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Physical Review A

Phase shifts and wave-packet displacements in neutron interferometry and a nondispersive, nondefocusing phase shifter

Hartmut Lemmel, Apoorva G. Wagh

Published Sep 30, 2010• 11 citations
Publisher

Abstract

A phase shifter in neutron interferometry creates not only a phase shift but also a spatial displacement of the neutron wave packet, leading to a reduced interference contrast. This wave-packet displacement constitutes a major hindrance in measuring large phase shifts. Here we present a nondispersive configuration with two identical phase shifters placed on one path in successive gaps of a symmetric triple Laue (LLL) interferometer. As compared to a single phase shifter, the dual phase shifter generates double the phase shift, yet a net null displacement of the wave packet. The interferometer thus remains fully focused however large the phase shift or the incident wavelength spread, permitting a white incident neutron beam as in the case of a purely topological phase measurement. Misalignment angles of a monolithic nondispersive dual phase shifter are equal and opposite in the two gaps. Its phase therefore remains nondispersive over a much wider angular range and attains a minimum magnitude at the correct orientation, obviating the need to alternate the phase shifter between the two interferometer paths during its alignment. The setup is hence ideally suited for measuring neutron coherent scattering lengths to ultrahigh precision.

DOI
10.1103/physreva.82.033626

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A phase shifter in neutron interferometry creates not only a phase shift but also a spatial displacement of the neutron wave packet, leading to a reduced interference contrast. This wave-packet displacement constitutes a major hindrance in measuring large phase shifts. Here we present a nondispersive configuration with two identical phase shifters placed on one path in successive gaps of a symmetric triple Laue (LLL) interferometer. As compared to a single phase shifter, the dual phase shifter generates double the phase shift, yet a net null displacement of the wave packet. The interferometer thus remains fully focused however large the phase shift or the incident wavelength spread, permitting a white incident neutron beam as in the case of a purely topological phase measurement. Misalignment angles of a monolithic nondispersive dual phase shifter are equal and opposite in the two gaps. Its phase therefore remains nondispersive over a much wider angular range and attains a minimum magnitude at the correct orientation, obviating the need to alternate the phase shifter between the two interferometer paths during its alignment. The setup is hence ideally suited for measuring neutron coherent scattering lengths to ultrahigh precision.
The concept of dispersion cancellation has been established in light optics to improve the resolution of interferometric measurements on dispersive media. Odd order dispersion cancellation allows to measure phase shifts without defocusing the interferometer due to wave packet displacements, while even order dispersion cancellation allows to measure time lags without losing resolution due to wave packet spreading. We report that either type of dispersion cancellation can be realized very easily in a triple Laue interferometer. Such interferometers are Mach–Zehnder interferometers based on Bragg diffraction, and are commonly used for neutrons and x-rays. Although the first x-ray interferometer was built nearly five decades ago, the feature of dispersion cancellation hasnʼt been recognized so far because the concept was hardly known in the neutron and x-ray community. However, it explains right away the surprising decoupling of phase shift and spatial displacement that we have discovered recently in neutron interferometry (Lemmel and Wagh 2010 Phys. Rev. A 82 033626). Furthermore, this article might inspire the light optics community to consider whether a triple Laue interferometer for laser light would be useful and feasible. We explain how dispersion cancellation works in neutron interferometry, and we describe the setup rigorously by solving the Schrodinger equation and by calculating the path integral. We point out, that the latter has to be evaluated with special care since in our setup the beam trajectory moves with respect to the crystal lattice of the interferometer.
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.
The phenomenon of interference plays a crucial role in the field of precision measurement science. Wave-particle duality has expanded the well-known interference effects of electromagnetic waves to massive particles. The majority of the wave-particle interference experiments require a near monochromatic beam which limits its applications due to the resulting low intensity. Here we demonstrate white beam interference in the far-field regime using a two-phase-grating neutron interferometer and its application to phase-contrast imaging. The functionality of this interferometer is based on the universal moir\'e effect that allows us to improve upon the standard Lau setup. Interference fringes were observed with monochromatic and polychromatic neutron beams for both continuous and pulsed beams. Far-field neutron interferometry allows for the full utilization of intense neutron sources for precision measurements of gradient fields. It also overcomes the alignment, stability, and fabrication challenges associated with the more familiar perfect-crystal neutron interferometer, as well as avoids the loss of intensity due to the absorption analyzer grating requirement in Talbot-Lau interferometer.
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.
The coherence length of a neutron wave packet depends on the spectral width of the distribution of wave vectors that make up the packet. The coherent overlap of the wave packets traversing the two beam paths in a perfect-silicon-crystal neutron interferometer (NI) is altered by placing a material with a neutron-nuclear optical potential in one of the beam paths in the NI. If the optical potential is positive, it causes a delay of the wave packet and a loss of fringe visibility. By use of an analyzer crystal, we narrow the spectral distribution after the mixing and interference has occurred in the last crystal slab of the NI. This increases the coherence length and restores some of the fringe visibility.