Stefan Baeßler

Gravitationally Bound States

Institut Laue-Langevin:H.G. BörnerL. LucovacV.V. NesvizhevskyA.K. PethoukovJ. Schrauwen

PNPI Gatchina:T.A. BaranovaA.M. GagarskiT.K. KuzminaG.A. Petrov

FIAN Moscow:A.Y. Voronin

JINR Dubna:A.V. Strelkov

University of Mainz:S. RaederS.B. (now at UVa)

LPSC Grenoble:K.V. Protasov

University of Heidelberg:H. AbeleS. NahrwoldC. KrantzF.J. RueßTh. StöferleA. Westphal

The Collaboration:

Gravitational Bound states – The idea

neutronneutron

Early proposals:•Neutrons: V.I. Lushikov (1977/78),

A.I. Frank (1978)•Atoms: H. Wallis et al. (1992)

V

z

E1

E2

E3

Collimator

Absorber/Scatterer

Bottom mirrors

Neutron detector

~10-12 cm

Gravitational Bound states – The experiment

Anti-Vibrational Feet

Inclinometers

UCN

Slit Height Measurement

• Count rates at ILL turbine: ~1/s to 1/h• Effective (vertical) temperature of neutrons is ~20 nK• Background suppression is a factor of ~108-109

• Parallelism of the bottom mirror and the absorber/scatterer is ~10-6

Res

onan

ce F

requ

ency

[kH

z]

0

10

20

30

Absorber Height Δh [μm]

0 10 20 30 40

Calibration of the Absorber Height

Absorber/Scatterer

Capacitors

Tools:

• Capacitors (To be calibrated)

• Micrometric Screw ( )

• Long-Range Microsocope ( )

• Wire Spacers ( )

Uncertainty in Δh:

Reached: 1-1.6 μm

Possible: < 0.5 μmBottom mirrors

How does an absorber work?

rough gadolinium absorber/scatterer

rough copper absorber/scatterer

coun

t rat

e [H

z]

Absorber Height Δh [μm]

0 10 20 30

0,001

0,01

3.0µm

Roughness (2002):

• Standard Deviation: 0,7 μm

• Correlation length: ~ 5 μm

Absorber/Scatterer

Bottom mirrors

Lesson: It’s the roughness which absorbs neutrons. A high imaginary part of the potential doesn’t, since the neutron cannot enter. (see A. Yu. Voronin et al., PRD 73, 44029 (2006))

Characteristic length scale:

Absorber Height Δh [μm]

0 10 20 30

coun

t rat

e [H

z]0

0.01

0.02

0.03

0.04

0.05

0.06

The tunneling model

z

ΨV = mgz

Absorber

E1

classicallyallowed

QMtunneling

Mirror

passage

,absorption

( , ) expnn

T h n N

2

30 2

5.87 m2

lm g

Results:

z1 = 12.2 ± 1.8(syst) ± 0.7(stat) μm

z2 = 21.6 ± 2.2(syst) ± 0.7(stat) μm

3/2

horiz 0

4exp ;

exp 3

0 ; otherwise

nn

n

h zLh z

N v l

Theoretical description:

• Tunneling model

V. Nesvizhevsky, Eur. Phys. J. C40 (2005) 479

• QM, Flat absorber doesn’t work:

• Roughness-induced absorption:

A.Westphal et al., arXiv: hep-ph/0602093

Absorber height [ m]h μ

0.05.9 11.7 17.6 23.5 29.4

0.5

1.0

1.5

Neu

tron

cou

nts

[A.U

.]

slit height Δh [μm]

coun

t rat

e [H

z]

1

0.1

0.01

20 40 60 80 100 120

• Time-dependent boundary

A.Voronin et al., Phys.Rev. D73 (2006) 044029

• Transport equation for all states:

R. Adhikari et al., Phys.Rev. A75, 044029 (2007)

Position-Sensitive Detector

120 mm

15 m

m

Plastic (CR39) 235U (or 10B)

Fissonfragments

Incomingneutrons

~ 0.5 μm

Δx

Picture of developed detector with tracks

Height above the mirror [μm ]

0 10 20 30 40 50 60 70

Neu

tron

cou

nts

0

´100

´200

´300

Results with the Position-Sensitive Detector

Absorber

Bottom mirrors

Position-sensitive detector

Application: Search for an Axion

Original Proposal (F. Wilczek, 1978): Solution to the “Strong CP Problem”:

Modern Interest: Dark Matter candidate. All couplings to matter are weak.

α

N

N

α

e-

e-

α

γ

f

γ

Experimental Signatures:

• Astronomy und Cosmology

• Particle accelerators (additional decay modes)

• Conversion of Galactic Axions in a magnet field into microwave photons:

• Light shining through walls:

LASER

Wall

PM

Magn. field

Axion causes three new Macroscopic Potentials

scalar-scalar: 1 2 1( ) exp

4S SV r g g rr

Allowed range: λ = 20 μm … 200 mm (corresponding to mα = 10-2 eV .. 10-6 eV)

Looks like 5th force

scalar-pseudoscalar: 1 2 22

2

ˆ 1 1( ) exp

8S P

rV r g g r

m c r r

Most often done with electrons as polarized particle. Coupling Constants are not equal.

pseudoscalar-pseudoscalar: 1 21 2 1 2

1 2

1ˆ ˆ( ) ( ) ( )

16P PV r g g f r r r g rm m c

Disappears for an unpolarized source

Integration of 2nd potential over mirror:

Effect on Gravitationally Bound States

neutronneutronAbsorber/Scatterer

Bottom mirrors

m2

n1

ˆ( ) exp8

N nS P nV z g g z z

m c

Inclusion of absorber:

m2

n2

const.

( ) exp exp ( )8

N nS P

z

W z g g z h zm c

After dropping the invisible constant piece,

W(z) is linear in z

meff 3

n

2

8N n

S Pg g g g gm c

2

31 2

2

32 2

2.34 13.7 m2

4.09 24.0 m2

zm g

zm g

Our limits are calculated from a shift of the turning point by 3 μm.

Absorber Height Δh [μm]

0 10 2015 255

coun

t rat

e [H

z]

0

0.01

0.02

0.03

0.04

0.05

Extraction of our Limit

Spin down

Spin up

Spin up + Spin down

Why can we use unpolarized neutrons?

Exclusion Plot

λ [m]

|gSg

P|/ħc

10-6

10-4

10-2

100

10-30

10-27

10-24

10-21

10-18

10-15

10-12

PVLAS

Youdin et al., 1996

Ni et al., 1999

Heckel et al., 2006

Heckel et al., 2006:

Ni et al., 1999:

Our limit

Polarized Particle is an electronPolarized Particle is a neutron

S. Hoedl et al.,

prospect

Hammond et al., 2007

Energy measurements

V

z

E1

E2

E3

Transition 2 ↔ 3

Idea: Induce state transitions through:

• Oscillating magnetic field gradients

• Oscillating Masses

• Vibrations

Typical energy differences: ΔE ~ h·140 Hz

→ preferably go to storage mode

Additional collaborators:

T. Soldner, P. Schmidt-Wellenburg, M. Kreuz (ILL Grenoble)

G. Pignol, D. Rebreyend, F. Vezzu (LPSC Grenoble)

D. Forest, P. Ganau, J.M. Mackowski, C. Michel, J.L. Montorio, N. Morgado, L. Pinard, A.Remillieux (LMA Villeurbanne)

The Future: the GRANIT spectrometer

30-50 cm

1. Population of ground state

2. Populate the initial state

3. Study transition to “final state”

4. Neutron Detection

Challenge: Tolerances to get a high neutron state lifetime

6~ 2 10n

E

E E

If lifetime is τn ~ 500 s,

Flatness of bottom mirror: < 100 nm

Accuracy of setting the side walls perpendicular: ~ 10-5

Vibrations, Count Rate, Holes, …

Summary

• Gravitationally Bound Quantum States detected with Ultracold Neutrons

• Characteristic size is ~ μm

• Applications: Limits on Fifth Forces, Limits on Spin-dependent Forces

• Future: Replace transmission measurements (with its need to rely on absorber models) by energy measurements.