Dark spherical shell solitons in three-dimensional Bose-Einstein condensates: Existence, stability, and dynamics

Abstract

In this work we study spherical shell dark soliton states in three-dimensional atomic Bose-Einstein condensates. Their symmetry is exploited in order to analyze their existence, as well as that of topologically charged variants of the structures, and, importantly, to identify their linear stability Bogolyubov-de Gennes spectrum. We compare our effective 1D spherical and 2D cylindrical computations with the full 3D numerics. An important conclusion is that such spherical shell solitons can be stable sufficiently close to the linear limit of the isotropic condensates considered herein. We have also identified their instabilities leading to the emergence of vortex line and vortex ring cages. In addition, we generalize effective particle pictures of lower dimensional dark solitons and ring dark solitons to the spherical shell solitons concerning their equilibrium radius and effective dynamics around it. In this case too, we favorably compare the resulting predictions such as the shell equilibrium radius, qualitatively and quantitatively, with full numerical solutions in 3D.

Single and multiple vortex rings in three-dimensional Bose-Einstein condensates: Existence, stability, and dynamics

“…Note that the µ → ∞ asymptotic prediction in the TF limit from Refs. [28,45] for the equilibrium radius r c :…”

“…Nevertheless, they have been experimentally observed in a range of different studies including, their realization through the decay of planar dark solitons in two-component BECs [24], creation via density engineering [25], spontaneous emergence via the collision of symmetric defects [26] and their detection through unusual collision outcomes of dark solitonic structures [27]. Recently, intriguing six-vortex-ring and six-vortex-line cages have been predicted as transient states in the decay of spherical-shell dark solitons [28].…”

SO(2)-induced breathing patterns in multicomponent Bose-Einstein condensates

“…We refer the interested reader to Refs. [37][38][39] for a detailed description of the numerical methods employed in this present work. In our numerical computations presented below, we consider values of the trap strength of 0.1,0.2, and 1 in the 1D, 2D, and 3D cases, respectively.…”

Adiabatic Invariant Approach to Transverse Instability: Landau Dynamics of Soliton Filaments

“…[11], as well as two quasi-1D dark soliton structures: the ring dark soliton (RDS) and the † URL: http://nlds.sdsu.edu dark spherical shell soliton (SSS), in 2D and 3D settings, respectively. RDSs were predicted [15] (and observed [16]) in optics, and in BECs [17], while SSSs were studied in optics and BECs [15,18,19], and observed as transient structures in a BEC experiment [20]. In earlier works, the so-called Landau dynamics approach (i.e., a semiclassical dynamics of the solitary wave as a quasi-particle relying on a local-density approximation) was developed for dark solitons [21,22] and for RDSs [23].…”

“…It is known that in 2D as the undulation intensifies along the transverse direction, the soliton eventually decays into vortex-antivortex pairs [12,25]. In 3D, the corresponding transverse instability gives rise to vortex rings and vortex lines [2,14,19,26].…”