Quantum-classical correspondence in resonant and nonresonant Rabi-Stark model

TL;DR

This paper investigates the quantum-classical correspondence in the Rabi-Stark model using mean field theory, revealing conditions under which semiclassical dynamics align with quantum entanglement measures, especially in the resonant case with nonlinear Stark coupling.

Contribution

It demonstrates that quantum-classical correspondence can be achieved in the resonant Rabi-Stark model with large atom-light ratios and specific Stark couplings, even with limited photon numbers.

Findings

Quantum-classical correspondence depends on Stark coupling strength.

Large atom-light ratio enhances quantum-classical correspondence.

Resonant RSM shows strong correlation between entanglement entropy and phase space when U approaches -1.

Abstract

Testing the correspondence principle in nonlinear quantum systems is a fundamental pursuit in quantum physics. In this paper, we employed mean field approximation theory to study the semiclassical dynamics in the Rabi-Stark model (RSM) and showed that the nonlinear Stark coupling significantly modulates the semiclassical phase space structure. By analyzing the linear entanglement entropy of coherent states prepared in the classical chaotic and regular regions of the semiclassical phase space, we demonstrate that quantum-classical correspondence can be achieved in the RSM with large atom-light frequency ratios. While this correspondence fails in the resonant Rabi model because its truncated photon number is insufficient to approach the large quantum number limit, we discovered that in the resonant RSM when the nonlinear Stark coupling $U \to \pm 1$, the time-averaged linear entanglement entropy correlates strongly with the semiclassical phase space. In particular, when $U \to -1$, the truncated photon number in the resonant RSM is very close to that in the resonant Rabi model, but the time-averaged linear entanglement entropy still corresponds well with the semiclassical phase space. This result demonstrates that quantum-classical correspondence can be realized in the few-body resonant RSM.