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arXiv:1505.06193 · Laser Physics Letters

Mobile vector soliton in a spin–orbit coupled spin-1 condensate

Sandeep Gautam, S K Adhikari

Published Mar 20, 2015• 50 citations
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Abstract

We study the formation of bound states and three-component bright vector solitons in a quasi-one-dimensional spin–orbit-coupled hyperfine spin f = 1 Bose–Einstein condensate using numerical solution and variational approximation of a mean-field model. In the antiferromagnetic domain, the solutions are time-reversal symmetric, and the component densities have multi-peak structure. In the ferromagnetic domain, the solutions violate time-reversal symmetry, and the component densities have single-peak structure. The dynamics of the system are not Galelian invariant. From an analysis of Galelian invariance, we establish that the single-peak ferromagnetic vector solitons are true solitons and can move maintaining constant component densities, whereas the antiferromagnetic solitons cannot move with constant component densities.

DOI
10.1088/1612-2011/12/4/045501

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We study the formation of bound states and three-component bright vector solitons in a quasi-one-dimensional spin–orbit-coupled hyperfine spin f = 1 Bose–Einstein condensate using numerical solution and variational approximation of a mean-field model. In the antiferromagnetic domain, the solutions are time-reversal symmetric, and the component densities have multi-peak structure. In the ferromagnetic domain, the solutions violate time-reversal symmetry, and the component densities have single-peak structure. The dynamics of the system are not Galelian invariant. From an analysis of Galelian invariance, we establish that the single-peak ferromagnetic vector solitons are true solitons and can move maintaining constant component densities, whereas the antiferromagnetic solitons cannot move with constant component densities.
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We demonstrate stable and metastable vortex-bright solitons in a three-dimensional spin-orbit-coupled three-component hyperfine spin-1 Bose-Einstein condensate (BEC) using numerical solution and variational approximation of a mean-field model. The spin-orbit coupling provides attraction to form vortex-bright solitons in both attractive and repulsive spinor BECs. The ground state of these vortex-bright solitons is axially symmetric for weak polar interaction. For a sufficiently strong ferromagnetic interaction, we observe the emergence of a fully asymmetric vortex-bright soliton as the ground state. We also numerically investigate moving solitons. The present mean-field model is not Galilean invariant, and we use a Galilean-transformed mean-field model for generating the moving solitons.
We study the phase separation in three-component bright vector solitons in a quasi-one-dimensional spin-orbit-coupled hyperfine spin F=1F=1F=1 ferromagnetic Bose-Einstein condensate upon an increase of the strength of spin-orbit (SO) coupling ${p}_{x}{\mathrm{\ensuremath{\Sigma}}}_{z}$ above a critical value, where px{p}_{x}px​ is the linear momentum and ${\mathrm{\ensuremath{\Sigma}}}_{z}$ is the zzz component of the spin-1 matrix. The bright vector solitons are demonstrated to be mobile and dynamically stable. The collision between two such vector solitons is found to be elastic at all velocities with the conservation of density of each vector soliton. The two colliding vector solitons repel at small separation and at very small colliding velocity, they come close and bounce back with the same velocity without ever encountering each other. This repulsion produced by SO coupling is responsible for the phase separation in a vector soliton for large strengths of SO coupling. The collision dynamics is found to be completely insensitive to the relative phase of the colliding solitons. However, in the absence of SO coupling, at very small velocity, the two colliding vector solitons attract each other and form a vector soliton molecule and the collision dynamics is sensitive to the relative phase as in scalar solitons. The present investigation is carried out through a numerical solution and an analytic variational approximation of the underlying mean-field Gross-Pitaevskii equation.
We study the vortex-bright solitons in a quasi-two-dimensional spin-orbit-coupled (SO-coupled) hyperfine spin-1 three-component Bose-Einstein condensate using variational method and numerical solution of a mean-field model. The ground state of these vortex-bright solitons is radially symmetric for weak ferromagnetic and polar interactions. For a sufficiently strong ferromagnetic interaction, we observe the emergence of an asymmetric vortex-bright soliton as the ground state. We also numerically investigate stable moving solitons and binary collision between them. The present mean-field model is not Galilean invariant, and we use a Galilean-transformed model for generating the moving solitons. At low velocities, the head-on collision between two in-phase solitons results either in collapse or fusion of the soliton pair. On the other hand, in head-on collision, the two out-of-phase solitons strongly repel each other and trace back their trajectories before the actual collision. At low velocities, in a collision with an impact parameter, the out-of-phase solitons get deflected from their original trajectory like two rigid classical disks. These out-of-phase solitons behave like classical disks, and their collision dynamics is governed by classical laws of motion. However, at large velocities two SO-coupled spinor solitons, irrespective of phase difference, can pass through each other in a head-on collision like two quantum solitons.
We study the formation of solitons in a uniform quasi-one-dimensional (quasi-1D) spin-orbit (SO) coupled self-repulsive pseudo spin-half and spin-one dipolar Bose-Einstein condensates (BEC), using the mean-field Gross-Pitaevskii equation. The dipolar atoms are taken to be polarized along the quasi-1D xxx direction. In the pseudo spin-half case, for small SO-coupling, one can have dark-bright and bright-bright solitons. For large SO coupling, the dark-bright and bright-bright solitons may acquire a spatially-periodic modulation in density; for certain values of contact interaction paramerers there is only the normal bright-bright soliton without spatially-periodic modulation in density. In the spin-one anti-ferromagnetic case, for small SO coupling, one can have bright-bright-bright, dark-bright-dark, and bright-dark-bright solitons; and for large SO coupling, the dark-bright-dark and bright-dark-bright solitons are found to have spatially-periodic modulation in density. In the spin-one ferromagnetic case, for both small and large SO coupling, we find only bright-bright-bright solitons. All these solitons, specially those with a dark-soliton component, are dynamically stable as demonstrated by real-time propagation using the converged stationary solution obtained by imaginary-time propagation as the initial state.