Optical Bistability Based Upon Atomic Correlation in a Small Volume

Abstract

A model for optical bistability which emphasizes the effects of atomic pair correlation in a small volume is presented. A unitary transformation is introduced to remove the explicit time dependence of the original Hamiltonian and an ensemble representation for the system is imposed by introducing a ficticious, (“spin”) temperature in the rotating frame. The ensemble averages have the effect, in the results, of breaking the J²-symmetry intrinsic to the Hamiltonian. Adiabatic elimination of the field variables in the mean-field limit leads to a mean-field, atomic-level Stark-shift-dependent interatomic interaction. We use this retarded dipole-dipole interaction in a small volume, to de-rive the properties of the quasi-thermodynamic ensemble representing the system in the rotating frame, and obtain the equation of state relating the externally-applied field y to the internal field x and the inverse of the effective temperature β_s. The equation shows hysteresis and bistability among the three quantities x, y, and β_s for suitable values of the parameters in the model. Stability conditions in the hysteresis zone in the limit of a single radiation field mode are analyzed and the optical spectrum is derived. The results predict intrinsic mirrorless optical bistability in a small volume.