Steady states of $\Lambda$-type three-level systems excited by quantum light in lossy cavities

TL;DR

This paper explores how lossy cavities influence the steady states of a three-level quantum system driven by quantum light, revealing controllable electronic occupations dependent on loss rates and initial quantum states.

Contribution

It provides analytical and numerical analysis of steady states in lossy cavities for $ ext{Lambda}$-type systems, highlighting the role of cavity losses in state control.

Findings

Cavity losses induce unique steady states in the system.

Steady states depend on loss rate and initial quantum field statistics.

Analytical expressions for steady states are derived.

Abstract

The interaction between quantum light and matter is being intensively studied for systems that are enclosed in high-$Q$ cavities which strongly enhance the light-matter coupling. However, for many applications, cavities with lower $Q$-factors are preferred due to the increased spectral width of the cavity mode. Here, we investigate the interaction between quantum light and matter represented by a $\Lambda$-type three-level system in lossy cavities, assuming that cavity losses are the dominant loss mechanism. We demonstrate that cavity losses lead to non-trivial steady states of the electronic occupations that can be controlled by the loss rate and the initial statistics of the quantum fields. The mechanism of formation of such steady states can be understood on the basis of the equations of motion. Analytical expressions for steady states and their numerical simulations are presented and discussed.