Excited states of two-dimensional solitons supported by spin-orbit coupling and field-induced dipole-dipole repulsion

Abstract

It was recently found that excited states of semi-vortex and mixed-mode solitons are unstable in spin-orbit-coupled Bose-Einstein condensates (BECs) with contact interactions. We demonstrate a possibility to stabilize such excited states in a setting based on repulsive dipole-dipole interactions induced by a polarizing field, oriented perpendicular to the plane in which the dipolar BEC is trapped. The strength of the field is assumed to grow in the radial direction ∼ r 4 . Excited states of semi-vortex solitons have vorticities S and S + 1 in their two components, each being an eigenstate of the angular momentum. They are fully stable up to S = 5. Excited state of mixed-mode solitons feature interweaving necklace structures with opposite fractional values of the angular momentum in the two components. They are stable if they are built of dominant angular harmonics ±S, with S ≤ 4. Characteristics and stability of these two types of previously unknown higher-order solitons are systematically analyzed. Their characteristic size is ∼ 10 µm, with the number of atoms 10 5 .

One-dimensional gap solitons in quintic and cubic–quintic fractional nonlinear Schrödinger equations with a periodically modulated linear potential

“…The solitons in the models with combined linear and nonlinear lattices have been and are still being comprehensively researched in recent years [71][72][73][74]. The purely nonlinear defocusing media with spatially inhomogeneous nonlinearity whose local strength grows quickly enough from the center toward periphery in the D-dimensional coordinate, which are built on self-defocusing background and therefore do not possess critical and supercritical collapsestypical characteristics for solitons in self-focusing media, enriched the generation of various families of stable solitons and soliton composites in the self-trapping regime [75][76][77][78][79][80][81][82][83][84][85][86][87][88], such as the fundamental solitons for all (D-dimensional) space coordiantes [75,76], 1D multihump states in forms of dipole and multipole solitons [75][76][77], 2D bright solitary vortices carrying with an arbitrarily high topological charge [75,76], 2D localized dark solitons and vortices [86], multifarious 3D localized modes that are comprised of soliton gyroscopes [81] and skyrmions [82], and very recently the flat-top solitons (in both 1D and 2D spaces) and 2D vortices [88,89], to name just some of them. Despite excellent research works on solitons in fractional Schrödinger equation are making headway in past few years [18,19,[23][24][25][26][27][...…”

Gaussian-like and flat-top solitons of atoms with spatially modulated repulsive interactions

“…In contrast to the common beliefs, recent studies demonstrated that a pure nonlinear medium with spatially inhomogeneous defocusing nonlinearity whose local strength grows * zengjh@opt.ac.cn fast enough toward the periphery [38][39][40][41][42][43][44][45][46], provides a fertile ground for the generation and stabilization of bright solitons and other localized modes in all three dimensions, including solitary vortices (with arbitrarily vorticity) and vortex rings [47], skyrmions [48], hopfions, soliton gyroscopes [49], complex hybrid modes, localized dark solitons and vortices [50], to name a few of them.…”

Two-dimensional composite solitons in Bose-Einstein condensates with spatially confined spin-orbit coupling

“…In this connection, it is relevant to mention that non-ground states in SO-coupled systems were previously produced by means of the imaginary-time integration, provided that the input and integration procedure are subject to specific constraints, and the numerical algorithm is precise enough, to prevent a spontaneous transition to the ground states, see Refs. [12], [23], [40], and [60,61].…”