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

TL;DR

This paper investigates the relationship between spin squeezing and entanglement in a nonlinear Tavis-Cummings model with a binomial cavity field, revealing how nonlinearities and off-resonant interactions influence entanglement dynamics and quantum state properties.

Contribution

It demonstrates how spin squeezing can serve as an indicator of entanglement in a nonlinear cavity system and explores the effects of nonlinear media strength on entanglement and quantum state formation.

Findings

Spin squeezing indicates entanglement in tripartite quantum states.

Large off-resonance interactions enhance the insight into entanglement via spin squeezing.

Weak nonlinear media facilitate clearer entanglement dynamics and Schrödinger cat state formation.

Abstract

We show that spin squeezing implies entanglement for quantum tripartite-state, where the subsystem of the bipartite-state is identical. We study the relation between spin squeezing parameters and entanglement through the quantum entropy of a system starts initially in a pure state when the cavity is binomial. We show that spin squeezing can be a convenient tool to give some insight into the subsystems entanglement dynamics when the bipartite subsystem interacts simultaneously with the cavity field subsystem, specially when the interaction occurs off-resonantly without and with a nonlinear medium contained in the cavity field subsystem. We illustrate that, in case of large off-resonance interaction, spin squeezing clarifies the properties of entanglement almost with full success. However, it is not a general rule when the cavity is assumed to be filled with a non-linear medium. In this case, we illustrate that the insight into entanglement dynamics becomes more clearly in case of a weak nonlinear medium than in strong nonlinear medium. In parallel, the role of the phase space distribution in quantifying entanglement is also studied. The numerical results of Husimi $Q$-function show that the integer strength of the nonlinear medium produces Schr\"{o}dinger cat states which is necessary for quantum entanglement.