Institute Laue-Langevin, Grenoble

Plan of this presentation 1. Short Introduction: Ultra Cold Neutrons - UCN. First experiment in 1968 in JINR, Dubna: V.I.Luschikov et al (1969). JETP Letters 9: 40-45. 2. Quantum states of neutrons in the Earth s gravitational field above a mirror. Textbooks on quantum mechanics + V.I.Luschikov at al (1978), JETP Letters 28(9): 559-561. 3. Observation and study. et al : Nature 415: 297-299 (2002); Physical Review D 87: 102002 (2003); Europ.Phys.Journ. C 40(4):479-491 (2005). Collaboration: ILL, LPSC (France), PNPI, Lebedev Inst., Khlopin Inst., JINR (Russia), Mainz Univ., Heidelberg Univ., DESY (Germany). 4. Multi-disciplinary: Search for spin-independent and spin-dependent short-range forces in the range of 1nm - 10µm; limit for the neutron electric charge; verification of extensions of the quantum mechanics; the loss of quantum phase coherence; a rare opportunity to measure distribution of hydrogen above/below surface; solution for the problem of neutron-tight valve for UCN traps; convenient tool to observe Andersen-type neutron localization, or to study interaction of waves with rough surfaces; advanced UCN guides. 5. Project GRANIT. Resonance transitions between the gravitationally bound quantum states of neutrons. ANR project 2005-2008: Collaboration: ILL-LPSC-LMA (France) + 17.03.06 INSTITUT MAX VON LAUE - PAUL LANGEVIN

1. Effective Fermi-potential and storage of UCN in traps Nuclei in matter Usually: ~99.99 % - elastic reflection ~10-4 - inelastic reflection at phonons to the thermal energy range ~10-5 - inelastic reflection at surface nanoparticles to the UCN energy range ~10-5 - absorption Neutron UCN V E H UCN UCN Earth ' field s UCN T ~ 1mK ~ (1 6) m / s ~ 10 7 ~ 1m ev 17.03.06 INSTITUT MAX VON LAUE - PAUL LANGEVIN

2. How to observe any quantum states of matter in a gravitational field? "Let us consider another possibility, an atom held together by gravity alone. For example, we might have two neutrons in a bound state. When we calculate the Bohr radius of such an atom, we find that it would be 10 8 light years, and that the atomic binding energy would be 10-70 Rydbergs. There is then little hope of ever observing gravitational effects on systems which are simple enough to be calculable in quantum mechanics." Brian Hatfield, in "Feynman Lectures on Gravitation" ; R.P. Feynman, F.B. Morinigo, W.G. Wagner, Ed. Brian Hatfield Addison-Wesley Publishing Company, 1995, p. 11

2. How to observe any quantum states of matter in a gravitational field? Neutron above a mirror in the Earth s gravitational field 1) Electric neutrality (usually any gravitational interaction in laboratory conditions is much weaker that other interactions) 2) Long lifetime 3) Small mass v x E h m h τ 4) Energy (temperature) of UCN is extremely small and not equal to the installation temperature Quantum state energy in the Bohr- Sommerfeld approximation : E n 3 9 m 8 n π h g n 1 4 2

2. Probability to observe a neutron above a mirror Height above a mirror in microns The precise solution of the corresponding Schrödinger equation

2. Probability to observe a neutron above a mirror How the experiment with neutrons is related to the falling down of an apple in the gravitational field? Higher probability to observe neutrons (an apple) at some heights and zero probability for a pure quantum state to observe them somewhere in between

2. Probability to observe a neutron above a mirror Neutrons spend longer time at the top of its trajectory and the spacing between the maxima is bigger at the top as well

2. General scheme of the experiment Selection of vertical and horizontal velocity components V horizont ~4-15 m/s V vertic ~2 cm/s E h τ -Effective temperature of neutrons is ~20 nk -Background suppression is a factor of ~10 8-10 9 -Absolute horizontal leveling precision is ~10-6 rad -Parallelism of the bottom mirror and the absorber/scatterer is ~10-6

2. Measurement v x h m

2. Measurement

INSTITUT MAX VON LAUE - PAUL LANGEVIN 17.03.06 2. Theoretical description The model of tunneling through gravitational barrier >> 1 ξ ], 3 4 [ ) ( 2 3 ξ ξ Exp D ) ( ) ( ξ ω ξ D n n = Γ h ( 1 n) / n n E E + ω > < = 0 ], 3 4 [ 0 1, ) ( 2 3 ξ ξ ξ ξ Exp A D n ) ) ( ( ) ( τ ξ ξ Γ = n P n Exp ) ) ( ( ) ( hor n n V L Exp P Γ = ξ ξ = n n n hor n hor z z z Exp C V L Exp V z F 2 3 0 2 3 4 ), ( α β

3. Results Narrow spectrum; soft fraction; comparison to the theoretical model Experiment 1999

3. Results Narrow spectrum; soft fraction; comparison to the theoretical model z exp 2 = 21.3 ± 2.2syst ± 0.7stat, µ m z exp 1 = 12.2 ± 1.8syst ± 0.7stat, µ m z z quasi. class 1 quasi. class 2 = 13.7µ m = 24.0µ m µmµm

3. Measurements with such a position-sensitive detector 3 4 1 2

4. Applications in fundamental physics Additional short-range forces Why additional forces? -Light particles -Additional spatial dimensions V ( / λ) V ( z) = V0 Exp z 2 0 = 2 π G α m G ρm λ G m1 m2 V ( r ) = G 12 r ( 1+ α exp( r / )) 12 λ 12

5. Resonance transitions between quantum states How to excite such a resonance transition : - Oscillations of a bottom mirror due to nuclear forces; - Oscillations of a mass due to gravitational forces; - Oscillations of electro-magnetic forces Quantum trap Resonance transition Probability of transition E i E j = h w ν 21 140Hz ij δe min 10 18 δemin E E 2 1 ev 10 6 Frequency of perturbation, Hz

5. Resonance transitions between quantum states P Ω 4Ω 2 2 0n 0n max ( ω) = = 2 2 2 Ωn ( ω ωn 1) + 4Ω0n Transitions due to electromagnetic forces easy β ~ 10Gs / cm Transitions due to gravitational forces the probability could be of ~0.01 for ~100 kg oscillating test mass could be measured Transitions due to oscillating mirror easy oscillation amplitude of <1µm

5. Resonance transitions between quantum states But parameters of this spectrometer are very challenging! It will not be easy to suppress many false effects, for instance: -Vibrations (have to be not too much higher than the seismic noise (extremely difficult inside a reactor building!); -Waviness of mirrors (have to be as small as a few times 10nm for a mirror of ~30cm size); -Adjustments and accuracy of production of optics elements at a typical level of 10-6 -10-5 ; -Expected neutron count rate is ~50 events/day at the best available today UCN source etc

5. Resonance transitions between quantum states Also! -Surface roughness (low life-tome in a quantum state); -Impurities on surface (produce roughness for even ideally flat mirror); -Dust on surface (huge coherent scattering); - Complete control of magnetic fields/ gradients of magnetic fields; -Low-background neutron detectors (remember the value for expected count rate); -Etc etc

5. Resonance transitions between quantum states 1. To populate a low quantum state 2. To populate an excited state using a resonant transition End 2008 (ANR) Storage time ~ 1 s 3. To study mixing between neighbouring states Idea of this experiment 4. To detect neutrons (for instance, using again a resonance transition) 100-1000 µm 30-50 cm

5. Resonance transitions between quantum states In order to review theoretical aspects of this project and to discuss physics, which could be done with this installation, we organize a MINI-WORKSOP on Resonance transitions between gravitationally bound quantum states of neutrons in Grenoble, 6-7 April 2006 Registration is still open at: http://lpsc.in2p3.congres/granit06/informations-pratiques.php

5. Scales of temperature and energy in neutron physics Ultra cold nanoparticles Cold moderators Reactor moderators 20 nk 10-3? 10 1 10 3 10-12 10-7 10-1 10 7 Neutron energy, ev 10-3 VUCN Fission Quantum states of neutrons in the Earth s gravitational field Temperature, K 17.03.06 INSTITUT MAX VON LAUE - PAUL LANGEVIN