1. SPIN2006 @ 京都 Y. Seki (Kyoto Univ. / RIKEN ) ( 京大理・関 義親 ) K. Taketani (Kyoto Univ.) H. Funahashi (Osaka Electro-Communication Univ.) M. Kitaguchi, M. Hino (KURRI) Y. Otake (RIKEN) H. M. Shimizu (KEK) 1/13 Development of Cold Neutron Interferometer with Wide-Gapped “BSE”s for Precision Measurements Y. Seki et al.

2. SPIN2006 @ 京都 Neutron Interferometer and Phase V1V1 V2V2 L path 1 path 2 phase difference small  V  enlarge and L cold-neutron interferometer using multilayer mirrors conventional neutron interferometer (Si crystal, thermal neutron) ～ 2 Å < 6 Å L ～ 10cm ～ 10-100 Å L ～ 1m  V ～ 1feV 2 Large dimensional cold-neutron interferometers are more sensitive to small interactions than conventional ones. m : neutron mass  : neutron wavelength h : Planck constant L : interaction path length  V = V 1 – V 2 Y. Seki et al.

3. SPIN2006 @ 京都 Aharonov-Casher Effect past experiments Si neutron interferometer (A.Cimmino et al., Phys.Rev. Lett., 63 380 (1989)) →topological but poor precision atom interferometer ( K.Zeiske et al., App.Phys. B60., 63 205 (1995)) → high precision but nontopological (particles do not go around the charge density.) AB effect e‐e‐B AC effect  E 3 Our neutron interferometers with completely spatially separated two paths are suitable to measure topological AC effect. The observed phase is nearly 2  above the theoretical value. Y. Seki et al.

4. SPIN2006 @ 京都 Development of Large Dimensional Cold-Neutron Interferometer 4 past now multilayer mirror + etalon → “BSE” Jamin-type cold-neutron spin interferometer with 10  m gapped BSEs → interference fringes of 60% contrast measurement of small phase shift induced by the magnetic field of a helmholtz coil →51.9±1.7mrad development of Jamin-type cold-neutron spin interferometer with 200  m gapped BSEs pilot experiment of nontopological Aharonov-Casher phase ～ 5mrad future precision measurement of small interaction ex. topological AC phase, gravitationally induced phase… Why do we want to enlarge the gap? How precise can we determine the phase shift? gap Investigation of phase resolution of neutron spin interferometry Enlargement of the spatial separation between two paths Y. Seki et al.

5. SPIN2006 @ 京都 4 Development of Large Dimensional Cold-Neutron Interferometer past now multilayer mirror + etalon → “BSE” Jamin-type cold-neutron spin interferometer with 10  m gapped BSEs → interference fringes of 60% contrast measurement of small phase shift induced by the magnetic field of a helmholtz coil →51.9±1.7mrad development of Jamin-type cold-neutron spin interferometer with 200  m gapped BSEs pilot experiment of nontopological Aharonov-Casher phase ～ 5mrad future precision measurement of small interaction ex. topological AC phase, gravitationally induced phase… Why do we want to enlarge the gap? How precise can we determine the phase shift? gap Investigation of phase resolution of neutron spin interferometry Enlargement of the spatial separation between two paths Y. Seki et al.

6. SPIN2006 @ 京都 Pilot Experiment -Nontopological AC Phase Setup polarizer detector analyzer  /2  electrode slit JRR-3M MINE2 beamline  = 8.8 Å,  / = 2.7% (FWHM) ・ |E 1 | = |E 2 | = 33.5kV/cm (111.7 statV / cm) ・ Phase difference generated between E 1 and E 2 was observed. 5 We measured the nontopological AC phase in atom interferometer –like setup to demonstrate the phase detectability in our facility. ・ NSI without BSEs E1E1 E2E2 ・ L = 20cm = 5.46mrad (theoretically) Y. Seki et al.  V = 4.04feV!

7. Data and Analysis To determine initial phase   of fringes, sin function was fitted. precision of each phase ～ 7.4mrad ． 6 We obtained the phase shifts from the interference fringes. parameter of phase shifter counts / 40sec SPIN2006 @ 京都 (initial) phase [rad] E1E1 E2E2 E1E2E1E2 run number

8. Y. Seki et al. on off phase shift [rad] (initial) phase [rad] E1E2E1E2 run number Analysis 7 phase shift [rad] Null experiment (E 1 = E 2 = 0) phase shift [rad] SPIN2006 @ 京都 total counts on : 2.0×10 6 n off : 1.6×10 6 n in 1 week ～ ±1/3000cycle = 3.5±2.1mrad = 5.46mrad We could detected the small phase shift ～ 5mrad with 38% precision in 1 week on MINE2 beamline. on off

9. SPIN2006 @ 京都 Development of Large Dimensional Cold-Neutron Interferometer past now multilayer mirror + etalon → “BSE” Jamin-type cold-neutron spin interferometer with 10  m gapped BSEs → interference fringes of 60% contrast measurement of small phase shift induced by the magnetic field of a helmholtz coil →51.9±1.7mrad development of Jamin-type cold-neutron spin interferometer with 200  m gapped BSEs pilot experiment of nontopological Aharonov-Casher phase ～ 5mrad future precision measurement of small interaction ex. topological AC phase, gravitationally induced phase… Why do we want to enlarge the gap? How precise can we determine the phase shift? gap Investigation of phase resolution of neutron spin interferometry Enlargement of the spatial separation between two paths Y. Seki et al.

10. SPIN2006 @ 京都 Multilayer Neutron Mirror two materials with different optical potential magnetic multilayer mirror ferro- magnetic Ｂ 50 ～ 200 Å normal multilayer mirror selective reflection about spin potential 8 Multilayer mirrors are artificial one-dimensional lattice which can Bragg reflect cold neutrons. potential to up-spin potential to down-spin m: neutron mass  average number density b: neutron scattering length of nucleus

11. Requirements for mirror arrangement SPIN2006 @ 京都 recombination of the two subbeam coherence length 2μm 17nm 50nm coherence volume detectable region moire fringe α two mirrors a pair of two mirrors degree of freedom of mirrors (horizontal) (vertical) crossing angle  rad   rad xx   x < 1.4  m  < 8.4  rad 9 In order to obtain the clear interference fringes we need to the recombine the two beam in the coherent volume without the large crossing angle.

12. SPIN2006 @ 京都 Beam Splitting Etalon (BSE) 10 specifications of etalon (within 32mm diameter) flatness (λ/ 100) parallelism λ/ 100 at λ = 633nm roughness (RMS) less than 2 Å magnetic mirror normal mirror space length BSE BSEs satisfy the requirements for the two mirrors arrangement. BSEs divide neutron beam into the two spin components. The parallelism of two planes in a BSE ensures that the two subbeam are also parallel to each other. up-spin down-spin parallel Y. Seki et al.

13. SPIN2006 @ 京都 polarizer B  /2 spin flipper BSE phase shifter coil analyzer B_guide up-spin down-spin  spin flipper  /2 spin flipper Jamin-type Neutron Spin Interferometer (NSI) 11 We succeeded in constructing a Jamin-type interferometer using two BSEs with 10  m gap. M.Kitaguchi et al., Phys. Rev. A67, 033609 (2003) contrast of 60% Y. Seki et al.

14. 500mm BSE SPIN2006 @ 京都 polarizer B  /2 BSE phase shifter coil analyzer B_guide up-spin down-spin   /2 Enlarging Gap of BSE 12 We have confirmed the beam separation with 200  m gapped BSEs. BSE 10  m 200  m counts / 500sec scanning position [mm] 300±30  m (incident angle 1.05) For experimental applications, we have to enlarge the gap of BSEs from 10  m to 200  m and separate the beam completely.

15. 500mm BSE SPIN2006 @ 京都 Enlarging Gap of BSE 12 The requirement for the two BSEs arrangement is achivable enough.   relative angle tilting angle Y. Seki et al. 40 130

16. SPIN2006 @ 京都 Summary and Future Plan 13 now development of Jamin-type cold-neutron spin interferometer with 200  m gapped BSEs pilot experiment of nontopological Aharonov-Casher phase ～ 5mrad past multilayer neutron mirror + etalon → “BSE” Jamin-type cold-neutron spin interferometer with 10  m gapped BSEs → interference fringes of 60% contrast measurement of small phase shift induced by the magnetic field of a helmholtz coil →51.9±1.7mrad future precision measurement of small interaction ex. topological AC phase, gravitationally induced phase… We develop large-dimension interferometers for long-wavelength neutrons with wide gapped BSEs, which enable us to carry out precision measurements of small interactions. We have confirmed the complete beam separation. We have established the method to estimate alignment of two BSEs. We have demonstrated that small phase shifts ～ 5mrad  V ～ 4feV  is detectable with the precision of ～ 1/3000 cycle in 1week on MINE2. near future Establishment of the interferogram of Jamin-type cold-neutron interferometer with 200  m gapped BSEs. Development of BSEs adapted to white beam with super mirrors. → J-PARC spallation neutron source (beam intensity : ×10 ～ 100) Y. Seki et al.

18. polarizer B  spin flipper BSE phase shifter analyzer  spin flipper  spin flipper detector ΔΦ Ｉ B + = B_guide SPIN2006 @ 京都 Jamin-type Neutron Spin Interferometer (NSI)

19. multilayer mirror SPIN2006 @ 京都 laminogram of multilayer mirror with transmission electron microscope

20. Specifications of Beam Splitting Etalon flatness : λ/ 100 parallelism : λ/ 100 at λ = 633nm (in clear aperture) Φ = 54mm effective diameter （ clear aperture ） : 32mm width : 12mm × 2 gap ： 189μm manufactured by SLS Optics (UK) gap magnetic mirror normal mirror spacer Ni / Ti Ge / Pa Ni / Ti SPIN2006 @ 京都

21. MINE2 beamline on JRR-3M in JAEA MINE2 beamline on JRR-3M in JAEA wavelengthλ = 0.88nm ， bandwidth 2.7% in FWHM measurement of wavelength by TOF SPIN2006 @ 京都

22. Requirement for mirror arrangement difference between two subbeam z x y coherence length 2μm 17nm 50nm crossing angle coherentce volume detectable region moire finge x y z z x y β α relative angle tilting angle degree of freedom of two mirrors degree of freedom of two BSEs → cause of difference (horizontal) (vertical) SPIN2006 @ 京都

23. 120mm 50mm 220mm Beam Operation by Solenoid SPIN2006 @ 京都

24. Vertical Coherence Length SPIN2006 @ 京都

25. Measurement of Relative Angle between Two BESs SPIN2006 @ 京都 polarizer detector

26. Measurement of Tilting Angle between Two BSEs BSE θ level laser d L 2θ 2θ = d / L The tilt angle is adjusted with shims. SPIN2006 @ 京都

27. Q Q vertical shift longitudinal shift α relative angle x y z β tilting angle z x y 112mm 50mm 120mm 50mm 220mm x y z ↓ ↓ requirement for the arrangement of two BSEs SPIN2006 @ 京都 Adaptive Optical Devices (Quadrupole magnet, Solenoid)

28. 112mm 50mm as adaptive optical device… parallel shift correction crossing angle correction 135nrad at 3A 300mm 40.5nm at 3A direction of magnetic gradient （ G = 0.471Gauss/mm at 3A ） Beam Operation with Quadrupole Magnets SPIN2006 @ 京都

29. Precision Measurement of Gravitational Interaction （ beyond COW Experiment ） COW experiment λ ： neutron wavelength A ： space enclosed by two paths θ ： tilting angle of interferometer S.A.Werner et al, Physica B 151(1988) 22 K.C.Littrell et al, Phys.Rev.A 56(1997) 1767 →Result of the COW experiment with a Si neutron interferometer had a discrepancy of 0.8% with the theoretical value. Disagreement with Newton approximation? Our cold-neutron interferometer with multilayer mirrors is ten times more sensitive to the phase shift than Si ones. And they are also free from dynamical diffraction effect. SPIN2006 @ 京都

30. Mach-Zehnder type Neutron Interferometer with BSEs Because the space enclosed by the two paths is large (20cm 2 ), this interferometer is suitable for measurement of gravitational interaction. BSE (solid etalon) rigid base 500mm 30mm BSEs are arranged on a precisely flat  rigid base. SPIN2006 @ 京都

31. Precedent Measurement of AC Phase Si neutron interferometer atom interferometer A.Cimmino et al., Phys.Rev. Lett., 63 380 (1989) K.Zeiske et al., App.Phys. B60., 63 205 (1995) dynamical diffraction effect large dimengional cold-neutron interferometer with BSEs Interaction path length is longer ( ～ 1m), so more sensitive to the phase shifts Dynamical diffraction can be negligible. Path can be separated completely spatially (topological). SPIN2006 @ 京都  1.50mrad  2.19±0.52mrad high precision but particle with a magnetic moment does not enclose the charge distribution (nontopological)

32. Ｓｕｐｅｒ Ｍ irror

33. Measurement of small phase shift induced by magnetic field polarizer π/2 detector analyzer phase shifter Helmholtz coil small magnetic field ～ 10.5mGauss 0.03A: 34.6mrad ～ 1/180 cycle 1run ： 1cycle 125sec × 9points 125mm 2巻2巻 counts / 125sec current of phase shiter[A] total 56run ～ 6million coutns offon 25k SPIN2006 @ 京都

34. Phase shift of 51.9 ±1.7mrad was detected. ON OFF precision of 1run ×√2 ～ 1/750cycle RMS ～ 1/530cycle precision of mean value ～ 1/3800cycle phase shift [rad] / 2  coil ON coil OFF phase [rad] / 2  run number phase run number SPIN2006 @ 京都 We need total 256million counts for the measurement of AC phase with 10% precision. Measurement of small phase shift induced by magnetic field

35. neutron spin interferometer without BSEs BSE SPIN2006 @ 京都 B_guide polarizer  /2 up-spin down-spin  B phase shifter coil analyzer  /2 9 Pilot Experiment -Nontopological AC Phase B Helmholtz coil phase shift 51.9 ± 1.7mrad detected

36. Analysis Approximation of phase drift E1E2E1E2 run number phase [rad] / 2  We approximated the phase drifts by a quadratic function. E1E1 E2E2 phase run number phase shift [rad] / 2  Null experiment (E 1 = E 2 = 0) phase shift [rad] / 2  SPIN2006 @ 京都 total E 1 : 608 runs E 2 : 612 runs