A master equation for a two-sided optical cavity

TL;DR

This paper introduces a master equation for two-sided optical cavities that accurately models photon emission and dynamics, aligning with classical and experimental results, and enabling analysis of complex cavity networks.

Contribution

It presents a novel master equation for two-sided optical cavities using traveling-wave photon modes, matching classical emission rates and cavity dynamics.

Findings

Predicts stationary photon emission rates consistent with classical theories

Accurately models time evolution of cavity photon number

Applicable to analyzing coherent cavity-fiber networks

Abstract

Quantum optical systems, like trapped ions, are routinely described by master equations. The purpose of this paper is to introduce a master equation for two-sided optical cavities with spontaneous photon emission. To do so, we use the same notion of photons as in linear optics scattering theory and consider a continuum of traveling-wave cavity photon modes. Our model predicts the same stationary state photon emission rates for the different sides of a laser-driven optical cavity as classical theories. Moreover, it predicts the same time evolution of the total cavity photon number as the standard standing-wave description in experiments with resonant and near-resonant laser driving. The proposed resonator Hamiltonian can be used, for example, to analyse coherent cavity-fiber networks [Kyoseva et al., New J. Phys. 14, 023023 (2012)].