Nondegenerate parametric conversion of light propagating in a nonlinear medium

Alexander A. Zabolotskii

Daniel F. Walls

A treatment of nonlinear optical phenomena beginning with a microscopically correct Hamiltonian containing the Bose operators of the light field and the Fermi operators for the optically active electrons in the medium is presented. Using techniques recently developed, a nonperturbative solution to the Schrodinger equation is possible. No linearization or semiclassical approximations are introduced. Two photon emission and absorption including both the degenerate and nondegenerate cases are considered. Parametric amplification and frequency conversion are investigated as examples of multiphoton processes. Atomic cooperation is shown to enhance the above phenomena. A formal treatment of a model illustrating super and subradiance is included.

В. Н. Горбачев, Andrew I. Trubilko, E. S. Yakovleva

The kinetic equation for the case of reflection of a broadband entangled light of a nondegenerate parametric source from a cavity is derived with the use of the technique of stochastic differential Ito equations. Statistical properties of the light reflected from a cavity with a nonlinear transparent medium, in which the process of special parametric interaction occurs, are considered on the basis of the obtained equation. Due to the integrals of motion, the entangled light, which is an EPR pair of continuous variables, can be amplified without destruction of the quantum correlation.

G.J. Papadopoulos

Izo I. Abram, E. Cohen

Starting with the canonical quantization procedure for the electromagnetic field inside an effective (linear or nonlinear) medium, we present a direct-space formulation of the theory of quantum optics. This approach does not use the conventional modal decomposition of the field, but relies on the electromagnetic momentum operator defined in terms of local electric- and magnetic-field operators. The momentum operator contains all the information on the spatial characteristics of the field, and can describe the translation of a short light pulse in a nonlinear medium, without a modal analysis of the pulse. Propagation is described through an operatorial wave equation that relates the temporal evolution of an electromagnetic pulse to its spatial progression. Through this equation, the direct-space approach to quantum optics can treat traveling-wave nonlinear-optical phenomena and, at the same time, account for their quantum statistics. The theory is applied to squeezed-light generation by the parametric down-conversion of a short laser pulse, as an illustration.

V. I. Bespalov