Limits to the validity of gravitational redshift as a quantum-optical multimode mixer

TL;DR

This paper critically examines the limitations of a quantum optical model describing gravitational redshift effects on photons in curved spacetime, highlighting the conditions under which the model remains valid.

Contribution

It identifies the first-order validity of the model for small redshift and proposes a necessary condition involving auxiliary modes for accurate transformation representation.

Findings

Model is valid only to first order for small redshift

A necessary condition involves using at least as many auxiliary modes as initial modes

Implications for quantum optics and photonics in curved spacetime

Abstract

We analyze the domain of validity of a quantum optical model that describes the effects of gravitational redshift on the quantum state of photons that propagate in curved spacetime. This model assumes that the modes defining the initial state of the photon are mixed with an auxiliary environment mode via an effective multimode mixer. We find that the model, as proposed, is consistent only to first order for small redshift, where the range of validity is conditional not only to the gravitational parameters, but also to those that define the photonic modes. We identify the problem and provide a partial solution in terms of a necessary condition on the transformation matrix representing the process, which requires the use of a number of auxiliary modes that is at least equal to the number of modes that define the photonic state. We conclude by discussing implications for theoretical quantum optics and photonics in curved spacetime, as well as for the development of quantum technologies.