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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 4r 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 8m2c 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 ) 16m1m2c 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 ~ 2 106 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.