Temporal factorization of a non-stationary electromagnetic cavity field

TL;DR

This paper demonstrates a method to factorize the time dependence of a non-stationary electromagnetic cavity field, revealing how photon production is limited by an effective temperature related to mirror velocity.

Contribution

It introduces a novel temporal factorization technique for the Hamiltonian of a non-stationary cavity, linking photon generation to an effective temperature and connecting to quantum thermodynamics concepts.

Findings

Photon production is proportional to a velocity-dependent effective temperature.

The factorization simplifies the analysis of non-stationary cavity fields.

Photon generation is limited even at ultra-relativistic mirror velocities.

Abstract

When an electromagnetic field is confined in a cavity of variable length, real photons may be generated from vacuum fluctuations due to highly nonadiabatic boundary conditions. The corresponding effective Hamiltonian is time-dependent and contains infinite intermode interactions. Considering one of the cavity mirrors fixed and the other describing uniform motion (zero acceleration), we show that it is possible to factorize the entire temporal dependency and write its formal solution, i.e., the Hamiltonian becomes a product of a time-dependent function and a time-independent operator. With this factorization, we prove in detail that the photon production is proportional to the Planck factor involving a velocity-dependent effective temperature. This temperature significantly limits photon generation even for ultra-relativistic motion. The time-dependent unitary transformations we introduce to obtain temporal factorization help establishing connections with the shortcuts to adiabaticity of quantum thermodynamics and with the quantum Arnold transformation.