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 suleft (2right ) 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.
Highlights
It is well known that there are three important processes in nonlinear optics, namely, up-conversion, down-conversion and Kerr-like process
In the previous sections of the present communication we have considered the problem of the interaction between a two-level atom and the co-directional Kerr nonlinear coupler in terms of su(2) Lie algebra
The wave function is obtained via the evolution operator and we managed to construct the time-dependent density operator
Summary
It is well known that there are three important processes in nonlinear optics, namely, up-conversion, down-conversion and Kerr-like process. The progress in the optics communication and quantum computing networks requires data transmission [2,3,4], and this simple device has potential applications in all-optical switching [5,6,7] It provides electromagnetic fields with an exceptionally wide range of nonclassical effects. Most importantly this device has been implemented [8,9,10,11,12,13,14] and applied in many experimental approaches, e.g. in picosecond switching induced by saturable absorption [15], optical multi-mode interference devices based on self-imaging [16], and photonic bandgap structures in planar nonlinear waveguides [17].
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