Gravity at Micron

Hartmut Abele

Hartmut Abele, Universität Heidelberg 2

Galileo in PisaObjekt: Neutron

Höhe: ~ 50 m

Fallhöhe > 50mFallhöhe < 50m

)1()( /21 rer

mmGrV

)1()( /21 re

r

mmGrV

Hartmut Abele, Universität Heidelberg 3

QM

Hydrogen atom

QM: bei gebundenen Zuständen diskrete EnergieniveausAufenthaltswahrscheinlichkeit: Quadrat der Wellenfunktion n,l,m(r,,)

Hartmut Abele, Universität Heidelberg 4

Gitarre

-12 -10 -8 -6 -4 -2 0 2 4 6 8

-0,4

-0,2

0,0

0,2

0,4

0,6

B

Airy-Funktion

Abstand vom Spiegel

Energie

Abstand vom Spiegel

mgz

Hartmut Abele, Universität Heidelberg 5

Rb Atoms Bouncing in a Stable Gravitatonial Cavity

E. Hinds et al.,Yale, Imperial College London

E. Hinds et al.,Yale, Imperial College

Hartmut Abele, Universität Heidelberg 6

The quantum bounce

Hartmut Abele, Universität Heidelberg 7

Quantum bounce

Hartmut Abele, Universität Heidelberg 8

Observation of Bound Quantum States

Energy

Distance to Mirror

mgz

Neutron mirror: polished glass plate 10 cm long

Nature 415 299 (2002), Phys. Rev. D 67 102002 (2003).

T~h3/2

Hartmut Abele, Universität Heidelberg 9

EzV

m

h )(

2

2 EzV

m

h )(

2

2

( ) for 0 and ( ) for 0V z mgz z V z z

0z

z

0z

zEE

mg

EzE

)()( nn Ai 23

0

3 1( ( )) .

4nz z n

2

Schrödinger Equation Energy

Distance to Mirror

mgz

Characteristic Energy Scale:

Characteristic Length Scale:

2 2 2

30

2

30 2

98

2

mg h

hz

mg

Characteristic Energy Scale:

Characteristic Length Scale:

2 2 2

30

2

30 2

98

2

mg h

hz

mg

Hartmut Abele, Universität Heidelberg 10

A comparison: Neutrons, Atoms and Electrons

e+n-Syste

m

1013ly

Hartmut Abele, Universität Heidelberg 11

2nd Run 2002

mz statsyst ,7.02.23.21exp2 mz statsyst ,7.02.23.21exp

2

mz statsyst ,7.08.12.12exp1 mz statsyst ,7.08.12.12exp

1

V. Nesvizhevsky et al., EPJ, 2005

Hartmut Abele, Universität Heidelberg 12

Reversed Geometry

A. Westphal, 2001

Hartmut Abele, Universität Heidelberg 13

the Experiment

Neutron detection:

a) He – detector

n + 3He t + p (no spatial resolution)

b) Track detector

n + 235U fissionn + 10B Li +

Neutron detection:

a) He – detector

n + 3He t + p (no spatial resolution)

b) Track detector

n + 235U fissionn + 10B Li +

Hartmut Abele, Universität Heidelberg 14

Fission fragment

X UCN neutrons

~0.2

120 mm

15

mm

How does thedetector work?

Uranium or Boron coating

CR39 Plastic

Hartmut Abele, Universität Heidelberg 15

CR39 track detector

Uranium Detector

Boron Detector

Hartmut Abele, Universität Heidelberg 16~ 10 cm

~ 200µm

Hartmut Abele, Universität Heidelberg 17

Neutron Density Distributionwith Spatial Resolution Detector

First three levels

V. Nesvizhevsky et al., EPJ, 2005

20 40 60 80

0.2

0.4

0.6

0.8

1

10 20 30 40 50m

Hartmut Abele, Universität Heidelberg 18

C. Krantz, Diploma thesis, 2006

Hartmut Abele, Universität Heidelberg 19

Bestimmung von g

g = (9.8 ± 0.2) m/s2g = (9.8 ± 0.2) m/s2

Hartmut Abele, Universität Heidelberg 20

3.2.2 Newton´s Law and the Question of Large Extra Dimension of Space and Time3.2.2 Newton´s Law and the Question of Large Extra Dimension of Space and Time

Deviations from Newton's law 1/r2 to 1/r2+n, for n extra large dimensions. Motivated by the problem of supersymmetry breaking, new scalar forces in the sub-millimeter range for a supersymmetry breaking scale of 1 – 10 TeV. These correspond to Compton wavelengths in the range of 1 mm to 10 mm. Repulsive forces mediated by possible abelian gauge fields in the bulk. The strength of the new force would be 109 to 1012 times stronger than gravity.

)1()( /21 rermm

GrV

)1()( /21 rermm

GrV

2)4(

2)4(

nnPl

nnPl MrM

2)4(

2)4(

nnPl

nnPl MrM

2)4(

2)4(

)4(2

24 ~

1~

M

M

Mrg n

nnn

2)4(

2)4(

)4(2

24 ~

1~

M

M

Mrg n

nnn

MPL

MnPL

Hartmut Abele, Universität Heidelberg 21

Limits for alpha and lambda

Green: Neutron Limits

)1()( /21 rermm

GrV

)1()( /21 rermm

GrV

Hartmut Abele, Universität Heidelberg 22

Kollaboration ILL GrenobleV. Nesvizhevsky, A. Petukhov, H. Boerner, L. Lukovac, S. Roccia

Universität Heidelberg N. Haverkamp, C. Krantz, D. Mund, S.Nahrwold, F. Rueß, T. Stöferle

U. MainzS. Baeßler

LPSC, Grenoble

K. Protasov

PNPI, Gatchina

A. Gagarsky, G. Petrov, S. Soloviev

SISSA (Italien)A. Westphal

JINR, Dubna A. Strelkov

LPI, Moscow A. Voronin

Univ. Gent J. Schrauwen