Nonlinear dynamics of the dissipative anisotropic two-photon Dicke model

TL;DR

This paper explores the complex nonlinear behaviors of the dissipative anisotropic two-photon Dicke model, revealing phases, bifurcations, chaos, and phase coexistence in its semiclassical dynamics.

Contribution

It provides a detailed analysis of the nonlinear dynamics, including bifurcations and chaos, in the dissipative anisotropic two-photon Dicke model, which was not previously characterized.

Findings

Identification of normal and superradiant-like phases.

Discovery of chaotic dynamics from period-doubling bifurcations.

Observation of phase coexistence and multiple basins of attraction.

Abstract

We study the semiclassical limit of the anisotropic two-photon Dicke model with a dissipative bosonic field and describe its rich nonlinear dynamics. Besides normal and 'superradiant'-like phases, the presence of localized fixed points reflects the spectral collapse of the closed-system Hamiltonian. Through Hopf bifurcations of superradiant and normal fixed points, limit cycles are formed in certain regions of parameters. We also identify a pole-flip transition induced by anisotropy and a region of chaotic dynamics, which appears from a cascade of period-doubling bifurcations. In the chaotic region, collision and fragmentation of symmetric attractors take place. Throughout the phase diagram we find several examples of phase coexistence, leading to the segmentation of phase space into distinct basins of attraction.