1. 1 Phase diffraction gratings for the transformation of neutron energy A. Frank FLNP of JINR, Dubna, Russia 3rd Workshop on Physics of Fundamental Symmetries and Interactions, PSI 2013

2. 2 Matter wave diffraction by a moving grating. Formulation of the problem V Frank. PSI-2013. 10 September 2013 ? V.G. Nosov and A.I.Frank, 1991

3. 3 Matter wave diffraction by a moving grating. Formulation of the problem V Frank. PSI-2013. 10 September 2013

4. 4 Elementary Theory 2. Galilean transformation of the wave problem. 1. Solving the diffraction problem (Fraunhofer diffraction) in a moving system. L – space period of grating A.Frank, V.Nosov, 1994 V k n = -1 n = +1 n = 0 k k In a limit L→ , V→ , V/ L = f = const q 0 →0 Amplitude or phase modulation of the transmitted wave Frank. PSI-2013. 10 September 2013

5. 5 Moving grating as a phase modulator and peculiarity of the phase π-grating E E a 0 = 0 ! E Only odd orders Phase π - modulation Frank. PSI-2013. 10 September 2013

6. 6 Experimental realization - rotating grating UCN Monochromator Phase π -grating where N is number of groves n L d E 1 Frank. PSI-2013. 10 September 2013 d = 0.14 mkm

7. 7 Energy of the state 121 Substrate Fabry-Perot interferometers (Neutron Interference Filters) as a spectrometric device Frank. PSI-2013. 10 September 2013

8. 8 First experimental results Splitting of the spectrum A.I.Frank et al. ILL annual report 2001 Phys.Lett.A 311 (2003) 6 Jetp Lett, 81 (2005) 427 Angular period of grating 0.3325mrad (20μ at the middle diameter) Detector Monochromator grating Analyzer Frank. PSI-2013. 10 September 2013

9. 9 Neutron focusing in time t L t a X Frank. PSI-2013. 10 September 2013 A.I.Frank and R.Gähler. Phys. of Atomic Nuclei, 63, (2000) 545

10. 10 Time lens is working! A. I. Frank, P. Geltenbort, G. V. Kulin et al. JETP Lett. 78, (2003) 188 S.N. Balashov, I.V. Bondarenko, A.I. Frank et al, Physica B, 350 (2004) 246 Frank. PSI-2013. 10 September 2013

11. 11 Test of the equivalence principle for neutrons Dubna-ILL-Kurchatov experiment of 2006 H E0  EE0  E E E 0 + mgH E 0 – ħ  1 + mgH HH E 0 – ħ  2 + mgH The idea was to compare the change of energy mgH with energy ħΩ transferred to neutron by a moving grating Frank. PSI-2013. 10 September 2013 g A.I. Frank, P. Geltenbort, M. Jentschel,et al. JETP Letters, 86, 225 (2007)

12. 12 Flux modulation TOF base E1E1 Detector count rate oscillations E2E2 E3E3 E 1 >E 2 >E 3 Comparing the energy m g g n H with energy ħΩ as before Combination of Neutron Interference Filters with peculiar TOF spectrometry Frank. PSI-2013. 10 September 2013 Test of the equivalence principle for neutrons New Dubna-ILL-Kurchatov experiment

13. 13 Chopper-modulator Stability of the modulation frequency was better than 10 -4 Frank. PSI-2013. 10 September 2013

14. 14 Experiment. Part I Detector Monochromator Calibration Variation of the monochromator vertical position leads to changing of the UCN energy, time of flight and total phase of the count rate oscillation Modulation frequency 75Hz Frank. PSI-2013. 10 September 2013

15. 15 The count rate oscillation phase of the UCN which energy shifted by the grating rotating with different frequency must be compared with the calibration curve Experiment. Part II (idea) ΔHΔHΔHΔH Frank. PSI-2013. 10 September 2013 Detector Monochromator grating

16. 16 Detector Monochromator grating The count rate oscillation phase of the UCN which energy shifted by rotating grating must be compared with the calibration curve Unfortunately -1 order of diffraction is accompanying by the +1. The problem related with 0-th and -2 orders was and diffraction orders of higher orders were underestimated Experiment. Part II Frank. PSI-2013. 10 September 2013

17. 17 Detector Monochromator grating By the using of special 9-layers filter with wide transmission band it is possible to select the UCN of -1 diffraction order Wide analyzer Frank. PSI-2013. 10 September 2013

18. 18 New spectrometer at the PF2@ILL. November 2010 Frank. PSI-2013. 10 September 2013

19. 19 Improved spectrometer at the PF2@ ILL. December 2011 and 2012 Frank. PSI-2013. 10 September 2013

20. 20 Present status of the experiment 1. The full scale test measurements with new spectrometer was performed. 2.2. The rate of the collection the statistical accuracy, was obtained as 5×10 -3 per day. That is enough to collect statistical accuracy of the order of 5×10 -4 during two cycle of statistic collection at PF2 source. 3.The statistical accuracy rate may be doubled after some improvements 4. The systematic effect due to admixture of zero order to the spectrum of -1st order was found. 5.Intensity of the diffraction line -1st order is decreasing with increasing of rotation frequency Frank. PSI-2013. 10 September 2013

21. 21 d L/2 CL/2 L/2(1+C)L/2  Transformation of the phase modulation function in a moving reference system. Phase modulation function in a moving reference system. (Naive representation) Frank. PSI-2013. 10 September 2013 Semi rigorous theory of neutron diffraction by a moving grating (in neglecting of reflection) now exists V.A. Bushuev, 2013

22. 22 Theoretical prediction for the neutron spectra Intensities of the first three orders as a function of parameter C Frank. PSI-2013. 10 September 2013

23. 23 Spectrum of the diffracted neutrons (calculation) Angular period of grating is 0.0831 mrad (5μ at the middle diameter) Frank. PSI-2013. 10 September 2013

24. 24 For the best separation of different orders it is necessary to decrease period of grating (or increase its velocity) That will lead to the remarkable increasing of the zero-th order Frank. PSI-2013. 10 September 2013 N ~ 75 000 → 100 000

25. 25 How it is possible to decrease the aspect ratio and parameter C? 1.Grooves in Si may be filled by the matter with negative ρb, say Ti We did not find the appropriate matters It is needed: а) extremely small capture cross section а) extremely small capture cross section б) effective potential 30 nev (Si) < U < ~100 nev (UCN energy) б) effective potential 30 nev (Si) < U < ~100 nev (UCN energy) 2. The replacing of Si wafer by matter with grater ρb. That will increase (n-1) The appropriate technology is unknown or not exists 3. Thin film of matter with relatively large ρb at Si wafer !! Frank. PSI-2013. 10 September 2013

26. 26 Two component grating phase  -grating Parameter C may be reduced of 1.66. Reflection from GaAs suppressed due to interference effect Reflection from GaAs suppressed due to interference effect Si GaAs 87nm instead of 144 nm Frank. PSI-2013. 10 September 2013

27. 27 Effect of the two component grating (estimations) Frank. PSI-2013. 10 September 2013 Si phase gratings with spacing L= 4 and 5μ Si phase gratings with spacing L=5μ and two component grating L = 4 μ N ~ 75 000 → 100 000

28. 28 One mode grating of special profile V v0v0 v1v1 Deceleration A.I. Fank. ISINN 13, Dubna, 2005 A.I.Frank Physics of Atomic Nuclei, 76, 544 (2013), Frank. PSI-2013. 10 September 2013 Disadvantages 1)Technological problems 2)Such grating is an ideal only for the defined velocity V Advantage: Only one diffraction order

29. 29 Conclusion 1.Diffraction grating moving across the direction of neutron propagation acts as a nonstationary device. That results in appearance of the line spectrum. 2.The phenomenon was theoretically predicted in 1994 and firstly observed in 2001 3.It may be used for the precise change of the neutron energy what was demonstrated in the experiment for neutron focusing in time and gravity experiments with UCN. 4.For the follow progress of new gravity experiment with neutron the more detailed theoretical and experimental investigations of the phenomenon are necessary. Frank. PSI-2013. 10 September 2013

30. 30 P. Geltenbort, P. Høghøj, M. Jentschel Many thanks to my coauthors I.V. Bondarenko, S.V.Goryunov, G.V.Kulin, D.Kustov. S.N. Balashov, S.V.Masalovich, V.G.Nosov S.N.Strepetov V. A. Bushuev Thank you for your attention!

31. 31 Micro structure of the first gratings The presence of the parasitic space frequencies might be a reason for loss of intensity and line widening Frank. PSI-2013. 10 September 2013

32. 32 New grating of high quality was available in 2012 The decreasing of intensity did not caused by the grating quality The nature of problems is probably more fundamental Frank. PSI-2013. 10 September 2013

33. 33 Variation of the line intensity Intensity of the -1 order line Angular period of grating 0.0831 mrad (5μ at the middle diameter) Frank. PSI-2013. 10 September 2013 Measurements of 2006