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Chinese Physics B

Moving bright solitons in a pseudo-spin polarization Bose–Einstein condensate

Tian-Fu Xu, Yu-Feng Zhang, Lei-Chao Xu, Zai-Dong Li

Published Sep 1, 2017• 8 citations
Publisher

Abstract

We study the moving bright solitons in the weak attractive Bose–Einstein condensate with a spin–orbit interaction. By solving the coupled nonlinear Schrödinger equation with the variational method and the imaginary time evolution method, two kinds of solitons (plane wave soliton and stripe solitons) are found in different parameter regions. It is shown that the soliton speed dominates its structure. The detuning between the Raman beam and energy states of the atoms decides the spin polarization strength of the system. The soliton dynamics is also studied for various moving speed and we find that the shape of individual components can be kept when the speed of soliton is low.

DOI
10.1088/1674-1056/26/10/100304

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We study the moving bright solitons in the weak attractive Bose–Einstein condensate with a spin–orbit interaction. By solving the coupled nonlinear Schrödinger equation with the variational method and the imaginary time evolution method, two kinds of solitons (plane wave soliton and stripe solitons) are found in different parameter regions. It is shown that the soliton speed dominates its structure. The detuning between the Raman beam and energy states of the atoms decides the spin polarization strength of the system. The soliton dynamics is also studied for various moving speed and we find that the shape of individual components can be kept when the speed of soliton is low.
We study two types of bright solitons in an attractive Bose–Einstein condensate with a spin–orbit interaction. By solving the coupled nonlinear Schrödinger equations with the variational method and the imaginary time evolution method, fundamental properties of solitons are carefully investigated in different parameter regimes. It is shown that the detuning between the Raman beam and energy states of the atoms dominates the ground state type and spin polarization strength. The soliton dynamics is also studied for various moving velocities for zero and nonzero detuning cases. We find that the shape of individual component solitons can be maintained when the moving speed of solitons is low and the detuning is small in the coupled harmonically trapped pseudo-spin polarization Bose–Einstein condensate.
We study a two-dimensional spin-orbit-coupled dipolar Bose-Einstein condensate with repulsive contact interactions by both the variational method and the imaginary-time evolution of the Gross-Pitaevskii equation. The dipoles are completely polarized along one direction in the two-dimensional plane to provide an effective attractive dipole-dipole interaction. We find two types of solitons as the ground states arising from such attractive dipole-dipole interactions: a plane-wave soliton with a spatially varying phase and a stripe soliton with a spatially oscillating density for each component. Both types of solitons possess smaller size and higher anisotropy than the soliton without spin-orbit coupling. Finally, we discuss the properties of moving solitons, which are nontrivial because of the violation of Galilean invariance.
We investigate the matter-wave solitons in a spin–orbit-coupled spin-1 Bose–Einstein condensate using a multiscale perturbation method. Beginning with the one-dimensional spin–orbit-coupled threecomponent Gross–Pitaevskii equations, we derive a single nonlinear Schrödinger equation, which allows determination of the analytical soliton solutions of the system. Stationary and moving solitons in the system are derived. In particular, a parameter space for different existing soliton types is provided. It is shown that there exist only dark or bright solitons when the spin–orbit coupling is weak, with the solitons depending on the atomic interactions. However, when the spin–orbit coupling is strong, both dark and bright solitons exist, being determined by the Raman coupling. Our analytical solutions are confirmed by direct numerical simulations.
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We investigate the moving matter-wave solitons in spin—orbit coupled Bose—Einstein condensates (BECs) by a perturbation method. Starting with the one-dimensional Gross—Pitaevskii equations, we derive a new KdV-like equation to which an approximate solution is obtained by assuming weak Raman coupling and strong spin—orbit coupling. The derivation of the KdV-like equation may be useful to understand the properties of solitons excitation in spin—orbit coupled BECs. We find different types of moving solitons: dark—bright, bright—bright and dark—dark solitons. Interestingly, moving dark—dark soliton for attractive intra- and inter-species interactions is found, which depends on the Raman coupling. The amplitude and velocity of the moving solitons strongly depend on the Raman coupling and spin—orbit coupling.
Abstract We explore the existence and stability domains of stationary and moving bright solitons in spin–orbit-coupled spin-1 Bose–Einstein condensates in an external Zeeman field. Two families of bell-shape bright solitons (plane-wave (PW) phases) and two families of stripe-shape bright solitons (standing-wave (SW) phases) are obtained. We find a relation between the existence of these bright solitons and the single-particle energy spectrum, as well as the requirements of their existence for atomic interactions. The stability of four families of bright solitons is systematically analyzed using the linear stability analysis method. For two families of PW bright solitons, they are unstable only when the strength of the Zeeman field is above a critical value. The critical value is affected by the spin–orbit coupling and hardly affected by atomic interactions. When the velocities of solitons are zero (nonzero), the critical values of these two families are equal (unequal). For two families of SW bright solitons, their stability domains are identical in the absence of the Zeeman field, and they are unstable when the ferromagnetic interaction is strong. In the presence of the Zeeman field, their stability domains are complementary and complex, and one family of SW bright solitons can exist stably in the area with stronger ferromagnetic interaction. Furthermore, we find the collisions of stable bright solitons with different velocities can generate intriguing dynamics.