Dark solitons and vortices in PT-symmetric nonlinear media: from spontaneous symmetry breaking to nonlinear PT phase transitions

TL;DR

This paper explores nonlinear PT-symmetric systems, revealing spontaneous symmetry breaking and nonlinear phase transitions involving dark solitons and vortices, with analytical and bifurcation analysis of state behaviors as potential applications.

Contribution

It introduces the concept of nonlinear PT-phase transitions in systems with defocusing nonlinearities, analyzing symmetry breaking and bifurcations of solitons and vortices.

Findings

Excited states undergo spontaneous symmetry breaking at weak PT potential strength.

State branches collide and disappear in blue-sky bifurcations as potential strength increases.

Post-critical point, spontaneous formation of solitons and vortices occurs from initial states.

Abstract

We consider nonlinear analogues of Parity-Time (PT) symmetric linear systems exhibiting defocusing nonlinearities. We study the ground state and excited states (dark solitons and vortices) of the system and report the following remarkable features. For relatively weak values of the parameter $\varepsilon$ controlling the strength of the PT-symmetric potential, excited states undergo (analytically tractable) spontaneous symmetry breaking; as $\varepsilon$ is further increased, the ground state and first excited state, as well as branches of higher multi-soliton (multi-vortex) states, collide in pairs and disappear in blue-sky bifurcations, in a way which is strongly reminiscent of the linear PT-phase transition ---thus termed the nonlinear PT-phase transition. Past this critical point, initialization of, e.g., the former ground state leads to spontaneously emerging solitons and vortices.