Quench Dynamics and Stability of Dark Solitons in Exciton Polariton Condensates

Abstract

Exciton polariton condensates (EPCs) have emerged as a paradigmatic platform for investigating nonequilibrium quantum many-body phenomena, particularly due to their intrinsic open-dissipative nature and strong nonlinear interactions governed by the interplay between stimulated scattering and reservoir-mediated damping. Recent advances in Feshbach resonance engineering now enable precise tuning of interaction strengths, opening new avenues to explore exotic nonlinear excitations in these driven-dissipative systems. In this work, we systematically investigate the quench dynamics and stability of dark solitons in repulsive one-dimensional EPCs under sudden parameter variations in both nonlinear interaction strength g and pump intensity P. Through a Hamiltonian variational approach that incorporates reservoir damping effects, we derive reduced equations of motion for soliton velocity evolution that exhibit remarkable qualitative agreement with direct numerical simulations of the underlying open-dissipative Gross Pitaevskii equation. Our results reveal three distinct dynamical regimes: (i) stable soliton propagation at intermediate pump powers, (ii) velocity-dependent soliton breakup above critical pumping thresholds, and (iii) parametric excitation of soliton trains under simultaneous interaction quenches. These findings establish a quantitative framework for understanding soliton dynamics in nonresonantly pumped EPCs, with implications for quantum fluid dynamics and nonequilibrium Bose Einstein condensates.

Figures (2)

• Figure 1: Quench dynamics of the dark soliton with the initial velocity $u=0.35$ after the quench $g_{1}$$\rightarrow$$g_{2}$. The varied strength of the interaction after the quench $g_{2}=1,~0.5,~2,~4$ corresponds to (a), (b), (c), and (d), respectively. The other parameters are set as $g_{1}=1$, $\bar{g}_{R}=2/30$, $\bar{\gamma}_{C}=3/30$, $\bar{\gamma}_{R}=15/30$, $\bar{R}=1.5/30$, and $\bar{P}=33/30$. The inset of (a) shows the evolution of the condensate density distribution $n=\left|\psi^{\prime}\right|^{2}$. The inset of (b--d) shows the profile of the dark soliton with $t=20$. The analytical solution for the minimum value of density $n_{\text{min}}$ using Equation (\ref{['eq.13']}) is plotted as a red solid line. The numerical solution obtained from evolution Equation (\ref{['eq.8']}) is plotted with a red star line. The numerical solution obtained from real-time evolution Equations (\ref{['eq.5']}) and (\ref{['eq.6']}) is plotted with blue circle.
• Figure 2: Quench dynamics of a 1D dark soliton with the initial velocity $u=0.35$ under quenching laser pumping intensity. In (a,d) we show the quench dynamics of the dark soliton in the absence of the open-dissipative with $g_{1}=1$ and $g_{2}=0.5$. In (b,c) we show the quench dynamics of the dark soliton in the presence of the open-dissipative. The varied strength of the pump after the quench $\bar{P}_{2}=27,~30$ corresponds to (b) and (c), respectively. The parameters are chosen as $g=1$, $\bar{g}_{R}=2$, $\bar{\gamma}_{C}=3$, $\bar{\gamma}_{R}=15$, $\bar{R}=1.5$, and $\bar{P}_{1}=33$. In (a--c), the meaning represented by different lines is the same as in Figure 1. In (d) the numerical solution is plotted with a red circle. The analytical solution is plotted as a blue solid line.