with a sinusoidalfunction of frequency 0.234 PHz (correspondingto an oscillation period of 4.3 fs), with lower andupper confidence bounds of 0.229 and 0.238 PHz,respectively (see supplementary materials). Theexperimental data have been also analyzed byusing a sliding-window Fourier transform, which,at the expense of frequency resolution, showsfrequency and time information on the sameplot. The result is shown in Fig. 3A. At shortpump-probe delays, two frequency componentsare present, around 0.14 and 0.3 PHz. A strongand broad peak around 0.24 PHz forms in about15 fs and vanishes after about 35 fs, with a spec-tral width that slightly increases upon increasingthe pump-probe delay, in agreement with thefrequency values obtained frombest fitting of thedata reported in Fig. 2C.From these results, we can draw the following

conclusions: (i) the ultrafast oscillations in thetemporal evolution of the dication yield cannotbe related to nuclear dynamics, which usuallycome into play on a longer temporal scale, ulti-mately leading to charge localization in a par-ticular molecular fragment. Indeed, standard

quantum chemistry calculations in phenylalanine(see supplementary materials) show that thehighest vibrational frequency is 0.11 PHz, whichcorresponds to a period of 9 fs, associated withX-H stretching modes, whereas skeleton vibra-tions are even slower, so that one can rule outthat the observed beatings are due to vibrationalmotion. In any case, some influence of the nu-clear motion cannot be completely excluded, be-cause, for example, stretching of the order of afew picometers of carbon bonds can occur in afew femtoseconds, and this could modify thecharge dynamics (24, 25). (ii) Clear oscillatoryevolution of the dication yield is observed evenwithout any conformer selection. It is well knownthat amino acids exist in many conformationsas a result of their structural flexibility. Typically,the energy barrier to interconversion betweendifferent conformers is small, of the order of afew kcal/mol, so that, even at room temperature,thermal energy is sufficient to induce conforma-tional changes. Theoretical investigations haveshown that such changes can affect the chargemigration process (26). In the case of phenylala-nine, 37 conformers have been found by ab initiocalculations (27), with a conformational distrib-ution that depends on temperature. In our ex-periment, at an average temperature of about430 K, only the six most stable conformers aresubstantially present, as discussed in the supple-mentary materials, with the most abundant con-figuration shown in Fig. 1.To further investigate themeasured dynamics,

we also varied the photon energy and spectralwidth of the attosecond pump pulse by insertingan indium foil in the XUV beam path. The newXUV spectrum was characterized by a 3-eV (fullwidth at half maximum) peak centered around15 eV, followed by a broad and weak spectralcomponent extending up to 25 eV. In this case,doubly charged immonium fragments were bare-ly visible, suggesting that the dication formationinvolves relatively highly excited states of thecation. We have calculated the energy level dia-gramwith all the states of singly charged phenyl-alanine generated by the XUV pump pulse andall the states of the dication (see supplementarymaterials). A number of transitions from excitedstates of the cation to the lowest states of thedication are possible, which involve the absorp-tion of just a few VIS/NIR photons. These statescannot be accessed by low-energy excitation, asin the case of XUV pulses transmitted by the in-dium foil. In this case, transitions from cationstates to the lowest dication states would requirethe less probable absorption of many VIS/NIRphotons.We also performed theoretical calculations to

describe the hole dynamics induced by an atto-second pulse similar to that used in the experi-ment. Details of the method can be found in thesupplementary materials. Because of the highcentral frequency and large spectral width ofthe pulse, a manifold of ionization channels isopen, thus leading to a superposition of manyone-hole (1h) cationic states, i.e., to an electronicwave packet. Ionization amplitudes for all 1h

SCIENCE sciencemag.org 17 OCTOBER 2014 • VOL 346 ISSUE 6207 337

Fig. 2. Pump-probemeasurements. (A) Yield of doubly charged immonium ion (mass/charge = 60) asa function of pump-probe delay, measured with 3-fs temporal steps.The red line is a fitting curve with anexponential rise time of 10 fs and an exponential relaxation time of 25 fs. (B) Yield of doubly chargedimmonium ion versus pump-probe delay measured with 0.5-fs temporal steps, within the temporalwindow shown as dotted box in (A). Error bars show the standard error of the results of four measure-ments.The red line is the fitting curve given by the sum of the fitting curve shown in (A) and a sinusoidalfunction of frequency 0.234 PHz (4.3-fs period). (C) Difference between the experimental data and theexponential fitting curve displayed in (A). Red curve is a sinusoidal function of frequency 0.234 PHz.

RESEARCH | REPORTS

dication yield oscillates with period ~ 4.3 fs

assigned to electron dynamics in the molecule


open channels (32 for a single conformer) werequantitatively determined bymeans of the static-exchange density functional theory (28–30),which has been thoroughly tested in systems ofsimilar complexity, and first-order time-dependentperturbation theory. A calculated photoelectronspectrum at 45-eV photon energy is in very goodagreement with that obtained at 100 eV in asynchrotron radiation experiment (31). From theionization amplitudes, the actual electronic wavepacket was calculated by using the experimentalfrequency spectrum of the attosecond pulse. Theevolution of the electronic wave packet was thenevaluated by using a standard time-dependentdensity matrix formalism (6), in which the systemis described by a sum of single-particle Hamil-tonians. This is a reasonable approximationwhen,as in the present case, changes in electronic den-sity aremostly due to the coherent superpositionof 1h cationic states induced by the XUV pulse(see supplementary materials). In other words,higher-order processes in which additional elec-trons are excited (e.g., correlation satellites) playa minor role in the observed dynamics. The hole-density was calculated as the difference betweenthe electronic density of the neutral molecule,which does not depend on time, and the elec-tronic density of the cation, from immediatelyafter XUV excitation up to a 500-fs delay. Be-cause, in the experiments, the molecules werenot aligned, we calculated the charge dynamicsresulting from excitation by pulses with the elec-tric field polarized along three orthogonal di-rections (shown in Fig. 1). The results were thenaveraged assuming randomly oriented mole-cules. For a better analysis, we integrated thehole density around selected portions of themolecule: Beating frequencies were observedwhen the charge density was integrated aroundthe amine group.The six most populated conformers at 430 K

were considered in the simulations. Althoughthe precise frequencies of the relevant peaks inthe calculated Fourier spectra depend on theparticular conformer, the common character-istic is the presence of three dominant groupsof Fourier peaks between 0.15 and 0.4 PHz. Ourcalculations show that the largest temporal mod-ulation of the hole dynamics occurs around theamine group. Because of this fact, in Fig. 3C weonly show the Fourier power spectrum of thecalculated hole density around this group forthe most abundant conformer. We have thenanalyzed the numerical results by using the samesliding-window Fourier transform procedure ap-plied to the experimental data. Figure 3B showsthe resulting spectrogram in a temporal windowup to 45 fs, considering an experimental tem-poral resolution of about 3 fs. A dominant peakaround 0.25 PHz is visible, which forms in about15 fs and vanishes after about 35 fs, in closeagreement with the results of the Fourier anal-ysis of the experimental data. A higher frequencycomponent is visible around 0.36 PHz in thedelay intervals below ~15 fs and above ~30 fs.At short delays, this component favorably com-pares with the experimental observation of the

frequency peak around 0.30 PHz in the samewindow of pump-probe delays. The temporalevolution of the main Fourier components is aconsequence of the complex interplay amongseveral beating processes initiated by the broad-band excitation pulse. Despite the agreementwith the experimental results, we cannot excludethat the nuclear dynamics, which are not in-cluded in the simulations, also play a role in thetemporal evolution of the measured oscillationfrequencies. The good agreement between sim-ulations and experimental results is rather re-markable in light of the fact that simulationsdo not take into account the interaction of theVIS/NIR probe pulse. The fact that the effectsof the probe pulse are not included in the simu-lations can explain why the calculated inten-sities of the different beatings differ from theexperimental ones. We note that the beating fre-quencies have been observed experimentallyeven though the initial hole density is highly de-localized. An important result of the simulations

is that the measured beating frequencies origi-nate from charge dynamics around the aminegroup. This leads to the conclusion that the pe-riodic modulations measured in the experimentare mainly related to the absorption of the probepulse by the amine group. The mechanism thatmakes the probe pulse sensitive specifically tothe charge density on this group is still not wellunderstood, and therefore it will not be furtherdiscussed in the manuscript. Moreover, we ob-serve that, in spite of the large number of poten-tial frequency beatings associated to the wavepacket motion induced by the attosecond pulse,only a few ones manifest in the experiment, thusreducing the impact of the modulations intro-duced by the probe pulse in the analysis of thewave packet motion. Figure 4 displays snapshotsof the variation of the hole density with respectto the time-averaged hole density as a functionof time for the most abundant conformer. In spiteof the very delocalized nature of the hole-densityresulting from the broadband XUV excitation, a


Fig. 3. Fourier analysis of charge dynamics. Spectrograms calculated for the measured data of Fig. 2C(A) and for the calculated hole density integrated over the amine group for the most abundant con-former (B). The sliding window Fourier transforms have been calculated by using a Gaussian windowfunction g(t – td) = exp[–(t – td)

2/t02], with t0 = 10 fs and peak at td (gate delay time).The spectrogram

(B) was calculated considering an experimental temporal resolution of about 3 fs. (C) Fourier powerspectrum of the calculated hole density integrated over the amine group for the most abundantconformer.

RESEARCH | REPORTS

time-frequency analysis

static-exchange DFT + first order time-dependent perturbation theory


report assignment




PERSPECTIVES


PHYSICS

H. W. van der Hart

Ultrafast spectroscopy and multielectron

calculations reveal complex electron dynamics

occurring just before an atom emits a

photoelectron.

The process of photoemission was one of the effects that led to the formu-lation of quantum mechanics. If an

atom or surface absorbs suffi cient energy from incoming light, it can transfer that energy to an electron, which is then emit-ted. Theories of photoemission mainly focus on energetics—the temporal or dynamic aspects are ignored—but complex electron interactions occur that will create a slight delay between light absorption and electron emission. This time delay has been poorly understood for a fundamental reason: We cannot “see” an atom absorbing a photon. At best, we can follow subsequent emis-sion events and use them to establish a “time zero” when the light was absorbed. A practi-cal challenge has been that the time delay is extremely short, and only recently have direct experiments been feasible with the advent of lasers that emit pulses on the attosecond (as, 10−18 s) time scale. On page 1658 of this issue ( 1), Schultze and co-workers present measurements of time delays between differ-ent photoemission processes generated by the same ultrashort light pulse. This fi nding not only allows further studies of the timing of photoemission but also provides a new way to investigate electron interactions in atoms.

The complex dynamics of atomic photo-emission has a simple origin—the emission of a negatively charged electron changes the neutral atom into a positive ion. The energy levels of the remaining electrons are different

in the positive ion, and as the electrons adjust to their new energy levels, they release energy that is transferred to the outgoing electron. The time needed for this transfer is the origin of the small time delays.

Centre for Theoretical Atomic, Molecular, and Optical Physics, School of Mathematics and Physics, Queen’s University Bel-fast, Belfast BT7 1NN, UK. E-mail: [email protected]

The inescapable conclusion is that a mem-brane protein containing four or fi ve trans-membrane helices, when associated with the translocon, remains in a topologically uncom-mitted state and can “fl ip” within the mem-brane to change its topology. There has been circumstantial evidence suggesting this for a number of membrane proteins for many years ( 10), but Seppälä et al. provide the fi rst sys-tematic analysis that suggests the phenome-non. But how can membrane protein fl ipping, when associated with the translocon, be rec-onciled with the energy required for tumbling within a membrane? Is it the privileged, pro-tected environment within the translocon that permits such topological gymnastics? This would require a translocon pore size with a diameter of ~50 Å, which is consistent with biochemical data ( 11) but which is too large

to be encompassed within a single translocon, thus implying the requirement for oligomers. However, the structure of a eukaryotic trans-locon (Sec61 complex) bound to a ribosome that is actively translocating a polypeptide chain supports the theory that it functions as a monomer ( 12), although higher oligomeric states could exist transiently during mem-brane protein biosynthesis. Structures of the ribosome bound to the translocon contain-ing a nascent polypeptide chain may provide some answers, but considerable work on the dynamics of membrane protein synthesis will be required to interpret these snapshots of the process. Engineering topological reporter proteins such as EmrE constitutes an impor-tant addition to this fi eld, which should even-tually lead to a better understanding of how membrane proteins fold.

References

1. K. R. Vinothkumar, R. Henderson, Q. Rev. Biophys. 42, 1 (2010).

2. S. Seppälä, J. S. Slusky, P. Lloris-Garcerá, M. Rapp, G. von Heijne, Science 328, 1698 (2010); published online 27 May 2010 (10.1126/science.1188950).

3. B. Van den Berg et al., Nature 427, 36 (2004). 4. K. Xie, R. E. Dalbey, Nat. Rev. Microbiol. 6, 234 (2008). 5. G. von Heijne, Nature 341, 456 (1989). 6. G. Gafvelin, G. von Heijne, Cell 77, 401 (1994). 7. V. M. Korkhov, C. G. Tate, Acta Crystallogr. D 65, 186

(2009). 8. S. Schuldiner, Biochim. Biophys. Acta 1794, 748 (2009). 9. M. Rapp, S. Seppälä, E. Granseth, G. von Heijne, Science

315, 1282 (2007); published online 25 January 2007 (10.1126/science.1135406).

10. W. Dowhan, M. Bogdanov, Annu. Rev. Biochem. 78, 515 (2009).

11. B. D. Hamman et al., Cell 89, 535 (1997). 12. T. Becker et al., Science 326, 1369 (2009); published

online 29 October 2009 (10.1126/science.1178535).

10.1126/science.1193065

Short light pulse

e–

e–

∆t2s

∆t2p

2s

Ne

Ne

NeNe+

Ne+

2p

Electron hesitation. Schematic diagram of a photoemission process for Ne. An incoming photon of an ultra-short light pulse is absorbed by either a 2s (top row) or a 2p (bottom row) electron. After photoabsorption, the electron escapes, while the orbitals of the other electrons adjust to the new surroundings as the atom becomes an ion. This adjustment leads to a time delay ∆t in the emission of the electron, which is longer for emission of a 2p electron than for emission of a 2s electron.

Published by AAAS o

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Delay in photoemission

47

from 2s (inner shell)

from 2p (outer shell)

photon absorption electron emission

how long does it take?

short light pulse


Neon atom

within the Coulomb-Volkov approximation (CVA)(29). To quantify the accuracy of the CVA, thesingle-electron time-dependent Schrödingerequation in three spatial dimensions was numer-ically solved with an effective potential that mod-eled Ne (29). The analysis of wave packetsyielded a spectrally averaged relative group delayof a2p − a2s ¼ 4:5 as. Although the CVAyieldsthe same value of the temporal shift betweenspectrograms, the numerical solution of theSchrödinger equation results in simulated spec-trograms that are shifted with respect to eachother by 6.8 as. The origin of this discrepancy liesin the fact that the photoelectron interacts withboth the streaking field and the ion, resulting in aquantum motion that is not exactly described byknown analytical approaches. Thus, for the cur-rent experimental parameters, the small devia-tions between the electron’s exact motion andthat modeled via the CVA give rise to a 2-asdiscrepancy in the relative delay.

Accepting this small discrepancy, many-electron models were applied to investigate theeffects of electron correlation. As a first attempt,the multiconfigurational Hartree-Fock method wasused to evaluate transition matrix elements fromthe ground state of Ne to states where the electronwave asymptotically propagated along the direc-tion of the streaking NIR electric field. These

matrix elements predict a relative delay ofa2p− a2s ¼ 4:0 as. The major drawback of thismodel is that it does not account for inter-channel coupling (6). This deficiency was over-come by modeling the interaction with the XUVpulse using the state-specific expansion approach(31, 32). This model accounts for electron corre-lations before and after photoionization and pre-dicts a relative group delay of a2p− a2s ¼ 6:4 as.Our modeling successfully predicts that the emis-sion of 2s electrons precedes that of 2p elec-trons, but the computed relative delay is ~15 as(3 SD) smaller than the measured value.

So far, the theoretical discussion has focusedon the relative delay between two photoemis-sion channels, which can be acquired experi-mentally. Precise determination of the zero oftime for allowing us to track the history ofmicroscopic phenomena accurately (Fig. 1A)calls for precise knowledge of the delay be-tween the XUV pulse and an outgoing electronwave packet (henceforth, absolute delay). Thiscan only be inferred from theory. For multi-electron systems, such as Ne, physical descrip-tion of the discrepancies revealed by this workproved to be a challenge. The sensitive exper-imental test to which time-dependent many-electronmodels can now be subjected will benefittheir development.

Meanwhile, it is possible to obtain reliableabsolute emission times for He, with which trulyab initio simulations (33) can be carried out withthe help of supercomputers. Such simulationswere performed for the He (1s2) ground state, andfor direct ionization with a 100-eV photon, a 5-astemporal shift of the spectrogram was found.Such modeling will allow precise timing calibra-tion of attosecond measurements, once suffi-ciently powerful attosecond sources will allowthe recording of spectrograms for He withsufficiently good statistics in spite of its smallphotoionization cross-section.

Conclusions and outlook. Establishing thezero of time in atomic chronoscopy is currentlytainted with an error of up to several tens ofattoseconds. Because attosecond streaking canmeasure only relative delays between differentphotoemission channels, the knowledge of abso-lute delays relies on the predictions of thoroughlytested time-dependent multielectron models.Presently, only two-electron ab initio simulationsprovide this degree of reliability, but the lowphotoionization cross-section of He limits (be-cause of low S/N) the timing accuracy. For morecomplex systems, phase-sensitive measurementsof the photoelectron wave packets via attosecondstreaking will put many-electron models ofatomic photoionization to comprehensive, highlysensitive tests, which is a prerequisite for grad-ually improving them and gaining trust in theirpredictions. These developments will improve ourunderstanding of subatomic electron correlationsand will make the absolute timing precision ofatomic chronoscopy approach the 1-as frontier.

References and Notes1. H. Hertz, Annalen Physik Chem. 267, 983 (1887).2. W. Hallwachs, Annalen Physik Chem. 269, 301 (1888).3. A. Einstein, Annalen Physik 17, 132 (1905).4. E. P. Wigner, Phys. Rev. 98, 145 (1955).5. C. A. A. de Carvalho, H. M. Nussenzveig, Phys. Rep. 364,

83 (2002).6. A. F. Starace, in Handbuch der Physik, W. Mehlhorn, Ed.

(Springer, Berlin, 1982), vol. 31.7. S. T. Manson, Radiat. Phys. Chem. 75, 2119 (2006).8. M. Y. Ivanov, J. P. Marangos, J. Mod. Opt. 54, 899

(2007).9. A. Baltuška et al., Nature 421, 611 (2003).

10. R. Kienberger et al., Nature 427, 817 (2004).11. M. Nisoli, G. Sansone, Prog. Quantum Electron. 33, 17

(2009).12. G. Sansone et al., Science 314, 443 (2006).13. M. Schultze et al., N. J. Phys. 9, 243 (2007).14. E. Goulielmakis et al., Science 320, 1614 (2008).15. M. Hentschel et al., Nature 414, 509 (2001).16. A. Borisov, D. Sánchez-Portal, R. Díez Muiño, P. M.

Echenique, Chem. Phys. Lett. 387, 95 (2004).17. A. L. Cavalieri et al., Nature 449, 1029 (2007).18. A. K. Kazansky, P. M. Echenique, Phys. Rev. Lett. 102,

177401 (2009).19. C. Lemell, B. Solleder, K. Tőkési, J. Burgdörfer, Phys. Rev.

A 79, 062901 (2009).20. J. C. Baggesen, L. B. Madsen, Phys. Rev. Lett. 104,

043602; and erratum, 209903 (2010).21. U. Becker, D. A. Shirley, in VUV and Soft X-Ray

Photoionization, U. Becker, D. A. Shirley, Eds.(Plenum, New York, 1997), chap. 5.

22. A. Rudenko et al., Phys. Rev. Lett. 101, 073003 (2008).23. J. Mauritsson et al., Phys. Rev. Lett. 100, 073003 (2008).

Fig. 3. The relative delay between photoemission from the 2p and 2s subshells of Ne atoms, induced bysub–200-as, near–100-eV XUV pulses. The depicted delays are extracted from measured attosecondstreaking spectrograms by fitting a spectrogram, within the strong-field approximation, with param-eterized NIR and XUV fields. Our optimization procedure matches the first derivatives along the time delaydimension of the measured and reconstructed spectrograms, thereby eliminating the influence of un-streaked background electrons [for details on the fitting algorithm, see (29)]. From the analysis of a set ofspectrograms, the measured delays and associated retrieval uncertainties are plotted against the amplitudeof the vector potential applied in the attosecond streak camera. Spectrograms measured in the presence ofa satellite attosecond pulse were found to exhibit a less accurate retrieval of the delay value. When a subsetof data (red diamonds) that represents scans with less than 3% satellite pulse content was evaluated, amean delay value of 21 as with a standard deviation of ~5 as was found. The green circles represent theresult of analyzing spectrograms recorded with an XUV pulse with narrower bandwidth in order to excludethe potential influence of shakeup states contributing to the electron kinetic energy spectrum.


RESEARCH ARTICLES

on

June

21,

201

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measured by attosecond streaking

Mechanism• Eisenbud-Wigner-Smith delay• Coulomb-laser coupling• laser-induced state distortion• unknown mechanisms ...

delay21 as

What%is%happening?� stationary-state correlation

laser effectDynamic multi-

electron correlation?


48

Time-dependent ab-initio simulation of inner-shell photoionizationof an excited He atom (e.g., 1s2p)

XUV pulse


Method: Time-dependent Schrödinger equation (TDSE)

Coupled spherical harmonics

Discretization of

Ishikawa et al., Phys. Rev. A 72, 013407 (2005), Phys. Rev. Lett. 108, 033003 (2012), Phys. Rev. Lett. 108, 093001 (2012)

49

on grid

!

i ""t#(r1,r2 ,t) = H atom + z1 + z2( )E(t)[ ]#(r1,r2 ,t)

!

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2r1"2r2

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inner-shell photoionizationof an excited helium atom

50

1D TDSE

H0 =2�

i=1

�p2

i

2� 2�

z2i + a2

�+

1�(z1 � z2)2 + b2

3D TDSE

H0 =2�

i=1

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i

2� 2

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�+

1|r1 � r2|

temporal evolution of the ionic state

XUV pulse

a = b = 0.8 a.u.

1. remove the bound states of the neutral below the first ionization threshold

2. remove doubly excited (autoionizing) states3. project on each ionic state


Photoionization of 1s2p1P He

51

72.9 eV, 5 cycles, 1012 W/cm2

knoc

k-up

the pulse ends

two distinct time scales

temporal evolution of the ionic state

10008006004002000

3.0x10-6

2.5

2.0

1.5

1.0

0.5

0.0

2p

3d

2s

3p

4f

XUV pulse shak

e-up

Sukiasyan, Ishikawa, Ivanov, Phys. Rev. A 86, 033423 (2012)

3D simulation


Similar dynamics is seen for 1D simulations

52

0 10 20 30 40Time, a.u.

0

1.10-6

2.10-6

3.10-6

2p

3p

3d2s3s

0 10 20 30 40Time, a.u.

0

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2

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(a) (b) (c)

from the 1st excited atom from the 2nd excited atom

1D simulation

only odd-number states can be populated by

photoabsorption

even-number states populated by knock-up

only even-number states can be populated by

photoabsorption

odd-number states populated by knock-up



knock-up lasts longer for higher ionic channels.

53

0 10 20 30 40Time, a.u.

0

1.10-6

2.10-6

3.10-6

2p

3p

3d2s3s

0 10 20 30 40Time, a.u.

0

4.10-4

8.10-43

2

15

4

3

0 10 20 30 40Time, a.u.

0

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1.10-3

4

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(a) (b) (c)

0 10 20 30 40 50Time, a.u.

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6.10-5

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-0.1

0

0.1

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XUV pulse knoc

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reflects the larger radii of the higher excited states


Time-dependent transition matrix element by the e-e interaction

54

0 10 20 30 40 50Time, a.u.

0

2.10-5

4.10-5

6.10-5

87

9

10

10 20 30 40 50Time, a.u.

0

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(z1 � z2)2 + b2 |�j(z1, z2, t)��2

7-88-9

6-8 8-10

attosecond cascades


increasing delays reflect the larger radii of the excited states involved


knock-up in attosecond photoionization of an excited helium atom

55

summary

Post-ionization interaction of the outgoing core electron with the outer spectator electron


PERSPECTIVES


PHYSICS

H. W. van der Hart

Ultrafast spectroscopy and multielectron

calculations reveal complex electron dynamics

occurring just before an atom emits a

photoelectron.

The process of photoemission was one of the effects that led to the formu-lation of quantum mechanics. If an

atom or surface absorbs suffi cient energy from incoming light, it can transfer that energy to an electron, which is then emit-ted. Theories of photoemission mainly focus on energetics—the temporal or dynamic aspects are ignored—but complex electron interactions occur that will create a slight delay between light absorption and electron emission. This time delay has been poorly understood for a fundamental reason: We cannot “see” an atom absorbing a photon. At best, we can follow subsequent emis-sion events and use them to establish a “time zero” when the light was absorbed. A practi-cal challenge has been that the time delay is extremely short, and only recently have direct experiments been feasible with the advent of lasers that emit pulses on the attosecond (as, 10−18 s) time scale. On page 1658 of this issue ( 1), Schultze and co-workers present measurements of time delays between differ-ent photoemission processes generated by the same ultrashort light pulse. This fi nding not only allows further studies of the timing of photoemission but also provides a new way to investigate electron interactions in atoms.

The complex dynamics of atomic photo-emission has a simple origin—the emission of a negatively charged electron changes the neutral atom into a positive ion. The energy levels of the remaining electrons are different

in the positive ion, and as the electrons adjust to their new energy levels, they release energy that is transferred to the outgoing electron. The time needed for this transfer is the origin of the small time delays.

Centre for Theoretical Atomic, Molecular, and Optical Physics, School of Mathematics and Physics, Queen’s University Bel-fast, Belfast BT7 1NN, UK. E-mail: [email protected]

The inescapable conclusion is that a mem-brane protein containing four or fi ve trans-membrane helices, when associated with the translocon, remains in a topologically uncom-mitted state and can “fl ip” within the mem-brane to change its topology. There has been circumstantial evidence suggesting this for a number of membrane proteins for many years ( 10), but Seppälä et al. provide the fi rst sys-tematic analysis that suggests the phenome-non. But how can membrane protein fl ipping, when associated with the translocon, be rec-onciled with the energy required for tumbling within a membrane? Is it the privileged, pro-tected environment within the translocon that permits such topological gymnastics? This would require a translocon pore size with a diameter of ~50 Å, which is consistent with biochemical data ( 11) but which is too large

to be encompassed within a single translocon, thus implying the requirement for oligomers. However, the structure of a eukaryotic trans-locon (Sec61 complex) bound to a ribosome that is actively translocating a polypeptide chain supports the theory that it functions as a monomer ( 12), although higher oligomeric states could exist transiently during mem-brane protein biosynthesis. Structures of the ribosome bound to the translocon contain-ing a nascent polypeptide chain may provide some answers, but considerable work on the dynamics of membrane protein synthesis will be required to interpret these snapshots of the process. Engineering topological reporter proteins such as EmrE constitutes an impor-tant addition to this fi eld, which should even-tually lead to a better understanding of how membrane proteins fold.

References

1. K. R. Vinothkumar, R. Henderson, Q. Rev. Biophys. 42, 1 (2010).

2. S. Seppälä, J. S. Slusky, P. Lloris-Garcerá, M. Rapp, G. von Heijne, Science 328, 1698 (2010); published online 27 May 2010 (10.1126/science.1188950).

3. B. Van den Berg et al., Nature 427, 36 (2004). 4. K. Xie, R. E. Dalbey, Nat. Rev. Microbiol. 6, 234 (2008). 5. G. von Heijne, Nature 341, 456 (1989). 6. G. Gafvelin, G. von Heijne, Cell 77, 401 (1994). 7. V. M. Korkhov, C. G. Tate, Acta Crystallogr. D 65, 186

(2009). 8. S. Schuldiner, Biochim. Biophys. Acta 1794, 748 (2009). 9. M. Rapp, S. Seppälä, E. Granseth, G. von Heijne, Science

315, 1282 (2007); published online 25 January 2007 (10.1126/science.1135406).

10. W. Dowhan, M. Bogdanov, Annu. Rev. Biochem. 78, 515 (2009).

11. B. D. Hamman et al., Cell 89, 535 (1997). 12. T. Becker et al., Science 326, 1369 (2009); published

online 29 October 2009 (10.1126/science.1178535).

10.1126/science.1193065

Short light pulse

e–

e–

∆t2s

∆t2p

2s

Ne

Ne

NeNe+

Ne+

2p

Electron hesitation. Schematic diagram of a photoemission process for Ne. An incoming photon of an ultra-short light pulse is absorbed by either a 2s (top row) or a 2p (bottom row) electron. After photoabsorption, the electron escapes, while the orbitals of the other electrons adjust to the new surroundings as the atom becomes an ion. This adjustment leads to a time delay ∆t in the emission of the electron, which is longer for emission of a 2p electron than for emission of a 2s electron.

Published by AAAS

on

June

21,

201

1w

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.org

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from

from 2s (inner shell)

from 2p (outer shell)

photon absorption electron emission

how long does it take?

short light pulse

Neon atom

What%is%happening?�

Dynamic multi-electron

correlation


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