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arXiv:2212.10145 · Physical Review A

Bessel vortices in spin-orbit-coupled spin-1 Bose-Einstein condensates

Jun-Zhu Li, Huan-Bo Luo, Lu Li

Published Dec 30, 2022• 6 citations
arXivHTMLPDF

Abstract

We investigate the stationary vortex solutions in two-dimensional Rashba spin-orbit-coupled spin-1 Bose-Einstein condensates. By introducing the generalized momentum operator, the linear version of the system can be solved exactly and its solutions are a set of the Bessel vortices. Based on the linear version solutions, the stationary vortex solutions of the full nonlinear system are constructed and determined entirely by the variational approximation. The results show that the variational results are in good agreement with the numerical ones. By means of the variational results, the vortex ground-state phase transition between the stationary vortex solutions, the stability, and the unit Bloch vector textures are discussed in detail. The results have the potential to be realized in experiment.

DOI
10.1103/physreva.106.063321

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We investigate the stationary vortex solutions in two-dimensional Rashba spin-orbit-coupled spin-1 Bose-Einstein condensates. By introducing the generalized momentum operator, the linear version of the system can be solved exactly and its solutions are a set of the Bessel vortices. Based on the linear version solutions, the stationary vortex solutions of the full nonlinear system are constructed and determined entirely by the variational approximation. The results show that the variational results are in good agreement with the numerical ones. By means of the variational results, the vortex ground-state phase transition between the stationary vortex solutions, the stability, and the unit Bloch vector textures are discussed in detail. The results have the potential to be realized in experiment.
Abstract We investigate the ground states of spin–orbit coupled spin-1 Bose–Einstein condensates in the presence of Zeeman splitting. By introducing the generalized momentum operator, the linear version of the system is solved exactly, yielding a set of Bessel vortices. Additionally, based on linear solution and using variational approximation, the solutions for the full nonlinear system and their ground state phase diagrams are derived, including the vortex states with quantum numbers m = 0, 1, as well as mixed states. In this work, mixed states in spin-1 spin–orbit coupling (SOC) BEC are interpreted for the first time as weighted superpositions of three vortex states. Furthermore, the results also indicate that under strong Zeeman splitting, the system cannot form localized states. The variational solutions align well with numerical simulations, showing stable evolution and meeting the criteria for long-term observation in experiments.
Static and dynamic properties of vortices in a two-component Bose-Einstein condensate with Rashba spin-orbit coupling are investigated. The mass current around a vortex core in the plane-wave phase is found to be deformed by the spin-orbit coupling, and this makes the dynamics of the vortex pairs quite different from those in a scalar Bose-Einstein condensate. The velocity of a vortex-antivortex pair is much smaller than that without spin-orbit coupling, and there exist stationary states. Two vortices with the same circulation move away from each other or unite to form a stationary state.
The present contribution explores phase transitions that occur in the ground state (GS) of spin-1 Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) under the action of gradient magnetic fields. By solving the corresponding linearized system in an exact fashion, we identify the conditions under which the GS phase transitions occur, thus transforming excited states into GS. The study of the full nonlinear system, including both density-density and spin-spin interactions, is numerically analyzed. For the case of repulsive spin-spin interactions, the results resemble the linear case, while attractive spin-spin interactions lead to the formation of mixed-states near the GS phase-transition points. Additionally, higher-order vortex solitons are found to be stable even in the nonlinear regime. These findings demonstrate that arbitrary winding numbers can be achieved as corresponding to stable GS and thus contributing to the understanding of topological properties in SOC BECs.
We investigate vortex states in Bose-Einstein condensates under the combined action of the spin-orbit coupling (SOC), gradient magnetic field, and harmonic-oscillator trapping potential. The linear version of the system is solved exactly. Through the linear-spectrum analysis, we find that by varying the SOC strength and magnetic-field gradient one can perform energy-level inversion. With suitable parameters, initial higher-order vortex states can be made the ground state (GS). The nonlinear system is solved numerically, revealing that the results are consistent with the linear predictions in the case of repulsive intercomponent interactions. On the other hand, intercomponent attraction creates the GS in the form of mixed-mode states in a vicinity of the GS phase-transition points. The spin texture of both vortex- and mixed-mode GSs reveals that they feature the structure of 2D (baby) skyrmions.
We study the vortex-lattice formation in a rotating Rashba spin-orbit (SO) coupled quasi-two-dimensional (quasi-2D) hyper-fine spin-1 spinor Bose-Einstein condensate (BEC) in the x-y plane using a numerical solution of the underlying mean-field Gross-Pitaevskii equation. In this case, the non-rotating Rashba SO-coupled spinor BEC can have topological excitation in the form of vortices of different angular momenta in the three components, e.g. the (0, +1, +2)- and (-1, 0, +1)-type states in ferromagnetic and anti-ferromagnetic spinor BEC: the numbers in the parenthesis denote the intrinsic angular momentum of the vortex states of the three components with the negative sign denoting an anti-vortex. The presence of these states with intrinsic vorticity breaks the symmetry between rotation with vorticity along the z and -z axes and thus generates a rich variety of vortex-lattice and anti-vortex-lattice states in a rotating quasi-2D spin-1 spinor ferromagnetic and anti-ferromagnetic BEC, not possible in a scalar BEC. For weak SO coupling, we find two types of symmetries of these states - hexagonal and 'square'. The hexagonal (square) symmetry state has vortices arranged in closed concentric orbits with a maximum of 6, 12, 18… (8, 12, 16…) vortices in successive orbits. Of these two symmetries, the square vortex-lattice state is found to have the smaller energy.
We analyze the dynamics of Josephson vortex states in two-component Bose-Einstein condensates with Rashba-Dresselhaus spin-orbit coupling by using the Gross-Pitaevskii equation. In one dimension, both in homogeneous and harmonically trapped systems, we report on stationary states containing doubly charged, static Josephson vortices. In multidimensional systems, we find stable Josephson vortices in a regime of parameters typical of current experiments with 87Rb^{87}\text{Rb}87Rb atoms. In addition, we discuss the instability regime of Josephson vortices in disk-shaped condensates, where the snake instability operates and vortex dipoles emerge. We study the rich dynamics that they exhibit in different regimes of the spin-orbit-coupled condensate depending on the orientation of the Josephson vortices.