25 research outputs found
Hydrodynamics and two-dimensional dark lump solitons for polariton superfluids
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 lumplike and vortexlike structures can spontaneously be formed as a result of the transverse “snaking” instability of dark soliton stripes.Europe Union project AEI/FEDER: MAT2016-79866-
Matter-wave dark solitons: stochastic vs. analytical results
The dynamics of dark matter-wave solitons in elongated atomic condensates are
discussed at finite temperatures. Simulations with the stochastic
Gross-Pitaevskii equation reveal a noticeable, experimentally observable spread
in individual soliton trajectories, attributed to inherent fluctuations in both
phase and density of the underlying medium. Averaging over a number of such
trajectories (as done in experiments) washes out such background fluctuations,
revealing a well-defined temperature-dependent temporal growth in the
oscillation amplitude. The average soliton dynamics is well captured by the
simpler dissipative Gross-Pitaevskii equation, both numerically and via an
analytically-derived equation for the soliton center based on perturbation
theory for dark solitons.Comment: 4 pages, 3 figures. Added several reference
A Korteweg-de Vries description of dark solitons in polariton superfluids
We study the dynamics of dark solitons in an incoherently pumped exciton-polariton condensate by means of a system composed by a generalized open-dissipative Gross-Pitaevskii equation for the polaritons’ wavefunction and a rate equation for the exciton reservoir density. Considering a perturbative regime of sufficiently small reservoir excitations, we use the reductive perturbation method, to reduce the system to a Korteweg-de Vries (KdV) equation with linear loss. This model is used to describe the analytical form and the dynamics of dark solitons. We show that the polariton field supports decaying dark soliton solutions with a decay rate determined analytically in the weak pumping regime. We also find that the dark soliton evolution is accompanied by a shelf, whose dynamics follows qualitatively the effective KdV picture