Superradiant Phase Transition and Statistical Properties in the Dicke-Stark Model

TL;DR

This paper investigates the quantum phase transition and statistical properties of the finite and infinite Dicke-Stark model, revealing how coupling strength and temperature influence photon correlations, entanglement, and spin squeezing.

Contribution

It provides analytical and numerical analysis of the superradiant phase transition and explores how Stark fields and temperature affect quantum correlations in the Dicke-Stark model.

Findings

Identified the critical point of the superradiant phase transition.

Showed the transition of photon statistics from bunching to anti-bunching and back.

Demonstrated temperature effects on entanglement and spin squeezing.

Abstract

In this study, the energy spectrum and thermal equilibrium states of the finite-size Dicke-Stark model were numerically obtained within the extended coherent state space by solving the dressed master equation for strongly coupled light-atom systems. The critical point of the superradiant phase transition in the infinite-size Dicke-Stark model was analytically derived using the mean-field approach and confirmed with numerical calculation. Under thermal equilibrium conditions, analyses of the negativity, zero-time-delay two-photon correlation function, and atom-spin squeezing parameters in the finite-size Dicke-Stark model reveal that as the coupling strength increases, the light field undergoes a transition from photon bunching to anti-bunching and then back to bunching. The Stark field can modulate both the maximum and minimum values of the two-photon correlation function and their corresponding coupling strengths. At low temperatures, the system exhibits entanglement and spin squeezing. As temperature rises, entanglement gradually diminishes, while strong coupling facilitates the preservation of entanglement in the system state. Atom-spin squeezing spin squeezing is highly sensitive to temperature and vanishes rapidly with increasing temperature. This work contributes to the fundamental understanding of quantum phenomena in Dicke-Stark systems.