Gravity tests with neutrons
0 likes403 views
The quantum bounce of neutrons has been observed at the peV energy level. An application of Ramsey's method of oscillating fields allows high-precision spectroscopy of neutrons bouncing on a surface. This technique could improve the sensitivity for testing neutron couplings to hypothetical short-range forces and influences on gravity. Future experiments aim to reach sensitivities needed to probe certain axion dark matter models and non-Newtonian gravity potentials.
![Application to gravity potential
Phys. Rev. D 81, 065019, 2010
a state detector
a state selector:
|p
15cm
Eq − E p 80cm
ωpq =
ω12 = 2π × 254 Hz
2 ∂ 2 ∂Ψ
[− 2
+ mgz + V0 Θ(−z + a sin ωt)]Ψ = i
2m ∂z ∂t
13
mirror repulsive potential, V0~100 neVE1](https://image.slidesharecdn.com/gravity-110413114449-phpapp02/85/Gravity-tests-with-neutrons-13-320.jpg)
Gravity tests with neutrons
- 1. Gravity tests with neutrons Pinghan Chu April 13, 2011 1
- 2. Missing Block in Standard Model ✤ Gravity is missing? ✤ Higgs? Dark Matter? Dark Energy? 2
- 3. Non-Newtonian interaction ✤ Higher dimension, gauge forces, massive scalar fields ✤ Newtonian gravitational potential should be modified? ✤ General expression of Newtonian gravitational potential m1 m2 −r/λ V (r) = −G (1 + α exp ) r ✤ α : strength ✤ λ : range 3
- 4. Possible sources ✤ Arkani-Hamed, Dimopoulos and Dvalis(PRD 59 086004, 1999) :repulsive forces in the bulk, solve the hierarchy problem ✤ α=106-1012, λ<30μm ✤ Callin and Burgess(hep-hp/0511216):cosmological constant linking size of extra dimensions to dark energy ✤ α<106, λ~10 μm ✤ Axion dark matter(Phys. Rep. 325 1 , 2000) ✤ 20μm<λ<200mm, i.e., 10-6 eV < ma c2= hc/2πλ< 10-2 eV, ✤ others.... 4
- 5. Tests with neutrons ✤ neutral ✤ small electrical polarizability (no van der Waals or Casimir forces) ✤ very sensitive: for example, neutron EDM. ✤ abundant amount in the universe ✤ neutron sources(ILL, PNPI, PSI, SNS, J-PARC, etc..) ✤ ultracold neutrons 5
- 6. Gravity tests with neutrons ✤ The first experiment. ✤ Half of Newton’s apple is made of neutrons. m1 m2 V (r) = −G r 6
- 7. Neutron sources Institut Laue-Langevin (ILL) ✤ 7
- 8. Quantum Bounce ✤ Energy conservation P2 E= + mgz 2m ✤ Uncertainty principle ∆p∆z = 2 ∂E 2 ✤ Minimize energy =− 3 + mg = 0 ∂z 4mz 2 1/3 ✤ Length scale z0 = ( 2 ) 2mn g = 5.87 µm 2 mg 2 1/3 ✤ Energy scale E0 = ( 2 ) = 0.602 peV 8
- 9. Schrödinger equation 2 2 − ∇ ψ + V (z)ψ = Eψ 2m V (z) = mgz if z ≥ 0, and V (z) = ∞ if z 0. ✤ scale with length scale z0, ζ=z/z0 ✤ solution is Airy function: ψn(ζ)=Ai(ζ-ζn) ✤ energy is En=mgzn with zn=z0ζn ✤ a displacement ζn=(3π/2(n-1/4))1/4 ✤ zn is related to the turning point of a classical neutron trajectory with energy En ✤ z1=13.7μm, z2=24.1μm ✤ E1=1.41peV, E2=2.46peV 9
- 10. Observation of bounded quantum states a rough mirror coated with a neutron absorbing alloy ✤ Nature, 417, 297, 2002 peV UCN polished granite stone+passive antivibration table 3He counter Δθ=3μrad 10
- 11. Experiment results z1 = 12.2 ± 1.8syst ± 0.7stat µm z2 = 21.6 ± 2.2syst ± 0.7stat µm 11
- 12. Ramsey’s separated field method Magnetic modulation or modulation mirror arXiv:0902.0156 12
- 13. Application to gravity potential Phys. Rev. D 81, 065019, 2010 a state detector a state selector: |p 15cm Eq − E p 80cm ωpq = ω12 = 2π × 254 Hz 2 ∂ 2 ∂Ψ [− 2 + mgz + V0 Θ(−z + a sin ωt)]Ψ = i 2m ∂z ∂t 13 mirror repulsive potential, V0~100 neVE1
- 14. Ramsey’s fringes nEDM sensitivity: ΔE=10-22eV 14
- 15. Relative frequency shift general express of non Newtonian potential m1 m2 V (r) = −G (1 + α exp−r/λ ) r ρ = 19.32 g/cm3 (gold or tungsten coating) ∆V (z) = 2πmραλ2 Ge−|z|/λ = 8.5 × 10−14 αλ2 e−|z|/λ peV α=1012 ∆Em = Ψn |∆V (z)|Ψn 15
- 16. Effect of hypothetical Yukawa-type forces ✤ consider transitions between 1-3. ✤ 50 days ✤ count rate 0.1 S-1 and N=430000 ✤ ΔΦΔN2π, ΔΦ~10-2rad ✤ interrogation time T=130 ms ✤ energy resolution ΔE=ΔΦh/2πT=5x10-17 eV ✤ for λ=z0, α=108 16
- 17. Effect of hypothetical Yukawa-type forces UCN should be stored as long as... ✤ In the future..... ✤ interrogation time T=130 s ✤ energy resolution ΔE=ΔΦh/2πT=5x10-20 eV ✤ with new neutron sources, ΔE=5x10-21 eV ✤ for λ=z0, α104 17
- 18. Axion · 1 σ n 1 −r/λ V () = gp gs r ( + 2 )e 8πmc λr r ✤ the axion window: 20μmλ200mm (10-6eVma10-2eV), allowed by cosmological data ✤ σ is neutron spin and n is a unit vector related to geometry of the macroscopic matter configuration ✤ for λ=z0, gpgs/hc ≤ 9x10-23/2π 18
- 19. Summary ✤ The quantum bounce of neutron has been observed successfully at energy level of peV. ✤ An application of Ramsey’s method of oscillating fields to the quantum bouncer allows high precision spectroscopy of a neutron bouncing on a flat surface. ✤ Improve the sensitivity for neutron’s coupling to gravity, to hypothetical short-ranged forces or the influence of the cosmological constant. 19
- 20. References ✤ T. J. Bowles, Nature, 415, 267, 2002 ✤ V. V. Nesvizhevsky, et al., Nature, 417, 297, 2002 ✤ V. V. Nesvizhevsky, et al., Phys. Rev. D, 67, 102002, 2003 ✤ H. Abele, Pro. Part. and Nucl. Phys. 60, 1-81,2008 ✤ H. Abele, Summer school on fundamental neutron physics 2009 ✤ H. Abele, et al., Phys. Rev. D, 81, 065019, 2010 20
- 21. Ramsey’s method of oscillating fields ω0 2 1 2 ΩR e−iωt H= 1 2 ΩR eiωt/2 − ω0 2 Ω R 2 2 Ω P (t) = ( ) sin ( R t) ΩR 2 Ω = R Ω2 + (ωpq − ω)2 R 21