Maxwell boundary conditions imply non-Lindblad master equation

TL;DR

This paper derives a non-Lindblad master equation from Maxwell boundary conditions for cavity systems with matter, showing it aligns better with classical electrodynamics than the traditional Lindblad form, especially in ultra-strong coupling regimes.

Contribution

It introduces a non-Lindblad master equation derived directly from Maxwell boundary conditions, improving the consistency with classical electrodynamics in ultra-strong light-matter interactions.

Findings

Non-Lindblad master equation better matches Maxwell boundary condition spectra.

Lindblad approximation can be transformed from the non-Lindblad form via rotating-wave approximation.

Discrepancies between equations are significant in ultra-strong coupling regimes.

Abstract

From the Hamiltonian connecting the inside and outside of an Fabry-Perot cavity, which is derived from the Maxwell boundary conditions at a mirror of the cavity, a master equation of a non-Lindblad form is derived when the cavity embeds matters, although we can transform it to the Lindblad form by performing the rotating-wave approximation to the connecting Hamiltonian. We calculate absorption spectra by these Lindblad and non-Lindblad master equations and also by the Maxwell boundary conditions in the framework of the classical electrodynamics, which we consider the most reliable approach. We found that, compared to the Lindblad master equation, the absorption spectra by the non-Lindblad one agree better with those by the Maxwell boundary conditions. Although the discrepancy is highlighted only in the ultra-strong light-matter interaction regime with a relatively large broadening, the master equation of the non-Lindblad form is preferable rather than of the Lindblad one for pursuing the consistency with the classical electrodynamics.