1. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky Institute Laue-Langevin, Grenoble

2. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky Grenoble “2.5” out of 7 European Research Centers (EUROFORUM): ILL, ESRF, ½ EMBL Institute Laue-Langevin, Grenoble The biggest worldwide research reactor France, Germany, England, Italy, Swiss, Autrish, Russia, Spain, Chekh. Rep. Dominant part of all World research in the field of fundamental physics of particles and fields with neutrons

3. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 1.Short Introduction: Ultra Cold Neutrons - UCN. First experiment of storage of UCN in 1968 in Joint Institute for Nuclear Research in Dubna: V.I.Luschikov, Yu.N.Pokotilovski, A.V.Strelkov and F.L.Shapiro (1969). JETP Letters 9: 40-45. V.V.Nesvizhevsky Plan of this presentation

4. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 2. Quantum states of neutrons in the Earth’s gravitational field above a mirror. - General analytical solution of the Schrödinger equation for an object in a gravitational field above a mirror is given in textbooks on quantum mechanics. - An experiment with UCN was proposed in 1976 : V.I.Luschikov (1977), Physics Today: 42- 51; V.I.Luschikov and A.I.Frank (1978), JETP Letters 28(9): 559-561. V.V.Nesvizhevsky Plan of this presentation

5. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 3. Experimental results. - Observation and study: H.Abele, S.Bäßler, H.G.Börner, A.M.Gagarski, V.V.Nesvizhevsky, A.K.Petukhov, K.V.Protasov, A.V.Strelkov, A.Yu.Voronin, A.Westphal et al : Nature 415: 297-299 (2002); Physical Review D 87: 102002 (2003); Europ.Phys.Journ. C 40(4):479-491 (2005). V.V.Nesvizhevsky Plan of this presentation Institute Laue-Langevin, Grenoble, France; Petersburg Nuclear Physics Institute, Gatchina, Russia; Laboratory of Sub-Atomic Physics and Cosmology, Grenoble, France; Lebedev Institute, Moscow, Russia; Mainz University, Germany; Heidelberg University, Germany; DESI, Hamburg, Germany; University Joseph-Furrier, Grenoble, France; Joint Institute for Nuclear research, Dubna, Russia

6. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 4. Prospects and applications. - Search for additional (spin-independent or spin-dependent) short-range forces at the distances of 1nm - 10µm - Improvement of the upper limit for the neutron electric charge - Verification of some extensions of the quantum mechanics, such the fundamental loss of quantum phase coherence due to interaction of quantum systems with gravitational field (with the observation time of up to 10 3 s), or logarithmic terms in the Schrödinger equation. - This method provides a rare opportunity to measure distribution of hydrogen above/below surface - This phenomenon allows to solve the problem of neutron-tight valve for UCN traps - It provides a convenient tool to study such phenomena as neutron localization (Andersen- type), or interaction of waves with rough surfaces. V.V.Nesvizhevsky Plan of this presentation

7. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 Neutron Nuclei in matterUsually: ~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 1. Effective Fermi-potential and storage of UCN in traps V.V.Nesvizhevsky

8. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky Uranium + water + neutrons + light Liquid-deuterium source of cold neutrons Curved neutron guide to extract UCN Very low background ! 1. UCN production UCN (Ultra Cold Neutrons) – soft fraction of spectrum of cold or thermal neutrons

9. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 1. UCN production New reactor in 1995 !

10. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 Nature 415, 297-299 (17 January 2002) Valery V. Nesvizhevsky *, Hans G. Börner *, Alexander K.Petoukhov * ‡, Hartmut Abele †, Stefan Baeßler †, Frank J.Rueß †, Thilo Stöferle †, Alexander Westphal †, Alexei M. Gagarski ‡, Guennady A. Petrov ‡ & Alexander V. Strelkov § * Institute Laue-Langevin, Grenoble, France; † University of Heidelberg, Germany; ‡ Petersburg Nuclear Physics Institute, Gatchina, Russia; § Joint Institute for Nuclear Research, Dubna, Russia. 2. Quantum states of neutrons in the gravitational field V.V.Nesvizhevsky

11. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 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 4)Energy (temperature) of UCN is extremely small and not equal to the installation temperature 2. How to observe any quantum states of matter in a gravitational field ? Quantum state energy in the Bohr- Sommerfeld approximation :

12. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 2. Probability to observe a neutron above a mirror The precise solution of the corresponding Schrödinger equation Height above a mirror in microns

13. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 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

14. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky Neutrons spend longer time at the top of its “trajectory” and the spacing between the maxima is bigger at the top as well 2. Probability to observe a neutron above a mirror

15. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky V horizont ~4-15 m/s V vertic ~2 cm/s Selection of vertical and horizontal velocity components 2. General scheme of the experiment

16. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 2. «Table-top experiment» Some parameters of the experimental installation and characteristic parameters of the phenomenon: -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

17. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 2. Measurement

18. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 2. Measurement

19. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 2. Measurement

20. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 2. Measurement

21. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 2. Measurement

22. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 2. Measurement

23. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 2. Measurement

24. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 3. Calibration of distances Calibrated wires-spacers Long-focus microscope Mechanical devices (“comparators”) The distance between a mirror and a scatterer/absorber is measured using the capacitors method Calibration :

25. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 3. Test of the mirrors quality General scheme to verify the quality of our mirrors mirror Neutron trajectories Neutron detector Collimator Why ? Non-specular reflections would cause false non-transparency of the slit mirror/scatterer mirror

26. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 3. Test of the mirrors quality μmμm

27. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 3. Surface of scatterers Image1234 Hauteur maxi.1.91.952.11.85 Distance moyenne5.04.65.644.4 Study of scatterer’s surfaces using an atomic force microscope or optical microscope

28. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 3. Measurement of neutron horizontal velocity components General scheme to select horizontal velocity components and to measure their spectrum Collimators Bottom mirror Scatterer/absorber Neutron trajectories

29. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky Average horizontal velocity component along the neutron beam axis is ~6.5 m/s for the broad initial spectrum 3. Measurement of neutron horizontal velocity components

30. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 3. Theoretical description The model of tunneling through gravitational barrier

31. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 3. Theoretical description μmμm Probability to observe neutron versus height Height above the classical turning point for any quantum state Penetrability of the gravitational barrier

32. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky μmμmμmμm 3. Results Narrow spectrum; soft fraction; comparison to the theoretical model

33. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 2. Results Narrow spectrum; soft fraction; comparison to the theoretical model

34. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky μmμm Expected : 0.2 μm/ms Measured : 0.16±0.04 μm/ms 3. Results The penetrating neutron flux versus the horizontal velocity component

35. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky Position-sensitive detector with the spatial resolution of 1-2 μm 3. Measurements with a position-sensitive detector

36. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 3. An example of such a position-sensitive detector

37. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky Preliminary results of measurement of density of neutron standing wave above a mirror using a position-sensitive detector with the spatial resolution of ~ 1.5 μm 3. Measurements with such a position-sensitive detector A few lowest quantum states

38. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 3. Measurements with such a position-sensitive detector Pure quantum states

39. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 3. Measurements with such a position-sensitive detector Pure quantum states step Two quantum states before the step One quantum state before the step

40. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 3. Measurements with such a position-sensitive detector 1 43 2

41. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 3. Measurements with such a position-sensitive detector

42. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 3. Measurements with such a position-sensitive detector

43. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky Frequency of perturbation, Hz Probability of transition Quantum trap Resonance transition 4. Resonance transitions between quantum states - Oscillations of a bottom mirror – due to nuclear forces; - Oscillations of a mass – due to gravitational forces; - Oscillations of electro-magnetic forces … How to excite such a resonance transition :

44. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 4. Resonance transitions between quantum states Scheme of an experiment to estimate the lifetime of neutrons in the quantum states Mirror Neutron detector Scatterer Neutron beam Scatterer Estimation of the lifetime of a neutron quantum state

45. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky 4. Applications in fundamental physics Additional short-range forces Why additional forces? -Light particles -Additional spatial dimensions

46. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky αGαG λ, m 4. Applications in fundamental physics 1 nm 10 μm10 μm Boundary for additional short-range forces Neutron experiments M=3 Casimir forces, M=2 Macroscopic measurements of gravitational forces M=2 Additional short-range forces Non-existence of additional bound state: (attractive interaction) Shift of the characteristic size of the neutron wave function : V.V. N. and K.V.P. Class. Quantum Grav. 21 4557– 4566 (2004)

47. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 V.V.Nesvizhevsky αGαG λ, m 4. Applications in fundamental physics 1 nm 10 μm10 μm Additional short-range forces Why neutrons ? -Due to their electric neutrality: small false effects -Wavelength in the range from 1 А (thermal neutrons) to 10 μm (quantum states in the gravitational field) -Significant methodical progress in this field allows us to carry out precision experiments “Conservative” perspectives: -high-density coatings (tungsten, gold) – factor 4-5 -Precision measurement of the wave- functions shape – factor 10 2 at 10 µm -Resonance transitions between quantum states – factor 10 3 -10 5 at 10 µm -Dedicated experiments with very cold neutrons – factor 10 2 -10 4 at 1 nm

48. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 - Neutrons in neutron guides - Particles/atoms in the top turning point of their classical trajectory in the gravitational field: atomic/neutron fountains 4. More examples V.V.Nesvizhevsky

49. INSTITUT MAX VON LAUE - PAUL LANGEVIN 14.03.16 4. Scales of temperature and energy in neutron physics V.V.Nesvizhevsky