Entanglement of Degenerate and Nondegenerate Parametric Amplifiers Interacting with a Single Two-Level Atom

Abstract

We consider the time-dependent interaction between a single two-level atom and a combination of degenerate and nondegenerate parametric amplifiers. Under certain canonical transforms, we manage to remove the nondegenerate term from the Hamiltonian. Using the definition of the su(1, 1) generators, the problem is treated as an interaction between two systems governed by the su(2) and su(1, 1) algebras. Consequently, we obtain the time-dependent wave function. Our discussion of the atomicpopulation inversion shows that the Bargmann index r and the Barut–Girardello state parameter χ taken as the initial state play a strong role of controlling the phenomena of revivals and collapses. The system is sensitive to the variation in the atomic-state parameter – atomic angle θ, which is controlling the behavior of both the variance squeezing and the entropy squeezing. We demonstrate that the atomic angle θ and the parameter χ are effective parameters determining the linear entropy.