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Physica B Condensed Matter

Advances in the measurement of gravity-induced quantum phase shifts

Kenneth C. Littrell, Brendan E. Allman, S. A. Werner

Published Dec 1, 1997• 2 citations
Publisher
DOI
10.1016/s0921-4526(97)00832-6

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Gravity curves space and time. This can lead to proper time differences between freely falling, nonlocal trajectories. A spatial superposition of a massive particle is predicted to be sensitive to this effect. We measure the gravitational phase shift induced in a matter-wave interferometer by a kilogram-scale source mass close to one of the wave packets. Deflections of each interferometer arm due to the source mass are independently measured. The phase shift deviates from the deflection-induced phase contribution, as predicted by quantum mechanics. In addition, the observed scaling of the phase shift is consistent with Heisenberg’s error-disturbance relation. These results show that gravity creates Aharonov-Bohm phase shifts analogous to those produced by electromagnetic interactions.
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 quest for a quantum theory of gravity remains a central challenge in modern physics, driven by the goal of unifying general relativity and quantum mechanics. Direct experimental access to quantum gravitational effects is notoriously difficult due to the inaccessibility of the Planck scale. Recent proposals, however, suggest that gravitationally induced quantum entanglement between two massive particles, realized through advanced quantum interferometric techniques, could provide empirical evidence for the quantum nature of gravity. We demonstrate that the geometrical configuration of an interferometer plays a decisive role in entanglement generation. Our analysis reveals that geometric optimization can substantially enhance the gravitationally induced phase shift, thereby improving the prospects for experimental detection of gravity-mediated entanglement. Moreover, we show that standard approximations employed in prior proposals may severely limit predictive accuracy and compromise experimental feasibility.