Stability Window of Trapless Polariton Bose-Einstein condensates

TL;DR

This paper theoretically investigates the stabilization of trapless polariton Bose-Einstein condensates using variational methods, stability analysis, and numerical simulations to identify parameter regimes for stable condensates and observe dynamic effects.

Contribution

It introduces a stability window for trapless polariton BECs by combining variational analysis with numerical simulations, advancing understanding of their stable regimes without trapping potentials.

Findings

Identified a stability window in the parameter space for trapless polariton BECs.

Observed beating effects in the real-time evolution of condensates with attractive interactions.

Demonstrated control over periodicity through manipulation of loss/gain terms.

Abstract

We theoretically explore the possibility of stabilizing the trapless polariton Bose-Einstein condensates (pBECs). Exploiting the variational method, we solve the associated nonlinear, complex Gross-Pitaevskii (cGP) equation and derive the equation of motion for the amplitude and width of the condensate. These variational results described by ordinary differential equations are rewritten to perform a linear stability analysis to generate a stability window in the repulsive domain. A set of coupled nonlinear ordinary differential equations obtained through variational approach are then solved by numerical simulations through the fourth order Runge-Kutta method, which are further supported by split-step Crank-Nicholson method, thereby setting the platform for stable pBECs. In particular, we generate a window containing system parameters in the $g_1-\gamma_{eff}$ space within which the system can admit stable condensates. The highlight of the results is that one observes beating effects in the real time evolution of the condensates with attractive interactions much similar to multicomponent BECs, and their periodicity can be varied by manipulating linear and nonlinear loss/gain terms. For repulsive condensates, one notices the stretching of the density.