Cavity elimination in cavity-QED: a self-consistent input-output approach

TL;DR

This paper presents a self-consistent method to eliminate cavity degrees of freedom in cavity-QED systems, accurately capturing non-Markovian effects and simplifying analysis beyond low-power regimes.

Contribution

The authors introduce a novel self-consistent approach for cavity elimination in CQED, enabling effective modeling of non-Markovian dynamics and steady states in complex regimes.

Findings

Accurately retrieves effective Purcell-enhanced emission rates.

Captures non-Markovian features with an effective Lindblad equation.

Shows excellent agreement with full CQED simulations in various regimes.

Abstract

Simplifying composite open quantum systems through model reduction is central to enable their analytical and numerical understanding. In this work, we introduce a self-consistent approach to eliminate the cavity degrees of freedom of cavity quantum electrodynamics (CQED) devices in the non-adiabatic regime, where the cavity memory time is comparable with the timescales of the atom dynamics. To do so, we consider a CQED system consisting of a two-level atom coupled to a single-mode cavity, both subsystems interacting with the environment through an arbitrary number of ports, within the input-output formalism. A self-consistency equation is derived for the reduced atom dynamics. This allows retrieving an exact expression for the effective Purcell-enhanced emission rate and, under reasonable approximations, a set of self-consistent dynamical equations and input-output relations for the effective two level atom. The resulting reduced model captures non-Markovian features, characterized through an effective Lindblad equation exhibiting two decoherence rates, a positive and a negative one. In the continuous-wave excitation regime, we benchmark our approach by computing effective steady states and output flux expressions beyond the low-power excitation regime, for which a semi-classical treatment is usually applied. We also compute two-time correlations and spectral densities, showing an excellent agreement with full cavity quantum electrodynamics simulations, except in the strong-coupling, high-excitation regime. Our results provide a practical framework for reducing the size of CQED models, which could be generalized to more complex atom and cavity configurations.