Gravitational effects on Hong-Ou-Mandel interference in terrestrial laboratory

TL;DR

This paper explores how Earth's gravity influences Hong-Ou-Mandel interference, analyzing relativistic and wave effects, and proposes using HOM pattern differences to detect gravitational impacts on quantum systems.

Contribution

It provides a detailed theoretical analysis of gravitational effects on HOM interference, including frame dragging and redshift, and suggests experimental methods to detect these effects.

Findings

Gravity affects both phase shift and time delay in HOM experiments.

Amplification of gravitational effects is possible with increased photon loops.

Differences in HOM patterns can serve as probes for gravitational influences on quantum states.

Abstract

In this study, we investigate how Earth's gravitational field affects Hong-Ou-Mandel (HOM) interference experiments conducted in a terrestrial laboratory. To second order, we calculate the relativistic time delay from the null geodesic equation (particle perspective), while the phase shift and the associated effective time delay are derived from the Klein-Gordon equation (wave perspective). Since gravity influences both the temporal and spatial parts of the phase shift, these two time delays differ and lead to different coincidence probabilities. The previous HOM experiment conducted on a rotating platform suggests that the wave perspective can explain the experimental results. We further explore the frame dragging and redshift effects in an arbitrarily oriented rectangular interferometer under two distinct scenarios with different photon paths, measuring one effect in each scenario. We find that both effects can be amplified by increasing the number of light loops. Additionally, we emphasize that the next-to-leading order Sagnac effect, arising from gravitational acceleration, is comparable to the Thomas precession, the geodetic effect, and the Lense-Thirring effect. To detect the leading order Sagnac effect and the redshift effect caused by gravitational acceleration, we estimate the number of loops that photons should travel in the interferometer. Furthermore, we propose that the difference between two HOM patterns can be used as a probe to detect gravitational effects on quantum systems.