Justification of the symmetric damping model of the dynamical Casimir effect in a cavity with a semiconductor mirror

TL;DR

This paper provides a microscopic justification for the symmetric damping model used in describing the dynamical Casimir effect in cavities with semiconductor mirrors, linking it to fundamental quantum oscillator-bath interactions.

Contribution

It derives the symmetric damping model from first principles, showing its validity for quantum oscillators coupled to a bath with time-dependent interactions in the context of the dynamical Casimir effect.

Findings

Most general bilinear coupling yields equal friction coefficients for both quadratures.

Coupling proportional to a single time-dependent function simplifies the model.

Rotating wave approximation leads to the minimum noise damping model.

Abstract

A "microscopic" justification of the "symmetric damping" model of a quantum oscillator with time-dependent frequency and time-dependent damping is given. This model is used to predict results of experiments on simulating the dynamical Casimir effect in a cavity with a photo-excited semiconductor mirror. It is shown that the most general bilinear time-dependent coupling of a selected oscillator (field mode) to a bath of harmonic oscillators results in two equal friction coefficients for the both quadratures, provided all the coupling coefficients are proportional to a single arbitrary function of time whose duration is much shorter than the periods of all oscillators. The choice of coupling in the rotating wave approximation form leads to the "mimimum noise" model of the quantum damped oscillator, introduced earlier in a pure phenomenological way.