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 βs. The equation shows hysteresis and bistability among the three quantities x, y, and βs 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.