Generalised Dispersion Relations and Optical Bistability in Squeezed Vacua

Abstract

We have derived¹ c-number Bloch-Maxwell type equations from a quantum theory for 2-level atoms occupying a macroscopic region of space stimulated by a coherent-state e.m. field of radial frequency  ω plus a broad-band correlated squeezed vacuum field of arbitrary 3-dimensional geometry with a carrier frequency ω _p , including geometries which could be created by an optical parametric oscillator. Expectation values of Heisenberg’s equations with a matter-field decorrelation followed by an ensemble average over atom sites x _i yield, in a frame rotating at the eqns. (1), (2). The sites x _i occupy a slab-like region V which ultimately forms a Fabry-Perot Cavity: there is no intermolecular correlation (the dielectric in V is ‘smooth’).