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Results in Physics

Vortex lattices in a rotating spin-orbit coupled spin-1/2 Bose-Einstein condensates with spatially modulated nonlinear interaction

Ji-Guo Wang, Yueqing Li

Published Apr 11, 2020• 12 citations
Publisher

Abstract

We study the ground-state phases of a two-dimensional rotating spin-orbit coupled spin-1/2 Bose-Einstein condensates with constant interaction and spatially modulated nonlinear interaction, respectively. By comparing with the ground-state phases with constant interaction, the spatially modulated nonlinear interaction not only promotes the realization of ground-state phase but also protects the stability of the vortex line structure. Under the action of the spatially modulated nonlinear interaction, we find that the number of vortices in the every layer along the azimuthal direction successively increases as the rotational frequency enhances, and the vortices are uniformed distributed around the center. The ground-state phase diagram with spatially modulated nonlinear interaction is also studied, a variety of the vortex lattice phases are found.

DOI
10.1016/j.rinp.2020.103099

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We study the ground-state phases of a two-dimensional rotating spin-orbit coupled spin-1/2 Bose-Einstein condensates with constant interaction and spatially modulated nonlinear interaction, respectively. By comparing with the ground-state phases with constant interaction, the spatially modulated nonlinear interaction not only promotes the realization of ground-state phase but also protects the stability of the vortex line structure. Under the action of the spatially modulated nonlinear interaction, we find that the number of vortices in the every layer along the azimuthal direction successively increases as the rotational frequency enhances, and the vortices are uniformed distributed around the center. The ground-state phase diagram with spatially modulated nonlinear interaction is also studied, a variety of the vortex lattice phases are found.
Abstract We study the ground-state phases of two-dimensional rotating spin–orbit coupled spin-1/2 Bose–Einstein condensates (BECs) in a gradient magnetic field. The competition between gradient magnetic field, spin–orbit coupling and rotation leads to a variety of ground-state phase structures. In the weakly rotation regime, as the increase of gradient magnetic field strength, the BECs experiences a phase transition from the unstable phase to the single vortex-line phase. The unstable phase presents the vortex lines structures along the off-diagonal direction. With magnetic field gradient strength increasing, the number of vortex lines changes accordingly. As the magnetic field gradient strength increases further, the single vortex-line phase with a single vortex line along the diagonal direction is formed. The phase diagram shows that the boundary between the two phases is linear with the relative repulsion λ ≥ 1 and is nonlinear with λ < 1. In the relatively strong rotation regime, in addition to the unstable phase and the single vortex-line phase, the vortex-ring phase is formed for the strong magnetic field gradient and rapid rotation. The vortex-ring phase shows the giant and hidden vortex structures at the center of ring. The strong magnetic field gradient makes the number of the vortices around the ring unchanged.
We study the ground-state phases of two-dimensional spin-orbit coupled spin-1 Bose-Einstein condensate loaded in a plane quadrupole field. In the absence of rotation, for the fixed spin-orbit coupling strength, the ordinary stripe phase is found when the strength of the magnetic field gradient is small. As the strength of magnetic field gradient enhances, the system realizes the phases with three layer vortices along the radial direction. The number of vortices in the second layer is successively increased and the vortices in the outermost layer disappear when the strength of magnetic field gradient surpass the critical value. For the large strength of magnetic field gradient, the system only has the inner layer vortices. The magnetic field inhibits the region of vortices. For the fixed magnetic field gradient strength, the vortices of the system elongate along the radial direction and form a series of vortex lines, the number of the vortex line increases as the strength of spin-orbit coupling enhances. By adding the rotation, for the fixed strengths of spin-orbit coupling and magnetic field gradient, the number of second layer vortices also successively increases as the rotational frequency increases. The number of vortices in the certain layer of the ground-state density can be regularly changed under the effects of the magnetic field and spin-orbit coupling.
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.
Abstract We consider the ground-state properties of a rotating spin-orbit-coupled Bose—Einstein condensate under extreme elongation in a harmonic plus quartic potential. The effects of spin-orbit coupling and rotation on the ground-state vortex structures are investigated. In the absence of spin-orbit coupling, new nucleated vortices gradually form vortex lines and annular vortex structures with the increase of the rotation frequency. In the presence of spin-orbit coupling, part of the vortices arrange in a line and form a stable vortex chain, and the remanent vortices coexist in pairs aside such vortex chain. More specially, the remanent vortices of each component repel each other and form vortex pair for isotropic spin-orbit coupling, while attract each other and locate in the same positions for anisotropic spin-orbit coupling.
The Gross–Pitaevskii equation for two-component rotating Bose–Einstein condensates with the Rashba-type spin–orbit (SO) coupling is studied with numerical simulations and variational analyses. A multiquantum vortex state becomes a ground state in a harmonic potential when mutual interaction is absent. When the attractive interaction is strong, the multiquantum vortex state exhibits modulational instability in the azimuthal direction, and a soliton-like state appears. When the repulsive interaction is strong, a vortex lattice state with a multiquantum vortex at the center is created. We find that the vortex lattice state is approximated at a linear combination of multiquantum vortex states.
The interplay of quantum fluctuation through the Lee-Huang-Yang (LHY) correction and spin-orbit coupling can modify the stability of the ultradilute Bose-Bose mixtures and result in rich nonlinear physics. Here, under the action of spin-orbit coupling, LHY correction, and rotation, the ground state and vortex excitation of spin-orbit coupled Bose-Einstein condensates (BECs) with LHY correction trapped in a rotating potential are studied. Stable isotropic and anisotropic ground states with zero momentum (in the zero-momentum phase) and nonzero momentum (in the plane wave phase) are obtained. It is shown that anisotropic ground states are persistent near the phase boundary. Particularly, unpolarized and polarized vortex states are predicted. The phase transition condition, the effective mass and quadrupole surface mode describing the anisotropic (deformation) of the condensates, and the critical rotation frequency for vortex excitation are provided analytically. Owing to the action of spin-orbit coupling, the effective mass of the condensates is spatially dependent and asymmetric in two phases, resulting in distinct quadrupole modes, deformations, and vortex excitations in the two phases, especially when the LHY correction is present. The LHY correction promotes the system in the zero-momentum phase with unpolarized vortex states, while the spin-orbit coupling promotes the emergence of a plane wave phase with polarized vortex states. The phase transition and vortex excitation can be well manipulated by spin-orbit coupling, Raman coupling, LHY correction, and external potential.