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Chinese Physics B

Spinor F = 1 Bose-Einstein condensates loaded in two types of radially-periodic potentials with spin-orbit coupling*

Ji-Guo Wang, Yueqing Li, Han-Zhao Tang, Ya-Fei Song

Published Jul 14, 2021• 2 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/ac1411

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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 investigate the ground states of spin-1 Bose–Einstein condensates (BECs) with spin–orbit coupling in a radially periodic potential by numerically solving the coupled Gross–Pitaevskii equations. In the radially periodic potential, we first demonstrate that spin–orbit-coupled antiferromagnetic BECs support a multiring petal phase. Polar–core vortex can be observed from phase profiles, which is manifested as circularly symmetric distribution. We further show that spin–orbit coupling can induce multiring soliton structure in ferromagnetic BECs. It is confirmed especially that the wave-function phase of the ring corresponding to uniform distribution satisfies the rotational symmetry, and the wave-function phase of the ring corresponding to partial splitting breaks the rotational symmetry. Adjusting the spin–orbit coupling strength can control the number of petal in antiferromagnetic BECs and the winding numbers of wave-function in ferromagnetic BECs. Finally, we discuss effects of spin-independent and spin-dependent interactions on the ground states.
We consider the spin-1 Bose-Einstein condensates with the isotropic Rashba spin-orbit coupling in a two-dimensional toroidal trap. Three types of striped phases are found in a nonrotational system, i.e., the stripe phase with the periodic density modulation along the azimuthal direction, the stripe phase with the periodic density modulation along both the azimuthal and the radial directions, and the stripe phase with the periodic density modulation along the radial direction. By adding the rotation, the condensates occupy the mF=0{m}_{F}=0mF​=0 component for small rotational frequency, while they occupy both the mF=1{m}_{F}=1mF​=1 and ${m}_{F}=\ensuremath{-}1$ components for large rotational frequency when both the relative interaction and the spin-orbit coupling are weak. For the stronger relative interaction and spin-orbit coupling, the vortices of the system are elongated along the radial direction and linked one after another. As the rotational frequency further increases, the density evolves from the elongated effect of the vortices into a laminar vortex ring.
We consider a pseudospin-1/2 Bose–Einstein condensate with Rashba type of spin–orbit coupling and trapped in radially periodic potentials. The effects of spin–orbit coupling, amplitude of the lattice potential, and contact interaction, on the ground-state phases of the system are investigated numerically for two different types of radial lattices, i.e., with phase constant δ = 0 and π. We show that the system has a rich variety of ground-state phases, showing strong dependence on these controllable parameters. In addition, we find that for both types of radial lattices, such parameters can be used to induce desirable ground-state structures.
We consider two-dimensional spin-orbit-coupled atomic Bose-Einstein condensate in a radially periodic potential. The system supports different types of stable self-sustained states including radially symmetric vorticity-carrying modes with different topological charges in two spinor components that may have multiring profiles and at the same time remain remarkably stable for repulsive interactions. Solitons of the second type show persistent rotation with constant angular frequency. They can be stable for both repulsive and attractive interatomic interactions. Because of the inequivalence between clockwise and counterclockwise rotation directions introduced by spin-orbit coupling, the properties of such solitons strongly differ for positive and negative rotation frequencies. The collision of solitons located in the same or different rings is accompanied by a change of the rotation frequency that depends on the phase difference between colliding solitons.
We study the ground-state phases of spin–orbit coupled spin-2 Bose–Einstein condensates in a two-dimensional concentrically coupled annular trap with the attractive and repulsive spin-exchange interactions, respectively. For the system with the attractive spin-exchange interaction, the ground-state phase densities in the inner ring show the bright solitons along the azimuthal direction with the weak spin–orbit coupling strength and the vortex line along the radial direction with the strong spin–orbit coupling strength. For the system with the repulsive spin-exchange interaction, the necklace-like state is shown. The number of petals of the necklace-like state continuous growth as the spin–orbit coupling strength enhanced. The momentum distributions of the ground-state phases are also studied.
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.