Collective atomic correlations in absorptive optical bistability without adiabatic elimination: exemplifying nonclassicality from a linearized treatment of fluctuations

TL;DR

This paper analyzes collective atomic correlations in absorptive optical bistability using a linearized approach without adiabatic elimination, revealing nonclassical features and differences from classical predictions.

Contribution

It introduces a linearized Fokker-Planck method in the positive P representation to study atomic correlations without adiabatic elimination, covering various cavity regimes.

Findings

Demonstrates nonclassicality in atomic correlations

Provides analytical expressions for stable states far from bistability turning points

Highlights differences between classical and quantum predictions in optical bistability

Abstract

We determine the incoherent spectrum, squeezing properties and second-order correlation function of the collective atomic degrees of freedom in absorptive optical bistability. This is accomplished via a linearized Fokker-Planck equation in the positive P representation, guided by the analysis of [H. J. Carmichael, Phys. Rev. A 33, 3262 (1986)] which does not resort to adiabatic elimination. We focus on the regimes of weak and strong intracavity excitation, addressing the good-cavity and bad-cavity limits as well as the limit of collective strong coupling. Adiabatic elimination of the intracavity field sustained by an auxiliary resonator coupled to the ensemble is used to probe the atomic correlations via the formation of a collective emission channel. We compare to the corresponding expressions for the forwards-scattered light with reference to experimental results, discussing key differences between the lower and upper branch of the steady-state semiclassical bistability curve. Our analysis is carried out around the stable states situated far away from the turning points, where analytical expressions can be obtained self-consistently, demonstrating a clear departure from classical behavior.