What is the spectral density of the reservoir for a lossy quantized cavity?

TL;DR

This paper derives the correct frequency-dependent spectral density of the reservoir for a lossy cavity, revealing gauge-dependent scaling and spatial corrections, crucial for understanding broadband strong coupling in quantum systems.

Contribution

It establishes the quantum form of the cavity-reservoir interaction for 3D geometries, extending beyond simple 1D models, with implications for broadband strong coupling.

Findings

Identifies the correct local spectral density form for lossy cavities.

Reveals gauge-dependent $requency^{ ext{±}1}$ scaling in the spectral density.

Shows significant impact on broadband strong coupling phenomena.

Abstract

By considering a two-level system weakly coupled to a single lossy three-dimensional cavity mode, and using a quasinormal mode expansion for the photonic medium, we show that the frequency-dependence of the quantum coupling interaction between the cavity and its photonic reservoir can not be simply constructed to be independent of the cavity contents. For the single quantum dipole case, we identify the correct form of the local spectral density, revealing a surprising gauge-dependent $\sim \omega^{\pm 1} prefactor scaling, as well as a spatially-dependent correction. We thus establish the correct quantum form for the cavity-reservoir interaction, which so far has only been worked out rigorously for simple 1D geometries, and show its significant impact on broadband strong coupling.