Symmetry-breaking Effects for Polariton Condensates in Double-Well Potentials

TL;DR

This paper investigates the behavior of polariton condensates in double-well potentials, revealing unique bifurcation phenomena and stability properties influenced by nonresonant pumping and nonlinear damping.

Contribution

It provides the first detailed analysis of symmetry-breaking effects and bifurcation structures in polariton condensates with double-well potentials, highlighting differences from atomic condensates.

Findings

Unstable nature of bifurcating solutions in polariton condensates.

Sub-critical bifurcation for attractive interactions.

Numerical simulations confirm bifurcation analysis results.

Abstract

We study the existence, stability, and dynamics of symmetric and anti-symmetric states of quasi-one-dimensional polariton condensates in double-well potentials, in the presence of nonresonant pumping and nonlinear damping. Some prototypical features of the system, such as the bifurcation of asymmetric solutions, are similar to the Hamiltonian analog of the double-well system considered in the realm of atomic condensates. Nevertheless, there are also some nontrivial differences including, e.g., the unstable nature of both the parent and the daughter branch emerging in the relevant pitchfork bifurcation for slightly larger values of atom numbers. Another interesting feature that does not appear in the atomic condensate case is that the bifurcation for attractive interactions is slightly sub-critical instead of supercritical. These conclusions of the bifurcation analysis are corroborated by direct numerical simulations examining the dynamics of the system in the unstable regime.