Gravitational distortion on photon state at the vicinity of the Earth

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 Schrödinger 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.

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Cited by in corpus (7)

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• Gravitational redshift induces quantum interference
• Introduction to gravitational redshift of quantum photons propagating in curved spacetime
• Astrophysically sourced quantum coherent photonic signals
• Trajectory of a massive localised wave function in a curved spacetime geometry
• Limits to the validity of gravitational redshift as a quantum-optical multimode mixer