Neutron wave functions and interference in the spin variable space.

1. Neutron wave functions and interference in the spin variable space. F. Mezei Technical coordinator www.europeanspallationsource.se 22 May 2019

2. Every generation has to rediscover quantum mechanics (paraphrasing J. Dewey) • Will you understand what I'm going to tell you? … No, you're not going to be able to understand it. … That is because I don't understand it. Nobody does.(R. Feynman) • Accept Nature as She is — absurd. (R. Feynman)

3. Bloch (1936): A neutron inside condensed matter is influenced by “(1)…interaction of the neutron with atomic nucleus…. (2)…inhomogeneous magnetic field in its surrounding acting on the magnetic moment of the neutron.” Otto R. Frisch, H. von Halban Jr, J. Koch (1937) Larmor precessions Larmor frequency  n ~ 2 B/1840 Larmor precession in Fe: scales with B (not H)

4. Bloch (1936): A neutron inside condensed matter is influenced by “(1)…interaction of the neutron with atomic nucleus…. (2)…inhomogeneous magnetic field in its surrounding acting on the magnetic moment of the neutron.” Otto R. Frisch, H. von Halban Jr, J. Koch (1937) Larmor precessions (next 1969 Drabkin et al) Larmor frequency  n ~ 2 B/1840 Larmor precession in Fe: scales with B (not H) (debated until 1951)

5. What do neutrons see? Bloch (April 28, 1937): the two results rather depend on the shape of the “hole” the neutron sits in: avoid overlap of electrons and neutrons Field in the hole: = H (Bloch) = B (Schwinger) Reality: in quantum mechanics electrons and neutrons overlap and the field inside a source of magnetic field depends on the model of magnetism:

6. What do neutrons see? The physical choice for the magnetic field of the electrons: H: + or B: ( B = H + 4M)  - Migdal (1938): it is B, if done right (i.e. take the formulae from Landau’s textbook) Eckstein (1949): theory cannot decide, experiments needed Shull, Wollan and Strauser(December 8, 1950, appeared February 1951) Hughes & Burgy(September 25, 1950, appeared March 1951) air (vacuum) iron film H: neutron total reflection on optically flat iron surface (critical angle < 1°) B:

7. The other side of the issue: how do the neutrons see? Magnetic forces are not the same for the two models of neutron magnetic moment! genuine potential energy Neither the electrons, nor the neutrons are magnetic dipoles!

8. Neutron beam reactor at Budapest: since 1959 By 1967: leading role in correlation spectroscopy

9. Electronic neutron beam correlation choppers KFKI, HU Kjeller, NO

10. Neutron beam reactor at Budapest: since 1959 1972: discovery of Neutron Spin Echo via search for a cheap neutron spin flipper

11. Flexible flipper  Neutron Spin Echo  Larmor precessions are high precision clocks to measure individual velocities on classical, point like particles  Measure for thefirst time velocity changes for individual neutrons! Analogy to NMR Spin Echo: Erwin L. Hahn, 1947

12. Key ideas for Neutron Spin Echo  Larmor precessions are clocks to measure individual neutron velocities  Measure for the first time velocity changes for individual neutrons: gets us around Liouville theorem

13. The final polarization: The probability of  energy exchange: For  energy exchange: High resolution with moderate beam monochromatization = 0 For elastic scattering:

14. Practical demonstration of world record resolution  ILL, 1972 June – November

15.  IN11 project decided (based on a proposal of 3 handwritten pages): Rudolf Mössbauer, January 1973  First high impact publication from user operation: 1978

16. The NSE spectrometer IN11 at ILL  In operation since 1978(J. B. Hayter, P. A. Dagleish,….)

17. Effective flight path precision needed / achieved 0.3 mm 0.01 mm 0.03 mm 0.003mm

18. length d = 2/Q [Å] 104 103 102 101 100 10-1 104 Ramanscattering VUV-FEL Inelasticx-ray 10-2 102 Chopper UT3 100 100 Infra-red Multi-Chopper Brillouinscattering Inelastic Neutron Scattering 102 energy E = h [meV] 10-2 time t [ps] Backscattering 104 NMR µSR 10-4 Spin Echo Photoncorrelation Dielectricspectroscopy 106 10-6 X-ray correlationspectroscopy 108 10-8 10-4 10-3 10-2 10-1 100 101 102 scattering vector Q [Å-1] NSE: at the center of nm – ns space-time domain > 1500 publications in of condensed matter research

19. Degrees of freedom in (most) scattering experiments Goal: measurement of transition probability between well defined initial and final states neutron spin wave function  eikr ’ eik’r Note: there is a confusion on beam coherence between different k states. It is irrelevant for scattering. Each initial state has infinite extension in space and time, can probe as far as the sample shows correlations (e.g. in perfect crystals) With finite resolution this transforms into measuring initial and final distributions beam polarization (vector) P, f(k) P’, f(k’) 1)Preparation of initial beam 2)Analysis of scattered beam (direction, velocity or wavelength, polarisation: 2x6 dimensional parameter space) P, kP’, k’

20. What makes neutrons coherent? Neutrons show all forms of behaviour in a single scattering experiment: particle propagation: instruments ( 0.1 mm - 100 m ) refraction: geometrical optics, index of refraction (10 nm - 0.01 mm) interference on microscopic objects (0.1 - 100 nm) Geometrical optics or interference (diffraction)? L d Path difference:  ~ d2/L (~ 0.1 mm for neutron experiments) . How does it compare to wavelength ? If , interference washed out:classical particle behaviour between quantum scattering events < : light scattering, synchrotron radiation

21. What makes neutrons coherent? Single neutron wave functions in the beam: most general wave packages Single neutron wave function (packet): can have 0spin! Best described: by an ensemble of point like classical particles: plane wave = classical particles with “infinite” coherence length expansion of wave packet = classical velocity differences correlated regions in sample = the only coherence length

22. What makes neutrons coherent? Classical plane wave approximation valid: coherence length of the sample << beam cross section  nearly all scattering experiment Most important exception: perfect crystals, neutron interferometry Forbeam interference phenomena : classical incoherent average over the single plane wave patterns with infinitely well defined position and velocity , and no coherence for different and :