Entanglement Dynamics and Spin Squeezing of The non-linear Tavis-Cummings model mediated by a Nonlinear Binomial Field

摘要

We show that spin squeezing implies entanglement for quantumtripartite-state, where the subsystem of the bipartite-state is identical. Westudy the relation between spin squeezing parameters and entanglement throughthe quantum entropy of a system starts initially in a pure state when thecavity is binomial. We show that spin squeezing can be a convenient tool togive some insight into the subsystems entanglement dynamics when the bipartitesubsystem interacts simultaneously with the cavity field subsystem, speciallywhen the interaction occurs off-resonantly without and with a nonlinear mediumcontained in the cavity field subsystem. We illustrate that, in case of largeoff-resonance interaction, spin squeezing clarifies the properties ofentanglement almost with full success. However, it is not a general rule whenthe cavity is assumed to be filled with a non-linear medium. In this case, weillustrate that the insight into entanglement dynamics becomes more clearly incase of a weak nonlinear medium than in strong nonlinear medium. In parallel,the role of the phase space distribution in quantifying entanglement is alsostudied. The numerical results of Husimi $Q$-function show that the integerstrength of the nonlinear medium produces Schr\"{o}dinger cat states which isnecessary for quantum entanglement.