Dynamical properties of the finite-size Dicke model coupled to a thermal reservoir

TL;DR

This paper studies the finite-size Dicke model's dynamics when coupled to a thermal reservoir, revealing how strong atom-cavity interactions influence superradiant transitions and coherence properties.

Contribution

It derives a Markovian master equation including counter-rotating terms in the dispersive regime, providing new insights into the system's steady states and dynamics.

Findings

Bifurcation of long-lived states corresponds to superradiant transition.

Strong atom-cavity coupling enhances coherence in the superradiant region.

Steady state solutions explicitly derived from the master equation.

Abstract

We investigate the dynamical properties of the finite-size Dicke model coupled to a photon reservoir in the dispersive regime. The system-reservoir coupling in our Hamiltonian includes counter-rotating terms, which are relevant in the strong atom-cavity coupling. Because the dispersive regime is considered, the dynamics of low-energy states are described sufficiently accurately within the finite-dimensional subspace of the dressed states. Using the separation of the time scales between the system and the reservoir, we derive the Markovian quantum master equation in the subspace without ignoring the counter-rotating terms. The temporal evolution of the expectation of the cavity mode shows that the bifurcation of the long-lived state corresponds to the superradiant transition in the isolated model. The master equation explicitly gives the steady state solution. The numerical results for the first-order correlation function on the steady state indicate that the strong atom-cavity coupling enhances the coherence and softens the dephasing in the superradiant region.