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

physical review. a/physical review, a

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