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Register a new userHydrodynamics and two-dimensional dark lump solitons for polariton superfluids
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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.
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A quantum fluid passing an obstacle behaves differently from a classical one. When the flow is slow enough, the quantum gas enters a superfluid regime and neither whirlpools nor waves form around the obstacle. For higher flow velocities, it has been predicted that the perturbation induced by the defect gives rise to the turbulent emission of quantised vortices and to the nucleation of solitons. Using an interacting Bose gas of exciton-polaritons in a semiconductor microcavity, we report the transition from superfluidity to the hydrodynamic formation of oblique dark solitons and vortex streets in the wake of a potential barrier. The direct observation of these topological excitations provides key information on the mechanisms of superflow and shows the potential of polariton condensates for quantum turbulence studies.
In this work we present a systematic study of the three-dimensional extension of the ring dark soliton examining its existence, stability, and dynamics in isotropic harmonically trapped Bose-Einstein condensates. Detuning the chemical potential from the linear limit, the ring dark soliton becomes unstable immediately, but can be fully stabilized by an external cylindrical potential. The ring has a large number of unstable modes which are analyzed through spectral stability analysis. Furthermore, a few typical destabilization dynamical scenarios are revealed with a number of interesting vortical structures emerging such as the two or four coaxial parallel vortex rings. In the process of considering the stability of the structure, we also develop a modified version of the degenerate perturbation theory method for characterizing the spectra of the coherent structure. This semi-analytical method can be reliably applied to any soliton with a linear limit to explore its spectral properties near this limit. The good agreement of the resulting spectrum is illustrated via a comparison with the full numerical Bogolyubov-de Gennes spectrum. The application of the method to the two-component ring dark-bright soliton is also discussed.
We develop stability analysis for matter-wave solitons in a two-dimensional (2D) Bose-Einstein condensate loaded in an optical lattice (OL), to which periodic time modulation is applied, in different forms. The stability is studied by dint of the variational approximation and systematic simulations. For solitons in the semi-infinite gap, well-defined stability patterns are produced under the action of the attractive nonlinearity, clearly exhibiting the presence of resonance frequencies. The analysis is reported for several time-modulation formats, including the case of in-phase modulations of both quasi-1D sublattices, which build the 2D square-shaped OL, and setups with asynchronous modulation of the sublattices. In particular, when the modulations of two sublattices are phase-shifted by {delta}={pi}/2, the stability map is not improved, as the originally well-structured stability pattern becomes fuzzy and the stability at high modulation frequencies is considerably reduced. Mixed results are obtained for anti-phase modulations of the sublattices ({delta}={pi}), where extended stability regions are found for low modulation frequencies, but for high frequencies the stability is weakened. The analysis is also performed in the case of the repulsive nonlinearity, for solitons in the first finite bandgap. It is concluded that, even though stability regions may be found, distinct stability boundaries for the gap solitons cannot be identified clearly. Finally, the stability is also explored for vortex solitons of both the square-shaped and rhombic types (i.e., off- and on-site-centered ones).
We report on the static and dynamical properties of multiple dark-antidark solitons (DADs) in two-component, repulsively interacting Bose-Einstein condensates. Motivated by experimental observations involving multiple DADs, we present a theoretical study which showcases that bound states consisting of dark (antidark) solitons in the first (second) component of the mixture exist for different values of interspecies interactions. It is found that ensembles of few DADs may exist as stable configurations, while for larger DAD arrays, the relevant windows of stability with respect to the interspecies interaction strength become progressively narrower. Moreover, the dynamical formation of states consisting of alternating DADs in the two components of the mixture is monitored. A complex dynamical evolution of these states is observed, leading either to sorted DADs or to beating dark-dark solitons depending on the strength of the interspecies coupling. This study demonstrates clear avenues for future investigations of DAD configurations.
We investigate dynamics of two-dimensional chiral solitons of semi-vortex (SV) and mixed-mode (MM) types in spin-orbit-coupled Bose-Einstein condensates with the Manakov nonlinearity, loaded in a dual-core (double-layer) trap. The system supports two novel manifestations of Josephson phenomenology: one in the form of persistent oscillations between SVs or MMs with opposite chiralities in the two cores, and another one demonstrating robust periodic switching (identity oscillations) between SV in one core and MM in the other, provided that the strength of the inter-core coupling exceeds a threshold value. Below the threshold, the system creates composite states, which are asymmetric with respect to the two cores, or suffer the collapse. Robustness of the chirality and identity oscillations against deviations from the Manakov nonlinearity is investigated too. These dynamical regimes are possible only in the nonlinear system. In the linear one, exact stationary and dynamical solutions for SVs and MMs of the Bessel type are found. They sustain Josephson self-oscillations in different modes, with no interconversion between them.
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