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Physical review. E

Vector gap solitons of spin-orbit-coupled Bose-Einstein condensate in honeycomb optical lattices

Hongjuan Meng, Jing Wang, Xiaobei Fan, Qingqing Wang, Kaihua Shao, Yuexin Zhao, Wen-Yuan Wang, Yu-Ren Shi

Published Sep 28, 2023• 10 citations
Publisher

Abstract

The combination of the two hot topics of spin-orbit coupling and honeycomb lattices leads to the appearance of fascinating issues. In this paper, we investigate the existence and stability of vector gap solitons of spin-orbit-coupled Bose-Einstein condensates loaded in honeycomb optical lattices. The existence and stability of vector gap solitons are highly sensitive to the properties of interspin and intraspin atomic interaction. We numerically obtain the parametric dependence of the existence of vector gap solitons both in the semi-infinite gap and in the first gap. Since only dynamically stable localized modes in nonlinear systems are likely to be generated and observed in experiments, we examine the stability of the vector gap solitons by using the direct evolution dynamics, and obtain the phase diagram of stable and unstable vector gap solitons on the parameter plane of interspin and intraspin atomic interactions.

DOI
10.1103/physreve.108.034215

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The combination of the two hot topics of spin-orbit coupling and honeycomb lattices leads to the appearance of fascinating issues. In this paper, we investigate the existence and stability of vector gap solitons of spin-orbit-coupled Bose-Einstein condensates loaded in honeycomb optical lattices. The existence and stability of vector gap solitons are highly sensitive to the properties of interspin and intraspin atomic interaction. We numerically obtain the parametric dependence of the existence of vector gap solitons both in the semi-infinite gap and in the first gap. Since only dynamically stable localized modes in nonlinear systems are likely to be generated and observed in experiments, we examine the stability of the vector gap solitons by using the direct evolution dynamics, and obtain the phase diagram of stable and unstable vector gap solitons on the parameter plane of interspin and intraspin atomic interactions.
Abstract Vector gap solitons in quasi-two-dimensional Bose–Einstein condensate loaded in a square optical lattice with spin-orbit and Rabi coupling are investigated theoretically. The solitons are obtained by the Newton-Conjugate-Gradient method for various physical parameters. The stability properties of gap solitons are theoretically analyzed by direct nonlinear dynamical evolution. It is found that the existence of gap solitons is sensitive to the spin-orbit and Rabi coupling strength. Smaller Rabi coupling strength is beneficial for the excitation of solitons in the semi-infinite gap. Conversely, larger Rabi coupling strength is beneficial for the soliton excitation in the first gap. The dynamical stability of these gap solitons depends on the spin-orbit and Rabi coupling strength, and the location of the soliton in the bandgap. These findings may contribute to understanding the topological excitations in condensed matter systems.
Abstract We investigate the properties of gap solitons in spin–orbit-coupled Bose–Einstein condensates in mixed linear–nonlinear optical lattices. The mixed linear–nonlinear optical lattices can support parity-time (PT)-symmetric soliton solutions, and these PT-symmetric solitons can stably exist in the semi-infinite gap of linear optical lattices. The PT-symmetric gap-stripe solitons are found by increasing the strength of the spin–orbit coupling. It is found that the amplitude of the nonlinear optical lattices can significantly affect the stability of these gap and gap-stripe solitons. With an increase of the amplitude of the nonlinear optical lattices, the stable domains of the gap and gap-stripe solitons are shrunk. The unstable solitons can show unique evolution characteristics and the stability analyses are also confirmed by the evolution simulations.
We investigate the existence and dynamical stability of multipole gap solitons in Bose–Einstein condensate loaded in a deformed honeycomb optical lattice. Honeycomb lattices possess a unique band structure, the first and second bands intersect at a set of so-called Dirac points. Deformation can result in the merging and disappearance of the Dirac points, and support the gap solitons. We find that the two-dimensional honeycomb optical lattices admit multipole gap solitons. These multipoles can have their bright solitary structures being in-phase or out-of-phase. We also investigate the linear stabilities and nonlinear stabilities of these gap solitons. These results have applications of the localized structures in nonlinear optics, and may helpful for exploiting topological properties of a deformed lattice.
Abstract In ultracold atomic gases, optical lattices and spin-orbit coupling are two important and useful linear means to study and control the nonlinear and quantum dynamics of matter waves, and both have been well realized in experiments. Here, nonlinear localization of spin-orbit-coupled Bose-Einstein condensates in moiré optical lattices is revealed theoretically, stressing the existence and stability of localized modes of diverse types including fundamental, half-vortex matter-wave gap solitons, and full-vortex ones (of both components). Notably, to our knowledge, a new type of vector vortex gap solitons, which is composed of a gap vortex soliton (singular mode) and a rhombic-array gap vortex (quadruple mode), is predicted in our two-component theoretical framework. It is also found that the model exhibits unique linear Bloch band structures including band splitting and extremely-flat bands, because of which all the predicted localized modes tend to be robustly stable, backed by our direct perturbed simulations. Our results demonstrate that the moiré pattern (and its joint cooperation with spin-orbit coupling) provides great possibilities to explore flat-band and moiré physics in ultracold atoms, and to further investigate the nonlinear dynamics.
Bose–Einstein condensate (BEC) exhibits a variety of fascinating and unexpected macroscopic phenomena, and has attracted sustained attention in recent years—particularly in the field of solitons and associated nonlinear phenomena. Meanwhile, optical lattices have emerged as a versatile toolbox for understanding the properties and controlling the dynamics of BEC, among which the realization of bright gap solitons is an iconic result. However, the dark gap solitons are still experimentally unproven, and their properties in more than one dimension remain unknown. In light of this, we describe, numerically and theoretically, the formation and stability properties of gap-type dark localized modes in the context of ultracold atoms trapped in optical lattices. Two kinds of stable dark localized modes—gap solitons and soliton clusters—are predicted in both the one- and two-dimensional geometries. The vortical counterparts of both modes are also constructed in two dimensions. A unique feature is the existence of a nonlinear Bloch-wave background on which all above gap modes are situated. By employing linear-stability analysis and direct simulations, stability regions of the predicted modes are obtained. Our results offer the possibility of observing dark gap localized structures with cutting-edge techniques in ultracold atoms experiments and beyond, including in optics with photonic crystals and lattices.
Using the parity and time reversal symmetries of a two-dimensional spin-orbit coupled Bose-Einstein condensate in a lattice created by the Zeeman field, we identify and find numerically various families of localized solutions, including multipole and half-vortex solitons. The obtained solutions may exist at any direction of the gauge field with respect to the lattice and can be found either in finite gaps (for repulsive interatomic interactions) or in a semi-infinite gap (for attractive interactions). The existence of half-vortices requires higher symmetry (the reflection with respect to the field direction). Stability of these modes makes them feasible for experimental observation.