Abstract

The Jaynes-Cummings model¹ modified by the introduction of a parametric interaction, and its completely classical version are considered. The Hamiltonian is: where is the Jaynes-Cummings Hamiltonian, and is the coupling to the second harmonic light. In Eqs. (2) and (3), w is the atomic and laser frequency, k is the atom-field coupling constant, and g is proportional to the nonlinear susceptibility and classical pump amplitude. In the quantum model, the other quantities are field and atom operators, while in the classical version they are physical variables, where dagger means complex conjugation. The dynamics are described quantum mechanically by the Schrodinger equation, and classically by the Poisson bracket formalism.

© 1994 IEEE