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Journal of Daqing Normal University

Analysis of Research Present Situation Soliton for Bose Einstein Condensation

Qian Tian

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

Through analyzing the current situation of optical soliton in the bose Einstein condensation,the research of optical soliton in the system elaborated the bose Einstein condensation method and model,and the current in the research of other scholars in the field of optical soliton in the bose Einstein condensation results must be analyzed,in order to further studies in this field provides a method and guidance.

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arXiv:cond-mat/0208136•Physical Review A•Dec 20, 2002•59 citations
Through analyzing the current situation of optical soliton in the bose Einstein condensation,the research of optical soliton in the system elaborated the bose Einstein condensation method and model,and the current in the research of other scholars in the field of optical soliton in the bose Einstein condensation results must be analyzed,in order to further studies in this field provides a method and guidance.
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.
A briefly formulated update of the recently published review [1] on the topic of multidimensional solitons (chiefly, in nonlinear optics and atomic Bose-Einstein condensates (BECs)) is presented. The update briefly summarizes some notable results on this topic that have been reported very recently, and offers a compact outline of the directions of the current experiment and theoretical work in this and related fields. In particular, as concerns newest experimental findings, included are the creation of multiple quantum droplets in prolate BEC, and the observation of expanding toroidal light structures in linear optics. The update of theoretical results includes the analysis of 2D solitons in the optical system with the quadratic nonlinearity and fractional diffraction, and the prediction of stable 3D vortex solitons in various BEC schemes with long-range interactions.
A briefly formulated update of the recently published review [1] on the topic of multidimensional solitons (chiefly, in nonlinear optics and atomic Bose-Einstein condensates (BECs)) is presented. The update briefly summarizes some notable results on this topic that have been reported very recently, and offers a compact outline of the directions of the current experiment and theoretical work in this and related fields. In particular, as concerns newest experimental findings, included are the creation of multiple _quantum droplets_ in prolate BEC, and the observation of expanding toroidal light structures in linear optics. The update of theoretical results includes the analysis of 2D solitons in the optical system with the quadratic nonlinearity and _fractional diffraction_, and the prediction of stable 3D _vortex solitons_ in various BEC schemes with long-range interactions.
A briefly formulated update of the recently published review [B.A. Malomed, Multidimensional soliton systems. Adv. Phys. 9(1) (2024), pp. 2301592] on the topic of multidimensional solitons (chiefly, in nonlinear optics and atomic Bose–Einstein condensates (BECs)) is presented. The update briefly summarizes some notable results on this topic that have been reported very recently, and offers a compact outline of the directions of the current experiment and theoretical work in this and related fields. In particular, as concerns newest experimental findings, included are the creation of multiple quantum droplets in prolate BEC, and the observation of expanding toroidal light structures in linear optics. The update of theoretical results includes the analysis of 2D solitons in the optical system with the quadratic nonlinearity and fractional diffraction, and the prediction of stable 3D vortex solitons in various BEC schemes with long-range interactions.
We analyze the dynamical stability of gap solitons formed in a quasi-one-dimensional Bose-Einstein condensate in an optical lattice. Using two different numerical methods we show that, under realistic assumptions for experimental parameters, a gap soliton is stable only in a truly one-dimensional situation. In two and three dimensions, resonant transverse excitations lead to dynamical instability. The time scale of the decay is numerically calculated and shown to be large compared to the characteristic time scale of solitons for realistic physical parameters.