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Physical Review Letters

Neutron Phase Shift in a Rotating Two-Crystal Interferometer

D. K. Atwood, Michael Horne, C. G. Shull, John Arthur

Published May 7, 1984• 73 citations
Publisher

Abstract

The phase shift introduced by rotational motion of a two-crystal neutron interferometer has been measured and found to agree with prediction within 0.4%. This agreement is obtained without making the in-crystal phase corrections employed in a recent study of a linearly accelerated three-crystal interferometer.
DOI
10.1103/physrevlett.52.1673

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Neutron interferometry performed in a noninertial frame is essentially influenced by dynamical diffraction effects occurring in the interferometer crystal which hitherto have not been taken into account. We have developed a corresponding theory from which a corrected phase shift is obtained which applies likewise to interferometry performed under the influence of gravity or on an accelerated neutron interferometer. The theory also predicts fading of interference contrast with increasing acceleration as was observed in the Colella-Overhauser-Werner gravity experiments but could not be explained unambiguously.
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.
Neutron interferometry has been performed on an accelerated interferometer under conditions where gravitational effects on the interfering beams very nearly compensate each other. The observed neutron phase shift is found to be in excellent agreement with that calculated from Schr\"odinger's equation transformed to the accelerated frame where it is found essential to include the spherical wave aspect. The present experiment thus verifies the validity of the classical transformation laws for noninertial frames also in the quantum limit.
Using a transit-time technique, the phase difference is calculated for a neutron traversing an interferometer accelerating in flat space-time. The result differs from that calculated in a gravitational setting by an amount five orders of magnitude smaller than that resolvable by current experiment. However, when identical slabs of matter are inserted into separate arms of an accelerating Mach-Zehnder interferometer a phase shift is calculated that is only two orders of magnitude smaller than that currently resolvable. This effect does not depend on dispersion in the material. Verification of this prediction, although beyond the resolution of current experiments, may be possible.
We have measured the phase shift induced by rotation of an atom interferometer at rates of $\ensuremath{-}2$ to +2+2+2 earth rates and obtained 11%1 agreement with the predicted Sagnac phase shift for atomic matter waves. The rotational rms noise of our interferometer was 424242 milliearth rates for 111 sec of integration time, within 99%9 of shot noise. The high sensitivity and agreement of predicted and measured behavior suggest useful future scientific applications of atom interferometers as inertial sensors.