Hartmut Häffner

Institut für Experimentalphysik, Universität Innsbruck andInstitut für Quantenoptik und Quanteninformation Innsbruck

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Quantum information processingwith trapped ions

1. Basic experimental techniques

2. Robust two-particle entanglement

3. Process tomography of a CNOT gate

4. Teleportation

5. Multi-particle entanglement

6. Outlook Quantum optics VI, 17.5. 2005

Quantum information offers a completely new view on quantum mechanics: we might “understand” what quantum mechanics is about.

In quantum information you can see natures strange rules at work: do “real“ bizarre Gedanken experiments!

A most fascinating topic is to look at non-local superpositions.

Why quantum information?

Pentium 4 (2002)

1 atom

1960 1970 1980 1990 2000 2010 2020

year

1910

1510

1110

710

310010

1 atom per bitnum

ber

of a

tom

s pe

r bi

t~ 2017

How many atoms per bit?How many atoms per bit?

faster = smallerfaster = smaller

ENIAC (1947)

Progress in technology …

S1/2

P1/2

D5/2

qubit

Experimental Setup

20th century

about the ENIAC:

„Where a calculator on the ENIAC is equipped with 18000 vacuum tubes and weighs 30 tons, computers in the future may have only 1000 tubes and weigh only 1 ½ tons.“

Popular Mechanics, March 1949

The fate of visionaries

qubit

qubit(quoctet)

Encoding of quantum information requires long-lived atomic states:

microwave transitions

9Be+, 25Mg+, 43Ca+, 87Sr+, 137Ba+, 111Cd+, 171Yb+

optical transitions

Ca+, Sr+, Ba+, Ra+, Yb+, Hg+ etc.

S1/2

P1/2

D5/2

S1/2

P3/2

Qubits with trapped ions

P1/2 D5/2

=1s

S1/2

40Ca+

P1/2

S1/2

D5/2

Dopplercooling Sideband

cooling

P1/2

S1/2

D5/2

Quantum statemanipulation

P1/2

S1/2

D5/2

Fluorescencedetection

Experimental procedure

1. Initialization in a pure quantum state: laser cooling,optical pumping

3. Quantum state measurement by fluorescence detection

2. Quantum state manipulation on S1/2 – D5/2 qubit transition

50 experiments / s

Repeat experiments100-200 times

One ion : Fluorescence histogram

counts per 2 ms0 20 40 60 80 100 120

0

1

2

3

4

5

6

7

8S1/2 stateD5/2 state

P1/2 D5/2

=1s

S1/2

40Ca+

Experimental procedure

1. Initialization in a pure quantum state: Laser sideband cooling

3. Quantum state measurement by fluorescence detection

2. Quantum state manipulation on S1/2 – D5/2 transition

P1/2

S1/2

D5/2

Dopplercooling Sideband

cooling

P1/2

S1/2

D5/2

Quantum statemanipulation

P1/2

S1/2

D5/2

Fluorescencedetection

50 experiments / s

Repeat experiments100-200 times

Spatially resolveddetection withCCD camera:

Multiple ions:

Addressing of individual ions

CCD

Paul trap

Fluorescencedetection

electrooptic deflector

coherentmanipulation of qubits

dichroicbeamsplitter

inter ion distance: ~ 4 µm

addressing waist: ~ 2 µm

< 0.1% intensity on neighbouring ions

-10 -8 -6 -4 -2 0 2 4 6 8 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Exc

itatio

n

Deflector Voltage (V)

D-s

tate

po

pul

atio

nAddressing of individual ionsRabi oscillations

D-s

tate

po

pul

atio

nRabi oscillations

Picture atomic polarization laser phase

D-s

tate

po

pul

atio

nRabi oscillations

To prepare the state shiftthe phase of the preparation -pulsewith respect to all other pulses by .

D-s

tate

po

pul

atio

nRabi oscillations

Coherent manipulationCoherent manipulation

0 10 20 30 40 50 60 700

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (s)

D-s

tate

pop

ulat

ion

Phase switched by /2

row of qubits in a linear Paul trap forms a quantum register

External degree of freedom: ion motion

50 µm

External degree of freedom: ion motion

The common motionacts as the quantumbus.

50 µm

External degree of freedom: ion motion

The common motionacts as the quantumbus.

harmonic trap

…

External degree of freedom: ion motion

harmonic trap

…

2-level-atom joint energy levels

External degree of freedom: ion motion

0,S

0,D1,D

1,S

carrier

sideband

D-s

tate

po

pul

atio

n

Coherent manipulationCoherent manipulation

0,S

0,D1,D

1,S

carrier and blue sidebandRabi oscillations

with Rabi frequencies

carrier

sideband

is the Lamb-Dicke parameter

and

Coherent manipulation

1. Basic experimental techniques

2. Robust two-particle entanglement

3. Implementation of a CNOT gate

4. Teleportation

5. Multi-particle entanglement

6. Outlook

…

… …

…

Creation of Bell states

…

… …

…

/2, BSB

Creation of Bell states

…

… …

…

/2, BSB

, carrier

Creation of Bell states

…

… …

…

/2, BSB

, BSB

, carrier

Creation of Bell states

Fluorescencedetection withCCD camera:

Coherent superposition or incoherent mixture ?

What is the relative phase of the superposition ?

SSSDDS

DD SSSDDSDD

Measurement of the density matrix:

Analysis of Bell states

A measurement yields the z-component of the Bloch vector

=> Diagonal of the density matrix

Rotation around the x- or the y-axis prior tothe measurement yields the phase informationof the qubit.

(a naïve persons point of view)

=> coherences of the density matrix

Obtaining a single qubits density matrix

Preparation and tomography of Bell states

SSSD

DSDD SSSDDSDD

SSSD

DSDD SSSDDSDD

SSSD

DSDD SSSDDSDD

Fidelity:

Entanglementof formation:

Violation of Bell inequality:

F = 0.91F = 0.91

E(exp) = 0.79

S(exp) = 2.52(6)

> 2

SSSD

DSDD SSSDDSDD

C. Roos et al., Phys. Rev. Lett. 92, 220402 (2004)

SSSD

DSDD SSSDDSDD

SSSD

DSDD SSSDDSDD

SSSD

DSDD SSSDDSDD

long lived (~ 1000 ms) short lived (1 ms)

Ene

rgy

(see e.g. Kielpinski et al.,Science 291, 1013-1015 (2001)

SSSD

DSDD SSSDDSDD

Ene

rgy

Life

time

limite

d on

ly b

y sp

onta

nteo

us d

ecay

of t

he D

leve

l

Life

time

limite

d on

ly b

y sp

onta

nteo

us d

ecay

of t

he D

leve

l

Life

time

limite

d by

lase

r fre

quen

cy s

tabi

lity

Life

time

limite

d by

lase

r fre

quen

cy s

tabi

lity

Creation of Bell statesDecoherence properties of the Bell states

Ultra-longlived Bell statesM

inim

um

fid

elity

D5/2

S1/2

Min

imu

m fi

del

ityUltra-longlived Bell states

Line possible death

Lifetime of entanglement > 20 s

control

target

1. Basic experimental techniques

2. Robust two-particle entanglement

3. Process tomography of a CNOT gate

4. Teleportation

5. Multi-particle entanglement

6. Outlook

other gate proposals include: • Cirac & Zoller • Mølmer & Sørensen, Milburn• Jonathan & Plenio & Knight• Geometric phases• Leibfried & Wineland

controlcontrol targettarget

...allows the realization of a universal quantum computer !

control

target

Cirac-Zoller two-ion controlled-NOT operation

ion 1

motion

ion 2

control qubit

target qubit

SWAP

Cirac-Zoller two-ion controlled-NOT operation

ion 1

motion

ion 2

control qubit

target qubit

Cirac-Zoller two-ion controlled-NOT operation

ion 1

motion

ion 2

SWAP-1

control qubit

target qubit

Cirac - Zoller two-ion controlled-NOT operation

F. Schmidt-Kaler et al., Nature 422, 408 (2003)

ion 1

motion

ion 2

SWAP-1SWAP

Ion 1Ion 1

Ion 2Ion 2

pulse sequence:pulse sequence:

Cirac - Zoller two-ion controlled-NOT operation

control qubitcontrol qubit

target qubittarget qubit

laser frequencypulse lengthoptical phase

Phase gate

Phase gate

Composite 2π-rotation:

Example:

CNOT

Mapping between product and Bell basis

Product states Bell states

Ion 1

Ion 2

CNOT

Mapping between Product and Bell basis

Experimental fidelity of Cirac-Zoller CNOT operation

input

output

F. Schmidt-Kaler et al.,Nature 422, 408 (2003)

Gate tomography

characterizes gate operation completely

Process tomography, theory

ideal CNOT gate operation

Process tomography, experiment

real CNOT gate operation

1. Basic experimental techniques

2. Robust two-particle entanglement

3. Process tomography of a CNOT gate

4. Teleportation

5. Multi-particle entanglement

6. Outlook

Alice

Bob

Bell state

unknowninput state

recoverinput state

rotation

classical communication

measurementin Bell basis

Phys. Rev. Lett. 70, 1895 (1993)

Teleportation protocol

Ion 3

Ion 2

Ion 1

Bell

state

initialize #1, #2, #3

classical communication

conditional rotations

CNOT -- Bell basis

Alice

Bob

Selectiveread out

Implementation of the teleportation protocol

recovered on ion #3

Protecting qubits from readout

detect quantum state of ion #1 only

D5/2

S1/2

D5/2

S1/2

D5/2

S1/2

D5/2

S1/2

D5/2

S1/2

D5/2

S1/2

ion #1 ion #2 ion #3

Protecting qubits from readout

detect quantum state of ion #1 onlysuperpositions of ions #2, #3 protected

D5/2

S1/2

D5/2

S1/2

D5/2

S1/2

D5/2

S1/2

D5/2

S1/2

D5/2

S1/2

ion #1 ion #2 ion #3

D D‘ DD‘

Ion 3

Ion 2

Ion 1

conditional rotations using electronic logic, triggered by PM signal

conditional rotations using electronic logic, triggered by PM signalP

U

U

P

C C C

B

B B B B C

CU P

B

C

C P

spin echo sequencespin echo sequence

full sequence:26 pulses + 2 measurements

full sequence:26 pulses + 2 measurements

B

C

blue sideband pulsesblue sideband pulses

carrier pulsescarrier pulses

P

C

B

B

Teleportation protocol, details

Input test states Output statesInitial Final

TPU U-1

Ion #1 Ion #3

Teleportation procedure, analysisTeleportation procedure, analysis

Similar results also from Boulder!

Fidelity: 0.83

Classicalthreshold

Quantum teleportation on demand

Teleportation on demand

no post-selection

it works for all Bell states

only 10 m

Deterministicteleportation

Process tomography of teleportation

represent input/output states with Bloch spheres:

input sphere

output sphere

Process tomography of the teleportation

1. Basic experimental techniques

2. Robust two-particle entanglement

3. Process tomography of a CNOT gate

4. Teleportation

5. Multi-particle entanglement

6. Outlook

Density matrix of W – state

experimental result theoretical expectation

DDDDDS

DSDDSS

SDDSDS

SSDSSS

Fidelity: 85 %

DDDDDS

DSDDSS

SDDSDS

SSDSSS

Bell statesurvives !

Photon-version: M. Eibl et al., Phys. Rev. Lett. 92, 077901 (2004).

projection of the center ion

Quantum mechanics at work

1. Basic experimental techniques

2. Robust wo-particle entanglement

3. Process tomography of a CNOT gate

4. Teleportation

5. Multi-particle entanglement

6. Outlook

- optimization of Cirac-Zoller gateachieve 3 - 5 CNOT gate operations

- error correction protocols with three and five qubits

- qubit manipulation in DFS

- implementation with 43Ca+

- test of segmented traps

Summary

- Robust entanglement (more than 20 s)

- Multi-particle entanglement

- Process tomography of a CNOT

- Process tomography of a

teleportation algorithm

The Innsbruck ion trap group

F. Schmidt-KalerA. Wilson P. Bushev

C. Becher

D. Rotter

G. Lancaster

C. Russo

M. Riebe

T. Körber

T. Deuschle

M. Chwalla

C. Roos M. Bacher

V. SteixnerA. KreuterR. Bhat

R. Blatt

J. Benhelm

W. Hänsel

F. Splatt

H. Häffner

http://heart-c704.uibk.ac.at

Ph.D. positions

available !!!

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