Role of nonlinearity in bounded parametric resonance of the periodically driven closed Dicke model

Abstract

Common analysis of the Dicke model involves transforming it into a linear oscillator model (LOM). This is done by using the Holstein-Primakoff representation (HPR) and truncating the Taylor series expansion of the spin operators up to the first linear term. However, such truncation is not enough to fully capture the dynamics of the periodically driven Dicke model at the thermodynamic limit. In this paper, we consider the effect of the first nonlinear term in the HPR approximation on the dynamics of the said model. We show that the nonlinearity forces the dynamics to remain bounded at the parametric resonances. This leads to a period doubling response, which manifests as a persistent beating oscillation on the spin operator J_x. The inclusion of nonlinearity gives us an avenue to access more phases absent in the LOM.