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

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.

arXiv comment16 pages, 3 figures, 59 references, with minor modifications and corrected typos (especially in Sec. VI), following the published version

References in corpus (15)

• Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip
• Cavity QED with a Bose-Einstein condensate
• Cavity Nonlinear Optics at Low Photon Numbers from Collective Atomic Motion
• Dynamical Coupling between a Bose-Einstein Condensate and a Cavity Optical Lattice
• Ensemble-induced strong light-matter coupling of a single quantum emitter
• Nonlinear dynamics of a cigar-shaped Bose-Einstein condensate coupled with a single cavity mode
• Controllability of optical bistability, cooling and entanglement in hybrid cavity optomechanical systems by nonlinear atom-atom interaction
• Optical nonlinear dynamics with cold atoms in a cavity
• Spontaneous dressed-state polarization in the strong driving regime of cavity QED
• Optical bistability in strong-coupling cavity QED with a few atoms
• Optical bistability at low light level due to collective atomic recoil
• Optical bistability and nonlinear dynamics by saturation of cold Yb atoms in a cavity
• Emission spectra and intrinsic optical bistability in a two-level medium
• Adiabatic elimination for ensembles of emitters in cavities with dissipative couplings
• Atom-field correlations in the weak-excitation limit of absorptive optical bistability