Ground-state phases of the spin-orbit-coupled spin-1 Bose gas in a toroidal trap

Abstract

We consider the spin-1 Bose-Einstein condensates with the isotropic Rashba spin-orbit coupling in a two-dimensional torodial trap. Three types of striped phases are found in a non-rotational 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 component for small rotational frequency while occupy both the mF = 1 and mF = −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.

Spin-orbit-coupled spin-1 Bose-Einstein condensates in a toroidal trap: even-petal-number necklacelike state and persistent flow

“…It is noting that only necklace states with four times number of petals are numerically found in Ref. [44]. These two different ground states have two common features.…”

“…Ground states and collective excitations of a homogeneously spin-orbit-coupled spin-1 BEC have been investigated theoretically [49][50][51][52][53]. With a toroidal trap, the system is described by the Gross-Pitaevskii equation (GPE) [44,52],…”

“…They are due to Bosons condense simultaneously into multiple energy-minimum states, as distinct from conventional condensations that condense into only one energy minimum. Putting spin-orbitcoupled BECs in a toroidal trap quickly attracts interests [40][41][42][43][44][45][46]. Phase diagram of spin-orbit-coupled spin- * yongping11@t.shu.edu.cn 1/2 BECs in a tight toroidal trap has been identified [41][42][43].…”

“…Spin-orbit-coupled spin-1 BECs support more enriching phases. The effort in existing studies on spin-1 has been put into investigating the interplay between spin-orbit coupling and rotation [44][45][46]. The characteristics of phase diagram for spin-orbit-coupled spin-1 BECs with a toroidal confinement are still lacking.…”

Dynamics of Rotating Spin-Orbit-Coupled Spin-1 Bose-Einstein Condensates With In-Plane Gradient Magnetic Field in an Anharmonic Trap

“…The magnetic field gradient causes a magnetic force so that the condensate is difficult to concentrate at the center and is divided into two parts, and on the other hand, due to the existence of rotation, the competition among the magnetic force, SOC, and the rotation, a vortex chain appears. The vortex chain structure has been observed in the literature [42,43], where only ground states with in-plane gradient magnetic fields are considered. The abovementioned research shows that in the dynamics, the combined effect of gradient magnetic fields, SOC, and rotation play a key role in the generation of exotic topological defects.…”