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Communications in Nonlinear Science and Numerical Simulation

One-dimensional localized modes of spin-orbit-coupled Bose-Einstein condensates with spatially periodic modulated atom-atom interactions: Nonlinear lattices

Junbo Chen, Jianhua Zeng

Published Feb 7, 2020• 17 citations
Publisher
DOI
10.1016/j.cnsns.2020.105217

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We propose a scheme for spin squeezing in the orbital motion of a Bose-Einstein condensate in a toroidal trap. A circular lattice couples two counterrotating modes and squeezing is generated by the nonlinear interaction spatially modulated at half the lattice period. By varying the amplitude and phase of the modulation, various cases of the twisting tensor can be directly realized, leading to different squeezing regimes. These include the one-axis twisting and two-axis countertwisting that are often discussed as the most important paradigms for spin squeezing. Our scheme naturally realizes the Lipkin-Meshkov-Glick model with the freedom to vary all its parameters simultaneously.
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.
Applying a variational approach and numerical analysis to the system of Gross-Pitaevskii equations, we find three-dimensional (3D) stable solitons in binary atomic Bose-Einstein condensates with spin-orbit coupling (SOC) and out-of-phase linear and nonlinear Bessel optical lattices. We discuss the stability of 3D solitons by utilizing their norm and energy. The introduction of Bessel potentials makes the evolution and collisions of solitons more stable and improves their resistance to collapse. Depending on the strength of the intra- and intercomponent spatial modulation of the nonlinearity and SOC, we find stable solitons of the semivortex and mixed-mode structures. Furthermore, we show that the solitons are stable against small perturbations in propagation and collisions.