Quantum Statistical Properties of the Codirectional Kerr Nonlinear Coupler in Terms of su 2 $\left (2\right ) $ Lie Group in Interaction with a Two-level Atom

Abstract

The problem of the codirectional Kerr coupler has been considered several times from different point of view. In the present paper we introduce the interaction between a two-level atom and the codirectional Kerr nonlinear coupler in terms of su(2) Lie algebra. Under certain conditions we have adjusted the Kerr coupler and consequently we have managed to handle the problem. The wave function is obtained by using the evolution operator where the Heisnberg equation of motion is invoked to get the constants of the motion. We note that the Kerr parameter χ as well as the quantum number j plays the role of controlling the atomic inversion behavior. Also the maximum entanglement occurs after a short period of time when χ = 0. On the other hand for the entropy and the variance squeezing we observe that there is exchange between the quadrature variances. Furthermore, the variation in the quantum number j as well as in the parameter χ leads to increase or decrease in the number of fluctuations. Finally we examined the second order correlation function where classical and nonclassical phenomena are observed.

A nonlinear interaction between SU(1,1) quantum system and a three-level atom in different configurations with damping term

“…The influence of Kerr medium on the Casimir operators interacting with Su(2) group has been studied [26], where the degree of entanglement is examined through the linear entropy, also, different types of squeezing have been studied. The effect of the classical field related to SU(1,1) and the damping terms on Su(1,1) system interacting with a two-level atom has been studied [23].…”