Hydrodynamics and two-dimensional dark lump solitons for polariton superfluids

TL;DR

This paper models two-dimensional polariton superfluids using hydrodynamics and predicts the existence of dark lump solitons, showing their stability and formation mechanisms through analytical and numerical methods.

Contribution

It derives new shallow water wave models for polariton condensates and predicts stable, localized dark lump solitons in a dissipative setting, supported by simulations.

Findings

Dark lump solitons are vorticity-free and weakly localized.

Dissipation extends the lifetime of dark lumps threefold.

Lump and vortex structures can form spontaneously from dark soliton instabilities.

Abstract

We study a two-dimensional incoherently pumped exciton-polariton condensate described by an open-dissipative Gross-Pitaevskii equation for the polariton dynamics coupled to a rate equation for the exciton density. Adopting a hydrodynamic approach, we use multiscale expansion methods to derive several models appearing in the context of shallow water waves with viscosity. In particular, we derive a Boussinesq/Benney-Luke type equation and its far-field expansion in terms of Kadomtsev-Petviashvili-I (KP-I) equations for right- and left-going waves. From the KP-I model, we predict the existence of vorticity-free, weakly (algebraically) localized two-dimensional dark-lump solitons. We find that, in the presence of dissipation, dark lumps exhibit a lifetime three times larger than that of planar dark solitons. Direct numerical simulations show that dark lumps do exist, and their dissipative dynamics is well captured by our analytical approximation. It is also shown that lump-like and vortex-like structures can spontaneously be formed as a result of the transverse "snaking" instability of dark soliton stripes.