Generalized dispersion relations and optical bistability in squeezed vacua

Abstract

We derive c-number Bloch-Maxwell (B-M) type equations from a quantum theory for 2-level atoms occupying a macroscopic slab-like region V of width L stimulated by a coherent-state electromagnetic field of radial frequency approximately ega plus a broad-band correlated squeezed vacuum field with carrier frequency approximately ega p. The squeezed vacuum field is in principle of arbitrary 3-dimensional geometry including geometries created by an optical parametric oscillator. The c-number spatially dependent B-M equations are solved self-consistently and 'exactly' in terms of a nonlinear dispersive refractive index m(approximately ega) while the slab V acts, also self-consistently, as a natural Fabry-Perot cavity of finite spacing L. Very preliminary results for optical bistability in the squeezed vacuum and more exact results for anomalous dispersion and absorption in the squeezed vacuum in linearized approximation are reported. Finally we compute the effect of the dielectric on the free-field modes of the squeezed vacuum.