Generalized Dispersion Relations for Dielectrics in Squeezed Vacua

Abstract

Substantially squeezed radiation fields are now available in a number of laboratories, and this offers an opportunity for studying the response of various physical systems to such nonclassical states of the electromagnetic field¹. In this paper our main interest is to examine the effect of a broad-band squeezed vacuum field on the refractive index of a dielectric made up of 2-level atoms. In principle we consider two aspects of the problem: one is the effect of the squeezed vacuum on a field transmitted through the dielectric, and the refractive index, which we call m(w) in this paper, determines the wave number of the transmitting field with respect to its wave number k ₀ = ωc ⁻¹ in free space; the other is the wave number developing in the modes of the squeezed vacuum field in the presence of the dielectric, namely the effect of the dielectric on the squeezed vacuum. For simplicity these two calculations are performed separately as first preliminary investigations of these two problems and pressure on space means that we can do little more than state the existence of the calculations on the second problem in this paper. In due course we hope to combine both aspects in a connected theory. The geometry of the dielectric is important and we choose this to be a slab of finite width $K \gg K_0^{ - 1}$ which then constitutes a Fabry-Perot cavity.