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Physical Review A

Measurement of gravitation-induced quantum interference for neutrons in a spin-echo spectrometer

V.O. de Haan, Jeroen Plomp, A.A. van Well, M.Th. Rekveldt, Yuji Hasegawa, Robert M. Dalgliesh, Nina‐Juliane Steinke

Published Jun 12, 2014• 24 citations
Publisher

Abstract

With a neutron spin-echo reflectometer (OffSpec at ISIS, UK) it is possible to measure the gravitation-induced quantum phase difference between the two spin states of the neutron wave function in a magnetic field. In the small-angle approximation, this phase depends linearly on the inclination angle of the neutron beam with respect to the horizontal. This also holds for the Bonse-Hart interferometer used in the Colella-Overhauser-Werner experiments and should be taken into account. Neglecting this term could yield deviations up to 1% per degree inclination angle. The gravitation-induced quantum phase as measured with OffSpec with an accuracy of 0.1% agrees with the theoretically expected results.

DOI
10.1103/physreva.89.063611

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With a neutron spin-echo reflectometer (OffSpec at ISIS, UK) it is possible to measure the gravitation-induced quantum phase difference between the two spin states of the neutron wave function in a magnetic field. In the small-angle approximation, this phase depends linearly on the inclination angle of the neutron beam with respect to the horizontal. This also holds for the Bonse-Hart interferometer used in the Colella-Overhauser-Werner experiments and should be taken into account. Neglecting this term could yield deviations up to 1% per degree inclination angle. The gravitation-induced quantum phase as measured with OffSpec with an accuracy of 0.1% agrees with the theoretically expected results.
One of the significant successes in the field of neutron interferometry has been the experimental observation of the phase shift of a neutron de Broglie wave due to the action of the Earth's gravitational field. Past experiments have clearly demonstrated the effect and verified the quantum-mechanical equivalence of gravitational and inertial masses to a precision of about 1%. In this experiment the gravitationally induced phase shift of the neutron is measured with a statistical uncertainty of order 1 part in 1000 in two different interferometers. Nearly harmonic pairs of neutron wavelengths are used to measure and compensate for effects due to the distortion of the interferometer as it is tilted about the incident beam direction. A discrepancy between the theoretically predicted and experimentally measured values of the phase shift due to gravity is observed at the 1% level. Extensions to the theoretical description of the shape of a neutron interferogram as a function of tilt in a gravitational field are discussed and compared with experiment.
Neutron resonance spin-echo (NRSE) phenomena are investigated experimentally and theoretically. In our experiments, spin precession produced in a classical manner and by neutron resonance is combined as two arms of a spin-echo machine. A magnetic-field scan in the classical SE coil reveals a spin-echo signal of the precession produced by the NRSE arm. The neutron spin-flip probability $\ensuremath{\rho}$ in the resonance coils turns out to be a key parameter of the NRSE arm. The limiting cases $\ensuremath{\rho}=0$ and $\ensuremath{\rho}=1$ lead, respectively, to Larmor precession with phase ${\ensuremath{\varphi}}_{1}$ in the static magnetic fields of the NR flippers or to NRSE precession with ${\ensuremath{\varphi}}_{2}.$ The case $0<\ensuremath{\rho}<1$ produces quantum interference resulting in additional echoes with phases ${\ensuremath{\varphi}}_{3}=({\ensuremath{\varphi}}_{1}+{\ensuremath{\varphi}}_{2})/2$ and ${\ensuremath{\varphi}}_{4}=\ifmmode\pm\else\textpm\fi{}({\ensuremath{\varphi}}_{1}\ensuremath{-}{\ensuremath{\varphi}}_{2})/2.$ The amplitude of each pattern depends on the spin-flip probability $\ensuremath{\rho}$ and the initial polarization. These experiments demonstrate explicitly the quantum-mechanical principle of linear spin state superposition of neutron particle waves, and the interference as a result of that.
Dynamical diffraction leads to an interesting, unavoidable set of interference effects for neutron interferometers. This experiment studies the interference signal from two and three successive Bragg diffractions in the Laue geometry. We find that intrinsic Bragg-plane misalignment in monolithic, "perfect" silicon neutron interferometers is relevant between successive diffracting crystals, as well as within the Borrmann fan for typical interferometer geometries. We show that the dynamical phase correction employed in the Colella, Overhauser, and Werner gravitationally induced quantum interference experiments is attenuated by slight, intrinsic misalignments between diffracting crystals, potentially explaining the long-standing 1% discrepancy between theory and experiment. This systematic may also impact precision measurements of the silicon structure factor, affecting previous and future measurements of the Debye-Waller factor and neutron-electron scattering length as well as potential fifth-force searches. For the interferometers used in this experiment, Bragg planes of different diffracting crystals were found to be misaligned by 10 to 40 nrad.
The interference effect between the neutron spinor components is investigated. It is shown that the diffusion of the neutron wave-packet under an unhomogeneous magnetic field is related to the phase shift angle between the two spinor components. We propose that this effect could be used to detect the phase-shift of a coherent neutron beam having passed through some medium. In the interference experiment based upon this principle one will not need to use Bragg reflection from crystal planes for splitting and recombining the beam, and the dimension of the phase shift region will be much longer than that of the usual Bonse-Kart type neutron interferometer.
The proper analysis of experiments to measure the quantum-mechanical phase shift due to potential gradients such as gravity across a perfect-silicon-crystal Mach–Zehnder interferometer for neutrons is complicated by the highly dispersive nature of the dynamical diffraction process describing the propagation of neutrons through a perfect crystal. Through dynamical diffraction, a coherent monochromatic incident beam of neutrons that does not exactly satisfy the Bragg condition is split into two currents within each crystal so that there are 16 possible coherent interfering trajectories by which the neutron can traverse the interferometer. In this work, previous calculations of the effects of dynamical diffraction on gravitationally induced phase-shift measurements are extended to include effects in all exit beams and internal effects within the subbeams for both symmetric and skew-symmetric interferometers. For the interferometers used in a recent experiment in which the gravitationally induced phase shift of the neutron is measured with a statistical uncertainty of the order of 1 part in 1000, it is found that these effects predict an increase of a few percent in the magnitude of the phase shift. Additionally, some consequences on the phase and contrast of restricting the beams within and after the interferometer are discussed. Agreement of this theory with experiment and the general applicability of the model is discussed.