Mean-field optical bistability of two-level atoms in structured reservoirs

TL;DR

This paper investigates optical bistability in a system of two-level atoms interacting with structured reservoirs, deriving a mean-field model that reveals how reservoir structure influences bistable behavior.

Contribution

It introduces a novel mean-field approach incorporating reservoir structure effects into the optical bistability of two-level atoms.

Findings

Bistability occurs in both amplitude and phase of the output field.

Structured reservoirs like Lorentzian and photonic band-gap significantly affect bistability.

The model predicts new reservoir-induced terms in the master equation.

Abstract

We consider N driven two-level atoms interacting with a structured reservoir. By dressing the collective operators within a semiclassical approach, we derive a master equation and a mean-field single particle effective Hamiltonian. This Hamiltonian describes the optical bistability phenomenon occurring in the relation between an input electromagnetic field and the effective output generated by the N atoms. The dissipative part of the master equation and the effective single-particle Hamiltonian contain new terms due the reservoir structure of modes. In plotting the output field amplitude and phase, for a structured reservoir, as function of the input amplitude, one verifies the bistable behavior in both. We illustrate our results for two structured reservoirs: one having a Lorentzian shape for the distribution of modes, and the second is modeled as a photonic band-gap structure.