Abstract We explore the manipulation of gray-ring dark solitons in a two-component Bose gas with tunable soft-core interactions through numerical simulations of the time-dependent Gross-Pitaevskii equation. Our results demonstrate that the lifetime of gray solitons with periodically modulated soft-core interactions significantly depends on their initial depth. Specifically, shallower initial depths lead to longer lifetimes when exceeding a critical depth threshold. Furthermore, the soliton depth also governs the number and dynamic of vortex pairs resulting from the collapse of the ring dark soliton. These depth-dependent topological transformations open new perspectives for quantum manipulation.
Abstract We explore the manipulation of gray-ring dark solitons in a two-component Bose gas with tunable soft-core interactions through numerical simulations of the time-dependent Gross-Pitaevskii equation. Our results demonstrate that the lifetime of gray solitons with periodically modulated soft-core interactions significantly depends on their initial depth. Specifically, shallower initial depths lead to longer lifetimes when exceeding a critical depth threshold. Furthermore, the soliton depth also governs the number and dynamic of vortex pairs resulting from the collapse of the ring dark soliton. These depth-dependent topological transformations open new perspectives for quantum manipulation.
We investigate the dynamics and pattern formation of two ring dark solitons in a two-dimensional binary Bose-Einstein condensate with tunable intercomponent interaction via numerical simulation of the time-dependent Gross-Pitaevskii equation. Both the black and gray ring dark solitons are considered for cases where the modulation frequency of the intercomponent interaction is resonant or nonresonant with the one of the trapping potential. Our results show that in the presence of periodic modulation of the intercomponent interaction not only are the lifetimes of the ring dark solitons largely extended but also their decaying dynamics are dramatically affected. Before snaking instability sets in, new ring dark solitons are formed, and both the numbers and depths of the ring dark solitons exhibit collective oscillations. With the development of instability, the system exhibits different decaying processes, and a variety of decay profiles, such as vortex necklace, distorted octagon, vortex-antivortex ring, and cross, are formed, showing a strong dependence on the modulation frequency of the intercomponent interaction and the initial depth of the ring dark soliton.
We consider the dynamics and formation of vortices from ring dark solitons in a two-dimensional Bose-Einstein condensate with the Rashba spin-orbit coupling based on the time-dependent coupled Gross-Pitaevskii equation. Compared with previous results, the system exhibits complex dynamical behaviors in the presence of the spin-orbit coupling. With the modulation of the spin-orbit coupling, not only the lifetime of ring dark solitons is greatly prolonged, but also their attenuation kinetics is significantly affected. For two shallow ring dark solitons with the equal strength of the spin-orbit coupling, the radius of ring dark solitons increases to a maximum value over time and then shrinks into a minimum value. Due to the effect of the snake instability, ring dark solitons split into a series of ring-like clusters of vortex pairs, which perform complex oscillations. This indicates that the system is strongly dependent on the presence of the spin-orbit coupling. Furthermore, the effect of different initial modulation depths on the dynamics of ring dark solitons is investigated.
We investigate both analytically and numerically the dynamics and modulation of ring dark solitons in two-dimensional Bose-Einstein condensates with tunable interaction. The analytic solutions for the ring dark soliton are derived by using a transformation method. A shallow ring dark soliton is stable when the ring is slightly distorted, while for large deformation of the ring, vortex pairs appear and demonstrate different dynamical behaviors: the vortex pairs transform into dark lumplike solitons and revert to ring dark solitons periodically. Moreover, our results show that the dynamical evolution of the ring dark soliton can be dramatically affected by the Feshbach resonance, and the lifetime of the ring dark soliton can be greatly extended, which offers a useful method for observing ring dark solitons in future experiments.
We explore the effects of system parameters on the dynamics of ring dark solitons (RDSs) and vortices followed by the collapse of RDSs in a two-component Bose-Einstein condensate (BEC). The system exhibits complicated dynamical behaviors, which are quite different from those in a scalar BEC. For two shallow RDSs with equal initial depths, the dynamical trajectories of generated vortex dipoles are similar to those in a scalar BEC, but the time for vortex dipoles to perform a periodic motion is increased. In particular, there exists a critical depth, above which vortex dipoles first move along the vertical direction and then preform complicated dynamics, including their rearrangement and recombination. Finally, we consider the case of unequal initial depths and find that the number of created vortices is determined by the depth of the shallow RDS, while their initial moving direction is determined by the deeper one.
Soliton is an exotic topological excitation, and it widely exists in various nonlinear systems, such as nonlinear optics, Bose-Einstein condensates, classical and quantum fluids, plasma, magnetic materials, etc. A stable soliton can propagate with constant amplitude and velocity, and maintain its shape. Two-dimensional and three-dimensional solitons are usually hard to stabilize, and how to realize stable two-dimensional or three-dimensional solitons has aroused the great interest of the researchers. Ring dark soliton is a kind of two-dimensional soliton, which was first theoretically predicted and experimentally realized in nonlinear optical systems. Compared with the usual two-dimensional solitons, ring dark solitons have good stability and rich dynamical behaviors. Owing to their highly controllable capability, Bose-Einstein condensates provide a new platform for studying the ring dark solitons. Based on the recent progress in Bose-Einstein condensates and solitons, this paper reviews the research on the analytic solutions, stability, as well as the decay dynamics of ring dark solitons in Bose-Einstein condensates. A transform method is introduced, which generalizes the analytic solutions of ring dark solitons from a homogeneous system with time-independent nonlinearity to a harmonically trapped inhomogeneous system with time-dependent nonlinearity. The stability phase diagram of the ring dark soliton under deformation perturbations is discussed by numerically solving the Gross-Pitaevskii equations in the mean-field theory. A method of enhancing the stability of ring dark solitons by periodically modulating the nonlinear coefficients is introduced. It is also shown that the periodically modulated nonlinear coefficient can be experimentally realized by the Feshbach resonance technology. In addition, we discuss the dynamics of the decay of ring dark solitons. It is found that the ring dark soliton can decay into various vortex clusters composed of vortices and antivortices. This opens a new avenue to the investigation of vortex dynamics and quantum turbulence. It is also found that the ring dark solitons combined with periodic modulated nonlinearity can give rise to the pattern formation, which is an interesting nonlinear phenomenon widely explored in all the fields of nature. Finally, some possible research subjects about ring dark solitons in future research are also discussed.
We study the dynamics of dark-bright (DB) solitons in binary mixtures of Bose gases at finite temperature using a system of two coupled dissipative Gross–Pitaevskii equations. We develop a perturbation theory for the two-component system to derive an equation of motion for the soliton centers and identify different temperature-dependent damping regimes. We show that the effect of the bright ('filling') soliton component is to partially stabilize 'bare' dark solitons against temperature-induced dissipation, thus providing longer lifetimes. We also study analytically thermal effects on DB soliton 'molecules' (i.e. two in-phase and out-of-phase DB solitons), showing that they undergo expanding oscillations while interacting. Our analytical findings are in good agreement with results obtained via a Bogoliubov–de Gennes analysis and direct numerical simulations.