Gravitational distortion on photon state at the vicinity of the Earth

TL;DR

This paper investigates how Earth's gravitational field distorts photon wave functions during propagation, deriving a measurable phase shift caused by spacetime curvature that impacts satellite communication.

Contribution

It introduces a novel method to quantify gravitational effects on photon states using Fermi coordinates and Schrödinger equation mapping, applicable to Earth-based satellite links.

Findings

Extra phase shift due to Earth's gravity is calculable.

Phase shift is measurable with current technology.

Implications for quantum communication accuracy.

Abstract

As a photon propagates along a null geodesic, the space-time curvature around the geodesic distorts its wave function. We utilise the Fermi coordinates adapted to a general null geodesic, and derive the equation for interaction between the Riemann tensor and the photon wave function. The equation is solved by being mapped to a time-dependent Schr\"odinger equation in $(2+1)$ dimensions. The results show that as a Gaussian time-bin wavepacket with a narrow bandwidth travels over a null geodesic, it gains an extra phase that is a function of the Riemann tensor evaluated and integrated over the propagation trajectory. This extra phase is calculated for communication between satellites around the Earth, and is shown to be measurable by current technology.