Stefan Baeßler

1. Gravitationally Bound States Stefan Baeßler The Collaboration: Institut Laue-Langevin: H.G. Börner L. Lucovac V.V. Nesvizhevsky A.K. Pethoukov J. Schrauwen University of Heidelberg: H. Abele S. Nahrwold C. Krantz F.J. Rueß Th. Stöferle A. Westphal JINR Dubna: A.V. Strelkov PNPI Gatchina: T.A. Baranova A.M. Gagarski T.K. Kuzmina G.A. Petrov LPSC Grenoble: K.V. Protasov University of Mainz: S. Raeder S.B. (now at UVa) FIAN Moscow: A.Y. Voronin

2. E3 neutron V n e u t r o n E2 E1 z Gravitational Bound states – The idea • Early proposals: • Neutrons: V.I. Lushikov (1977/78), • A.I. Frank (1978) • Atoms: H. Wallis et al. (1992)

3. Gravitational Bound states – The experiment Slit Height Measurement Inclinometers Collimator Neutron detector Absorber/Scatterer UCN Bottom mirrors Anti-Vibrational Feet ~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

4. 30 20 Resonance Frequency [kHz] 10 0 0 10 20 30 40 Absorber Height Δh [μm] Calibration of the Absorber Height • Tools: • Capacitors (To be calibrated) • Micrometric Screw ( ) • Long-Range Microsocope ( ) • Wire Spacers ( ) Capacitors Absorber/Scatterer Uncertainty in Δh: Reached: 1-1.6 μm Possible: < 0.5 μm Bottom mirrors

5. rough copper absorber/scatterer rough gadolinium absorber/scatterer 0,01 count rate [Hz] 0,001 10 30 0 20 Absorber Height Δh[μm] How does an absorber work? Absorber/Scatterer Bottom mirrors • Roughness (2002): • Standard Deviation: 0,7 μm • Correlation length: ~ 5 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))

6. 0.06 0.05 Mirror QM classically Absorber tunneling allowed 0.04 E 1 count rate [Hz] V = mgz Ψ 0.03 0.02 z 0.01 0 0 10 20 30 Absorber Height Δh [μm] The tunneling model Results: z1 = 12.2 ± 1.8(syst) ± 0.7(stat) μm z2 = 21.6 ± 2.2(syst) ± 0.7(stat) μm Characteristic length scale:

7. 1 0.1 count rate [Hz] 0.01 20 40 60 80 100 120 slit height Δh [μm] Theoretical description: • Tunneling model • V. Nesvizhevsky, Eur. Phys. J. C40 (2005) 479 • QM, Flat absorber doesn’t work: • Roughness-induced absorption: • A.Westphalet al., arXiv: hep-ph/0602093 • 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)

8. Position-Sensitive Detector 235U (or 10B) Plastic (CR39) 15 mm Δx Incoming neutrons Fisson fragments 120 mm ~ 0.5 μm Picture of developed detector with tracks

9. Results with the Position-Sensitive Detector ´300 Neutron counts ´200 Position-sensitive detector Absorber ´100 Bottom mirrors 0 0 10 40 70 30 60 20 50 Height above the mirror [μm ]

10. 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. γ N e- α f 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

11. Axion causes three new Macroscopic Potentials scalar-scalar: Allowed range: λ = 20 μm … 200 mm (corresponding to mα = 10-2 eV .. 10-6 eV) Looks like 5th force scalar-pseudoscalar: Most often done with electrons as polarized particle. Coupling Constants are not equal. pseudoscalar-pseudoscalar: Disappears for an unpolarized source

12. Absorber/Scatterer neutron n e u t r o n Bottom mirrors Effect on Gravitationally Bound States Integration of 2nd potential over mirror: Inclusion of absorber: After dropping the invisible constant piece, W(z) is linear in z Our limits are calculated from a shift of the turning point by 3 μm.

13. Extraction of our Limit Why can we use unpolarized neutrons? 0.05 Spin up + Spin down 0.04 0.03 count rate [Hz] Spin up 0.02 0.01 Spin down 0 0 5 10 20 25 15 Absorber Height Δh [μm]

14. Exclusion Plot - 1 2 1 0 Ni et al., 1999: Hammond et al., 2007 - 1 5 Our limit 1 0 Ni et al., 1999 - 1 8 1 0 |gSgP|/ħc - 2 1 S. Hoedl et al., prospect 1 0 - 2 4 Youdin et al., 1996 1 0 Heckel et al., 2006: - 2 7 1 0 PVLAS - 3 0 1 0 Heckel et al., 2006 - 6 - 4 - 2 0 1 0 1 0 1 0 1 0 λ [m] Polarized Particle is an electron Polarized Particle is a neutron

15. Energy measurements • Idea: Induce state transitions through: • Oscillating magnetic field gradients • Oscillating Masses • Vibrations • Typical energy differences: ΔE ~ h·140 Hz • → preferably go to storage mode V E3 Transition 2 ↔ 3 E2 E1 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)

16. 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 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, …

17. 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.