Dynamics of an adiabatically effective two-level atom interacting with a star-like system

摘要

Using the adiabatic elimination we have managed to deal with the problem of the interaction between a single three-level atom and $N$ two-level non-interacting atoms. The adiabatic elimination is used to obtain the effective Hamiltonian that describes a nonlinear interaction in the form of a Stark-like shift between a two-level atom and su$(2)N$ two-level atoms. The time evolution operator is calculated in the presence of a Stark-like shift and the detuning parameters. The time-dependent wave function is determined through the evolution operator and consequently the density matrix is obtained. We adopt an initial wave function for the $N$ two-level atoms that takes into account the structural degeneracies occurring in the system and thus generalize the atomic coherent state. The phenomenon of the collapses and revivals of the atomic population inversion for different values of the Stark shift parameters is considered. The degree of entanglement is also investigated and discussed, where the linear entropy is used. Finally we examine the variance squeezing for the system for different values of the involved parameters. It is shown that different values of the Stark shift parameters lead to different observations of the squeezing in the quadratures.