Neutron quantum states in a gravitational field

Transcription

1 Neutron quantum states in a gravitational field 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: UVa)

2 The The neutron source of the ILL/Grenoble / European Synchrotron Radiation Facility Institut Laue-Langevin (neutrons)

3 The Spallation Neutron Source SNS Proton Accelerator Spallation Target

4 Production of free neutrons Neutron moderation T30K T293K 10 1 Neutron production in a spallation source P (E n ) h λ = ~ 100 nm m v n λ ~ 1 Å UCN Cold Thermal E n [ev]

5 Ultracold Neutrons Moderator Fuel Element Cold Moderator Neutron Guide (cold and thermal neutrons)

6 Interactions of low energy neutrons with matter Transport 2 2πh VFermi = biδ ( x xi ) m λ big: V n Fermi i 2πh m n 2 nb ~ 100 nev V Polarization V = V Fermi n mµ B 100 nev 100 nev V 100 nev σ B σ

7 Properties of Ultracold Neutrons (UCN) Ultracold neutrons (UCN): Neutrons with energies less than the Fermi potential of a given piece of matter. Typical properties: Energy: E UCN ~ 100 nev Velocity: v UCN ~ 5 m/s Height: h UCN ~ 1 m UCN Main usage: Precise fundamental physics Neutron lifetime Electric Dipole Moment and other EM moments Gravitation Typical wall interaction rates for good walls: ~99.99 % - elastic reflection ~0.01% - inelastic scattering (phonon absorption) to the thermal energy range 0.001% - absorption

8 Experiment: Gravitational Bound States electron Electromagnetic Bound State Gravitational Bound State Strong Interaction Bound States Nucleus ( 12 C) neutron proton d u d

9 Gravitational Bound states The idea neutron g Potential V E 3 E 2 E 1 V mgz = ; z > 0 ; otherwise Absorber/Scatterer Height z Early proposals: Neutrons: V.I. Lushikov (1977/78), A.I. Frank (1978) Atoms: H. Wallis et al. (1992)

10 Gravitational Bound States The experiment Slit Height Measurement Inclinometers Collimator UCN Absorber/Scatterer Bottom mirrors (Glass) Neutron detector ~10-12 cm Anti- Vibrational Feet UCN selected with very small (vertical) energy: Effective (vertical) temperature of neutrons is ~20 nk, horizontal temperature is 10 mk Horizontal velocity spectrum: 4..9 m/s Control of geometry: Parallelism of the bottom mirror and the absorber/scatterer is ~ µrad Accuracy of absorber height determination is ideally < 0.5 µm Efficient detection necessary: Count rates at ILL turbine: ~1/s to 1/h Background suppression is a factor of ~

11 Calibration of the absorber height 30 Tools: Capacitors (To be calibrated) Resonan nce Frequency [khz] Micrometric Screw ( ) Long-Range Microsocope ( ) Wire Spacers ( ) Absorber Height h [µm] Capacitors Uncertainty in h: Reached: µm Possible: < 0.5 µm Absorber/Scatterer Bottom mirrors

12 Detection of the size of the quantum states Absorber/Scatterer h [Hz] Count rate N Bottom mirrors Absorber Height h [µm] background

13 Phenomenological model: The tunneling model τ = passage L v hor ( n ) T ( h, n) = N β exp Γ τ 0 n passage Γ = w P ε n n n,tunnel absorber Mirror E 1 0 classically allowed Ψ QM tunneling V = mgz h Absorber Height z P 3/2 4 h z n exp ; h > zn = 3 l 1 ; otherwise n,tunnel 0 Characteristic length scale: l h 2m g 2 = 3 = µ m 2 N 3/2 L 4 h z n v horiz 3 l 0 = N0 n exp β n L α α exp ; h > z v horiz n ; otherwise

14 Detection of the size of the quantum states Tunneling model fit [Hz] Count rate N Results: z 1 = 12.2 ± 1.8(syst) ± 0.7(stat) µm z 2 = 21.6 ± 2.2(syst) ± 0.7(stat) µm Absorber Height h [µm] background Comparison to theory, undisturbed wave functions: z 1 = 13.7 µm z 2 = 24.0µm

15 Why are only the eigenstates discussed? Neutron flux N after slit: L N f ( vhor ) Ψ z, τ passage = dz v v hor hor 2 with 1 τ Γ τ h 2h = nψ n n ψ ( z, t) C ( z) e e i En passage n passage Initial occupation numbers: n in (, passage 0) n ( ) C = ψ z τ = ψ z dz v hor i 1 * h 2h hor n k ψ n ψ k n, k ( ) ( E E ) τ ( Γ +Γ ) N f v C C e e n k passage n k passage τ Doesn t vanish for n k! (Non-unitary Hamiltonian) v hor τ i n k * ( E E ) τ Γ +Γ Γ h h h 2 hor τ n hor n k ψ n ψ k n v n k ( ) ( ) = f v C e + f v C C e e n passage n k passage passage hor This term is small for polychromatic neutron beam

16 The horizontal velocity spectrum Defines max. v hor Movable Collimator Slit Height Measurement Inclinometers UCN Absorber/Scatterer Bottom mirrors Neutron detector Defines min. v hor 4 ~10-12 cm Anti- Vibrational Feet count rate [Hz] Drop upper collimator blade Lift lower collimator blade horiz. velocity v hor [m/s]

17 How does an absorber work? rough copper absorber/scatterer rough gadolinium absorber/scatterer count rate [Hz] 0,01 Absorber/Scatterer Bottom mirrors 0, Roughness (2002): Standard Deviation: 0,7 µm Correlation length: ~ 5 µm Absorber Height h [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, (2006)) Cf. Optics: R 1 n = 1 + n 3.0µm

18 Theoretical description: Tunneling model V. Nesvizhevsky, Eur. Phys. J. C40 (2005) 479 QM, Flat absorber doesn t work: Roughness-induced absorption: Neutron counts [A.U.] A.Westphal et al., Eur. Phys. J. C51, 367 (2007) data Absorber height h [µm] Neutron count rate [Hz] Roughness-induced absorption h Time-dependent boundary 1999 data No gravity (model-dependent) Reversed geometry (No fit parameters) background Absorber height h [µm] Absorber 2σ A.Voronin et al., Phys. Rev. D73 (2006) h ψ n( z) Ai n( z) Transport equation for all states: R. Adhikari et al., Phys. Rev. A75, (2007) Mirror Γ = α n h+ σ σ σ ψ n 2 dz

19 Position-Sensitive Detector Plastic (CR39) 235 U (or 10 B) Fisson fragments Incoming neutrons ~ 0.5 µm Picture of developed detector with tracks

20 Results with the Position-Sensitive Detector Absorber Positionsensitive detector Bottom mirrors 300 Neutron counts Neutron counts [µ µm -1 ] Χ 2 = 145 at 124 DoF Height [µm ] Horizontal position [mm] Model from Westphal 2007, ground state suppressed Absorber Height: 50 µm Ch. Krantz, Diploma thesis, Heidelberg (2006)

21 Results with the Position-Sensitive Detector Plastic (CR39) 235 U (or 10 B) Fisson fragments Incoming neutrons Absorber ~ 0.5 µm Bottom mirrors Positionsensitive detector Neutron counts [µm -1 ] Χ 2 = 145 at 124 DoF Height [µm ] Ch. Krantz, Diploma thesis, Heidelberg (2006)

22 Application: Search for a new pseudoscalar boson (Axion-like Particle) Original Proposal for Axion (F. Wilczek, 1978): Solution to the Strong CP Problem : Modern Interest: Dark Matter candidate. N 1 N 2 All couplings to matter are weak. g S + ig γ P 5 α Signature of a new pseudoscalar boson: New Short-Range Potential Monopole-monopole: ( hc) ( ) 1 2 V ( r) = gs gs exp r λ with λ = 4πr Looks like 5 th force, which is motivated now by theories with extra dimensions. Limits from our experiment exist, but other methods give better limits. hc m c α 2 N 1 N 2 (Westphal et al., hep-ph/ , hep-ph/ , Nesvizhevsky et al., Class. Quant. Grav. 21, 4557 (2004)) Monopole-dipole: ( hc) ( ) S P 2 2 exp 2 8πm2c rλ r ( ˆ) ( ) V r = g g σ r + r λ Most often done with electrons as polarized particle. Coupling Constants depend on the species. 1 2 Dipole-dipole: ( σ σ ) + ( σ ˆ)( σ ˆ) V ( r) gp gp 1 2 f ( r) 1 r 2 r g( r) Disappears for an unpolarized source

23 Application: Search for a new pseudoscalar Boson (Axion-like Particle) Original Proposal (F. Wilczek, 1978): Solution to the Strong CP Problem : Modern Interest: Dark Matter candidate. All couplings to matter are weak. Maybe to weak for us. γ N e - α α α f N Experimental Signatures: Astrophysics und Cosmology Particle accelerators (additional decay modes) Conversion of Galactic Axions in a magnet field into microwave photons: Light shining through walls: e - γ Wall LASER PM Magn. field

24 Effect on Gravitationally Bound States Integration of 2 nd potential over mirror: ( hc) ρ λ V ( z) = g g exp z λ σ z ( )( ˆ) N n m mirror S P 2 2 n 8mn c ± 1 Inclusion of absorber: ( hc) N n m slit S P 2 2 8mn c 2 2z + const. λ Mirror Potential V ρ λ V ( z) = ± g g exp( z λ) exp ( ( h z) λ) Absorber mgz + V ; z > 0 V = ; otherwise Height z After dropping the invisible constant piece, V slit (z) is linear in z 2 ( c) 2 ρm N n h 2 h eff S P 3 2 z 3 8mn c 1 2 g g = g ± g g z = 2.34 = 13.7 µ m 2m g 2 h = 4.09 = 24.0 µ m 2m g 3 2 2

25 Extraction of our Limit Why can we use unpolarized neutrons? 0.05 Limits are calculated from a shift of the turning point by 3 µm [Hz] Count rate N[ (PRD 75, (2007), 0.03 hep-ph/ , spin up + spin down 5 10 spin up spin down background hep-ph/ )) Sensitivity only to magnetic field gradients: Signal > 1 mt/cm Absorber Height h [µm]

26 Exclusion Plot for new spin-dependent forces m α [ev] Ni et al., 1999: Gravitational Bound States, unpolarized Gravitational Bound States, polarized, projected Electron spin Neutron spin Ritter et al., 1992 g S g P Hammond et al., 2007 Heckel et al., 2006: Ni et al., Youdin et al., 1996 Heckel et al., λ [m]

27 Projected improvement: Polarized experiment Polarizing foil with guide field wires Spin transport zone B 0 up or B 0 down Magnetization UCN 25 mm Bottom mirrors Absorber/Scatterer Neutron detector 0.06 Sensitivity gain due to relative measurement, stronger UCN source, wider mirror, longer run time. Count rate [s -1 ] Absorber Height h[µm] Possible false effect due to magnetic field gradient > 1 µt/cm from holding field or ferromagnetic particles in mirror Test: Reverse magnetic field, check absorber height dependence, magnetize mirror in strong field Experiment to be performed in Summer 2009

28 Energy measurements Accuracy of position-observables: ~ 10% Improvement: do spectroscopy V E 3 Transition 2 3 E 2 Idea: Induce state transitions through: E 1 Oscillating magnetic field gradients Oscillating Masses Vibrations Typical energy differences: E ~ h 260 Hz Additional collaborators: T. Soldner, P. Schmidt-Wellenburg, M. Kreuz (ILL Grenoble) F. Naraghi, 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) L. A. Grigoryeva (PNPI Gatchina) A. Meyerovitch, (U Rhodes Island) z

29 Theory of resonance transitions 2 h iωt H = + mgz + Re( V { ( z) e ) 2mn z Bz H, defines ψ 0 n i.e. V ( z) = µ z z z Ω ab ω = E E ab b a 2 = b V ( z ) a h P ( ω ω ) passage sin ab + Ωab 2 2 a b ( τ passage ) = Ω ab 2 2 ( ω ω ab ) + Ω ab τ 0 Transition probability P a b τ passage = 0.05 s τ passage = 0.5 s ω a b /2π [Hz] G. Pignol et al., 2008

30 Projected first measurement of resonance transitions Prepare initial states Suppress ground state Periodic magnetic field gradient Filter ground state Measure horizontal velocity New UCN Source Bottom mirror Position n-sensitive De etector 1. Preparation of initial state 2. Suppress ground state 3. Induce Transitions in time-dependent magnetic field gradient 4. Detect ground state in dependence of horizontal velocity (that is: oscillation frequency) G. Pignol et al., 2008

31 Under construction: the GRANIT spectrometer 1. Population of ground state 3. Study transition to final state 2. Populate the initial state 4. Neutron Detection cm Challenge: Tolerances to get a high neutron lifetime in a given state: Flatness of bottom mirror: < 100 nm Accuracy of setting the side walls perpendicular: ~ 10-5 Vibrations, Count Rate, Holes, Vacuum, Dust,

32 Summary Gravitationally Bound Quantum States detected with Ultracold Neutrons Characteristic size is ~ µm Applications in fundamental physics: Limits on fifth Forces, limits on spin-dependent forces, and others Future: Replace transmission measurements (with its need to rely on absorber models) by energy measurements. Ultimately, E/E ~ E ~ pev might be reached. Thank you for your interest!

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34 Example: Neutron Lifetime Measurements Decrease of Neutron Counts N with storage time t: N(t) = N(0)exp{-t/τ eff } 1/ τ eff = 1/τ β +1/ τ wall losses Neutron lifetime [s] Spivak Nesvizhevsky 92 Byrne Mampe Arzumanov 00 Mampe Dewey 03 PDG2006 MAMBO Serebrov Year of Publication Many new attempts planned, mostly with magnetic bottles

35 A neutron electric dipole moment (EDM) and T violation E E + + Time Reversal T (equivalent to CP) If T were a good symmetry and d n 0, then the ground state of the neutron in a shell modell would be fourfold degenerate

36 Idea of the EDM measurement B o +E -E neutron ω n = -B o µ/ h ω n ( ) = [-B 0 µ 2Ed n ] / h ω n ( ) = [-B o µ + 2Ed n ] / h The difference in the precession frequency ω n for different electric field directions is proportional to d n : ω n = (ω n ( ) ω n ( )) = -4Ed n / h

37 The Ramsey Method of Separated Oscillatory Fields T ~ 100 s 5. Polarization Analysis θ P final = -P initial cos(θ), θ = ω n T

38 The Ramsey Resonance Curve /T s neu tron spin u p count working points resonance frequency applied frequency [Hz]