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:

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

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 ~ Parallelism of the bottom mirror and the absorber/scatterer is ~10 -6

Calibration of the Absorber Height Absorber/Scatterer Capacitors Tools: Capacitors (To be calibrated) Micrometric Screw ( ) Long-Range Microsocope ( ) Wire Spacers ( ) Uncertainty in Δh: Reached: μm Possible: < 0.5 μm Bottom mirrors

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, (2006))

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

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

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/ slit height Δh [μm] count rate [Hz] Time-dependent boundary A.Voronin et al., Phys.Rev. D73 (2006) Transport equation for all states: R. Adhikari et al., Phys.Rev. A75, (2007)

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

Height above the mirror [μm ] Neutron counts 0 ´100 ´200 ´300 Results with the Position-Sensitive Detector Absorber Bottom mirrors Position- sensitive detector

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

Axion causes three new Macroscopic Potentials scalar-scalar: Allowed range: λ = 20 μm … 200 mm (corresponding to m α = eV 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

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.

Absorber Height Δh [μm] count rate [Hz] Extraction of our Limit Spin down Spin up Spin up + Spin down Why can we use unpolarized neutrons?

Exclusion Plot λ [m] | g S g P |/ ħc 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

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)

The Future: the GRANIT spectrometer 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: ~ Vibrations, Count Rate, Holes, …

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.