Atom–photon, two-mode entanglement and two-mode squeezing in the presence of cross-Kerr nonlinearity

The interaction of two quantized fields and three-level quantum system in a Λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Lambda $$\end{document}-type configuration is investigated in the presence of cross-Kerr nonlinearity. We consider three models of coupling for the atom–photon interaction. First, we study the dynamical behavior of the atom–photon entanglement and show that increasing the cross-Kerr nonlinearity results in different behaviors in three considered models. Moreover, it is demonstrated that the two quantized modes can be entangled, on the other hand, by applying a classical driving field to the lower levels. Increasing the classical driving field destroys the long time atom–photon entanglement. Our results show that an oscillatory two-mode squeezing can be generated in the absence of a driving classical field and the cross-Kerr nonlinearity.