Folie 1

Report
Gravitationally Bound States
Stefan Baeßler
The Collaboration:
Institut Laue-Langevin:
H.G. Börner
L. Lucovac
V.V. Nesvizhevsky
A.K. Pethoukov
J. Schrauwen
LPSC Grenoble:
K.V. Protasov
JINR Dubna:
A.V. Strelkov
PNPI Gatchina:
T.A. Baranova
A.M. Gagarski
T.K. Kuzmina
G.A. Petrov
FIAN Moscow:
A.Y. Voronin
University of Heidelberg:
H. Abele
S. Nahrwold
C. Krantz
F.J. Rueß
Th. Stöferle
A. Westphal
University of Mainz:
S. Raeder
S.B. (now at UVa)
Gravitational Bound states – The idea
V
neutron
neutron
E3
E2
E1
z
Early proposals:
•Neutrons: V.I. Lushikov (1977/78),
A.I. Frank (1978)
•Atoms: H. Wallis et al. (1992)
Gravitational Bound states – The experiment
Slit Height
Measurement
Inclinometers
Collimator
Absorber/Scatterer
Neutron
detector
UCN
Bottom mirrors
~10-12 cm
• 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
AntiVibrational
Feet
Calibration of the Absorber Height
Tools:
30
Resonance Frequency [kHz]
• Capacitors (To be calibrated)
• Micrometric Screw ( )
• Long-Range Microsocope ( )
20
• Wire Spacers ( )
10
Capacitors
0
0
10
20
30
40
Absorber Height Δh [μm]
Uncertainty in Δh:
Absorber/Scatterer
Reached: 1-1.6 μm
Possible: < 0.5 μm
Bottom mirrors
How does an absorber work?
rough copper absorber/scatterer
rough gadolinium absorber/scatterer
count rate [Hz]
Absorber/Scatterer
0,01
Bottom mirrors
Roughness (2002):
• Standard Deviation: 0,7 μm
0,001
• Correlation length: ~ 5 μm
0
10
20
30
Absorber Height Δh [μm]
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))
3.0µm
The tunneling model
0.06
Mirror
classically
allowed
QM
Absorber
tunneling
0.05
Ψ
count rate [Hz]
E1
V = mgz
z
 passage
T (h, n)  N n exp  
 
 n ,absorption



0.04
0.03
0.02
0.01

 4  h  z 
L
n

exp   
 3  l0 
 N n exp  vhoriz


0

3/2




0
; h  z n
0
10
20
Absorber Height Δh [μm]
; otherwise
Results:
Characteristic length scale: l0 
2
3
2m 2 g
 5.87 m
z1 = 12.2 ± 1.8(syst) ± 0.7(stat) μm
z2 = 21.6 ± 2.2(syst) ± 0.7(stat) μm
30
Theoretical description:
1
•
count rate [Hz]
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
0.1
0.01
Neutron counts [A.U.]
1.5
20
40
60
80
100
slit height Δh [μm]
120
1.0
•
0.5
A.Voronin et al., Phys.Rev. D73 (2006) 044029
•
0.0
Time-dependent boundary
Transport equation for all states:
R. Adhikari et al., Phys.Rev. A75, 044029 (2007)
5.9
11.7
17.6
23.5
Absorber height h [ μm]
29.4
Position-Sensitive Detector
235U
Plastic (CR39)
(or 10B)
Fisson
fragments
~ 0.5 μm
Picture of developed detector with tracks
Incoming
neutrons
Results with the Position-Sensitive Detector
Neutron counts
´300
´200
Positionsensitive
detector
Absorber
´100
Bottom mirrors
0
0
10
20
30
40
50
Height above the mirror [μm ]
60
70
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.
N
γ
e-
α
α
α
N
e-
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:
Wall
PM
LASER
Magn. field
f
Axion causes three new Macroscopic Potentials
scalar-scalar:
V (r )   g S 1 g S 2
1
exp   r  
4r
Allowed range: λ = 20 μm … 200 mm (corresponding to mα = 10-2 eV .. 10-6 eV)
Looks like 5th force
scalar-pseudoscalar:
V (r )   g S 1 g P 2
2  rˆ  1 1 
 2  exp   r  

8m2c  r r 
Most often done with electrons as polarized particle. Coupling Constants are not equal.
1
2
pseudoscalar-pseudoscalar: V (r )   g P g P
Disappears for an unpolarized source
1
 1  2  f (r )   1  rˆ  2  rˆ  g (r ) 
16m1m2c
Effect on Gravitationally Bound States
Integration of 2nd potential over mirror:
Absorber/Scatterer
neutron
neutron
 
V ( z )   g S N g P n m2 exp   z   n  zˆ 
8mn c
1
Bottom mirrors
Inclusion of absorber:
W ( z)   gS N gPn
m 
exp   z    exp   (h  z )   
8mn 2 c 
2z
 const.

After dropping the invisible constant piece,
W(z) is linear in z
g  geff
2 m
 g  gS N gPn
8mn 3c
Our limits are calculated from a shift of the turning
point by 3 μm.
z1  2.34 3
z2  4.09 3
2
2m 2 g
2
2m 2 g
 13.7 m
 24.0 m
Extraction of our Limit
Why can we use unpolarized neutrons?
0.05
Spin up + Spin
down
count rate [Hz]
0.04
0.03
Spin up
0.02
0.01
Spin down
0
0
5
10
15
Absorber Height Δh [μm]
20
25
Exclusion Plot
10
-12
Ni et al., 1999:
Hammond et al., 2007
10
|gSgP|/ħc
10
10
-15
Our limit
Ni et al., 1999
-18
-21
S. Hoedl et al.,
prospect
10
10
10
-24
Youdin et al., 1996
Heckel et al., 2006:
-27
-30
PVLAS
Heckel et al., 2006
-6
10
-4
10
-2
10
λ [m]
Polarized Particle is an electron
Polarized Particle is a neutron
10
0
Energy measurements
Idea: Induce state transitions through:
V
• Oscillating magnetic field gradients
E3
• Oscillating Masses
E2
• Vibrations
E1
Transition 2 ↔ 3
Typical energy differences: ΔE ~ h·140 Hz
→ preferably go to storage mode
z
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
1. Population of
ground state
3. Study transition to “final state”
2. Populate the initial state
4. Neutron Detection
30-50 cm
Challenge: Tolerances to get a high neutron state lifetime
E
~
 2 106
If lifetime is τn ~ 500 s,
E
n E
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 Spindependent Forces
• Future: Replace transmission measurements (with its
need to rely on absorber models) by energy
measurements.

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