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Physical Review A

Dynamics of vortices followed by the collapse of ring dark solitons in a two-component Bose-Einstein condensate

Lin-Xue Wang, Chao‐Qing Dai, Lin Wen, Tao Liu, Haifeng Jiang, Hiroki Saito, Shougang Zhang, Xiao-Fei Zhang

Published Jun 11, 2018• 43 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.97.063607

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Abstract This work focuses on the evolution behaviors of ring dark solitons (RDSs) and the following vortices after the collapses of RDSs in spin-1 Bose–Einstein condensates. We find that the weighted average of the initial depths of three components determines the number and motion trajectories of vortex dipoles. For the weighted average of the initial depths below the critical depth, two vortex dipoles form and start moving along the horizontal axis. For the weighted average depth above the critical depth, two or four vortex dipoles form, and all start moving along the vertical axis. For the RDS with weighted average depth at exactly the critical point, four vortex dipoles form, half of the vortex dipoles initiate movement vertically, and the other half initiate movement horizontally. Our conclusion is applicable to the two-component system studied in earlier research, indicating its universality.
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 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.
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 have created spatial dark solitons in two-component Bose-Einstein condensates in which the soliton exists in one of the condensate components and the soliton nodal plane is filled with the second component. The filled solitons are stable for hundreds of milliseconds. The filling can be selectively removed, making the soliton more susceptible to dynamical instabilities. For a condensate in a spherically symmetric potential, these instabilities cause the dark soliton to decay into stable vortex rings. We have imaged the resulting vortex rings.