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Chinese Physics B

Lattice configurations in spin-1 Bose–Einstein condensates with the SU(3) spin–orbit coupling*

Ji-Guo Wang, Yueqing Li, Yu-Fei Dong

Published Aug 1, 2020• 8 citations
Publisher

Abstract

We consider the SU(3) spin–orbit coupled spin-1 Bose–Einstein condensates in a two-dimensional harmonic trap. The competition between the SU(3) spin–orbit coupling and the spin-exchange interaction results in a rich variety of lattice configurations. The ground-state phase diagram spanned by the isotropic SU(3) spin–orbit coupling and the spin–spin interaction is presented. Five ground-state phases can be identified on the phase diagram, including the plane wave phase, the stripe phase, the kagome lattice phase, the stripe-honeycomb lattice phase, and the honeycomb hexagonal lattice phase. The system undergoes a sequence of phase transitions from the rectangular lattice phase to the honeycomb hexagonal lattice phase, and to the triangular lattice phase in spin-1 Bose–Einstein condensates with anisotrpic SU(3) spin–orbit coupling.

DOI
10.1088/1674-1056/abab72

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We study the ground-state phases of two-dimensional spin-orbit coupled spin-2 Bose-Einstein condensates in a one-dimensional spin-dependent optical lattice. Due to the competition among optical lattice, spin-orbit coupling and spin-exchange interaction, the exotic ground-state phases are found, i.e. three types of the stripe phases and three types of the supersolid phases. The spin-exchange interaction can adjust the direction of the stripe in the stripe phase and generate various vortex lattice structures in the supersolid phase, which shows that the spin-exchange interaction plays an important role in the formation of the stripe and supersolid phases of spin-orbit coupled spin-2 Bose-Einstein condensates in an optical lattice.
We consider a SU(3) spin-orbit-coupled Bose gas with nonlocal soft-core interactions confined in a harmonic trapping potential. The presence of SU(3) spin-orbit coupling induces three minima of the single-particle spectrum. In the absence of spin-exchange interaction, our results show that regardless of the sign of the soft-core interaction, the ground state occupies one single minimum in the momentum space and corresponds to a threefold-degenerate magnetized phase. For the ferromagnetic condensate, the ground state shows an amplitude-modulated plane-wave state, where its modulated amplitude and frequency are related to the strength of the soft-core interaction and SU(3) spin-orbit coupling, respectively. In particular, due to the subtle balance of the soft-core interaction and SU(3) spin-orbit coupling, a stable higher-order spin vortex lattice can be formed in the lattice phase of an antiferromagnetic condensate, where the density distributions of each component and the total system show spatial configurations with threefold and sixfold symmetries, respectively. We also give an experimental protocol to observe such states within current experimental capacity.
We study trapped 2D atomic Bose-Einstein condensates with spin-independent interactions in the presence of an isotropic spin-orbit coupling, showing that a rich physics results from the nontrivial interplay between spin-orbit coupling, confinement and interatomic interactions. For low interactions two types of half-vortex solutions with different winding occur, whereas strong-enough repulsive interactions result in a stripe-phase similar to that predicted for homogeneous condensates. Intermediate interaction regimes are characterized for large enough spin-orbit coupling by an hexagonally-symmetric phase with a triangular lattice of density minima similar to that observed in rapidly rotating condensates.
We consider two-dimensional spinor F = 1 Bose–Einstein condensates in two types of radially-periodic potentials with spin–orbit coupling, i.e. , spin-independent and spin-dependent radially-periodic potentials. For the Bose–Einstein condensates in a spin-independent radially-periodic potential, the density of each component exhibits the periodic density modulation along the azimuthal direction, which realizes the necklacelike state in the ferromagnetic Bose–Einstein condensates. As the spin-exchange interaction increases, the necklacelike state gradually transition to the plane wave phase for the antiferromagnetic Bose–Einstein condensates with larger spin–orbit coupling. The competition of the spin-dependent radially-periodic potential, spin–orbit coupling, and spin-exchange interaction gives rise to the exotic ground-state phases when the Bose–Einstein condensates in a spin-dependent radially-periodic potential.
We study the ground-state phases of a two-dimensional rotating spin-orbit–coupled Bose-Einstein condensate loaded in a one-dimensional spin-dependent optical lattice. In the absence of rotation, the system undergoes a phase transition from the stripe phase to the supersolid phase gradually for weak spin-orbit coupling strength and directly for strong spin-orbit coupling strength as the depth of the optical lattice increases. With increasing the rotation strength, the stripe phase transforms to the ringlike state, and the domain number of the ringlike state increases when the Bose-Einstein condensate is in the weak depth of the optical lattice. The supersolid phase transforms to the phase with a single domain of a vortex line for small rotation strength, and alternating vortex lines along the x -direction appear for large rotation strength when the Bose-Einstein condensate is in the strong depth of the optical lattice. The spin textures of the ground-state phases are also discussed.