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

2. Gravitational Bound states – The idea neutron neutron Early proposals: Neutrons: V.I. Lushikov (1977/78), A.I. Frank (1978) Atoms: H. Wallis et al. (1992) V z E1E1 E2E2 E3E3

3. 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 ~10 8 -10 9 Parallelism of the bottom mirror and the absorber/scatterer is ~10 -6

4. 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 μm Bottom mirrors

5. How does an absorber work? Roughness (2002): Standard Deviation: 0,7 μm Correlation length: ~ 5 μm Absorber/Scatterer Bottom mirrors Lesson: Its the roughness which absorbs neutrons. A high imaginary part of the potential doesnt, since the neutron cannot enter. (see A. Yu. Voronin et al., PRD 73, 44029 (2006))

6. Characteristic length scale: The tunneling model z Ψ V = mgz Absorber E 1 classically allowed QM tunneling Mirror Results: z 1 = 12.2 ± 1.8(syst) ± 0.7(stat) μm z 2 = 21.6 ± 2.2(syst) ± 0.7(stat) μm

7. Why are only the eigenstates discussed? Neutron flux after slit: 0 for n k, if n,k are absorbing states This term vanishes for polychromatic neutron beam

8. Theoretical description: Tunneling model V. Nesvizhevsky, Eur. Phys. J. C40 (2005) 479 QM, Flat absorber doesnt work: Roughness-induced absorption: A.Westphal et al., arXiv: hep-ph/0602093 slit height Δh [μm] count rate [Hz] 1 0.1 0.01 20406080100120 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)

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

10. Height above the mirror [μm ] 010 20 30 40 50 60 70 Neutron counts 0 ´100 ´200 ´300 Results with the Position-Sensitive Detector Absorber Bottom mirrors Position- sensitive detector

11. 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- 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

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

13. Integration of 2 nd potential over mirror: Effect on Gravitationally Bound States neutron neutron Absorber/Scatterer Bottom mirrors 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.

14. Absorber Height Δh [μm] 01020 15 255 count rate [Hz] 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?

15. Exclusion Plot λ [m] | g S g P |/ ħc 10 -6 10 -4 10 -2 10 0 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 electron Polarized Particle is a neutron S. Hoedl et al., prospect Hammond et al., 2007

16. Energy measurements V z E1E1 E2E2 E3E3 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)

17. 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 If lifetime is τ n ~ 500 s, Flatness of bottom mirror: < 100 nm Accuracy of setting the side walls perpendicular: ~ 10 -5 Vibrations, Count Rate, Holes, …

18. 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.