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Physical review. E

Solitary matter wave in spin-orbit-coupled Bose-Einstein condensates with helicoidal gauge potential

X. X. Li, Rui-Jin Cheng, Ji-Li Ma, Ai‐Xia Zhang, Ju-Kui Xue

Published Sep 21, 2021• 13 citations
Publisher

Abstract

We analytically and numerically study the different types of solitary wave in the two-component helicoidal spin-orbit coupled Bose-Einstein condensates (BECs). Adopting the multiscale perturbation method, we derive the analytical bright and dark solitary wave solutions of the system, and the stationary and moving bright (dark) solitary waves are obtained. The effects of spin-orbit coupling, the helicoidal gauge potential, the momentum, the Zeeman splitting, and the atomic interactions on the solitary wave types are discussed, and it is found that the coupling of these physical parameters can manipulate different types of solitary waves in the system. The results indicate that the helicoidal gauge potential breaks the symmetric properties of the energy band of the system and adjusts the energy band structure, thus further effecting the solitary wave properties, i.e., stationary or moving solitary wave, bright, or dark solitary wave. Correspondingly, the analytical predictions for exciting stationary or moving bright (dark) solitary wave in parameter space are obtained. In particular, the helicoidal gauge potential changes the solitary wave types drastically for the weak spin-orbit coupling, i.e., in the absence of the helicoidal gauge potential, only dark (bright) solitary wave solutions exist in the system with repulsive (attractive) atomic interaction; however, in the presence of the helicoidal gauge potential, both dark and bright solitary waves can exist in the system regardless of whether the atomic interaction is repulsive or attractive. In addition, we investigate the stability of solitary waves and obtain the stability regions of different types of solitary waves by applying the linear stability analysis. The dynamic evolution results of the solitary waves by the direct numerical simulation not only validate the linear stability analysis but also confirm the analytical prediction of the solitary waves. Finally, the collision effects between solitary waves are also presented by the numerical simulation. It is shown that the interactions between solitary waves in the system have both elastic and inelastic collisions, which are closely related to the position of solitary wave states in the linear energy band. Our results provide a potential way to adjust the types of solitary waves in BECs with helicoidal gauge potential.

DOI
10.1103/physreve.104.034214

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We theoretically study the modulation instability (MI) of the two-component helicoidal spin-orbit coupled Bose-Einstein condensates (BECs). The effects of spin-orbit coupling, the helicoidal gauge potential, and atomic interactions on MI are investigated. The results indicate that the presence of the helicoidal gauge potential breaks the symmetric properties of MI, strongly modifies the distribution of the MI region and the MI gain in parameters space, and the MI can be excited even when the miscibility condition for the atomic interactions is satisfied. Furthermore, the effect of the helicoidal gauge potential on MI is strongly coupled with the intra and intercomponent atomic interactions. Particularly, with the increase of the helical gauge potential, the MI gain increases for the repulsive atomic interaction case, however, the MI gain decreases for the attractive atomic interaction case. The direct numerical simulations are performed to support the analytical predictions, and a good agreement is found. Our results provide a potential way to manipulate the MI in BECs with helicoidal gauge potential.
We investigate the matter-wave solitons in a spin–orbit-coupled spin-1 Bose–Einstein condensate using a multiscale perturbation method. Beginning with the one-dimensional spin–orbit-coupled threecomponent Gross–Pitaevskii equations, we derive a single nonlinear Schrödinger equation, which allows determination of the analytical soliton solutions of the system. Stationary and moving solitons in the system are derived. In particular, a parameter space for different existing soliton types is provided. It is shown that there exist only dark or bright solitons when the spin–orbit coupling is weak, with the solitons depending on the atomic interactions. However, when the spin–orbit coupling is strong, both dark and bright solitons exist, being determined by the Raman coupling. Our analytical solutions are confirmed by direct numerical simulations.
Solitons as self-supported solitary waves are one of the most fundamental objects in nonlinear science. With the realization of Bose-Einstein condensate, matter-wave solitons have aroused enormous interest due to their potential applications in atomic transport and atomic interferometer. In recent years, the artificial spin-orbit coupling has been realized in ultracold atoms, thus providing a new platform to study the nonlinear matter wave solitons under a gauge field, and a variety of novel soliton phenomena have been successively predicted. In this paper, we analyze the effects of linear Zeeman splitting on the dynamics of bright-bright solitons in spin-orbit coupled two-component Bose-Einstein condensate, via the variational approximation and the numerical simulation of Gross-Pitaevskii (GP) equations. For the SU(2) spin-rotational invariant attractive atomic interaction in a uniform case without external trap, we take a hyperbolic secant function as the variational Ansatz for bright soliton in variational approximation, and derive the Euler-Lagrange equations describing the evolution of the Ansatz parameters. By solving the time-independent Euler-Lagrange equations, we find two stationary solitons each with a finite momentum for a weak spin-orbit coupling due to the linear Zeeman splitting. Linearizing the Euler-Lagrange equations around these stationary solitons, we further obtain a zero-energy Goldstone mode and an oscillation mode with frequency related to linear Zeeman splitting: the former indicates that the continuous translational symmetry of the stationary solitons will be broken under a perturbation, and the later shows that the stationary solitons will oscillate under a perturbation. Furthermore, by solving the time-dependent Euler-Lagrange equations, we also obtain the exact full dynamical solutions of Ansatz parameters, and observe that the linear Zeeman splitting affects the period and velocity of soliton's oscillation and linear motion, which may provide a new method to control the dynamics of solitons. All the variational calculations are also confirmed directly by the numerical simulation of GP equations.
The paper studies the modulational instability (MI), both theoretically and numerically, of the helicoidal spin-orbit coupled Bose-Bose mixture. An expression of the MI growth rate is found through the linear stability analysis of continuous wave, followed by a comprehensive parametric study of the MI regions, emphasizing the effects of the spin-orbit coupling, the helicoidal gauge potential, and interatomic interactions. Direct numerical simulations concur with the analytical predictions. Under suitable balance between nonlinear and dispersive effects, trains of solitonlike objects are obtained, and their behaviors are very sensitive to parameter variations. Attention is particularly paid to the impact of the left- and right-handed helicoidal spin-orbit couplings on the appearance of matter waves that have the form soliton molecules in the Bose-Bose mixture. Additionally, for qualitative support of the obtained structures, the formation of a bright solitons train is also reported numerically using two neighboring solitons subjected to a fixed phase difference. Their behavior under the action of the helicoidal spin-orbit coupling is also debated, especially when left- and right-handed helicoidal couplings are interchanged.
We investigate the different types of matter-wave solitons in spin-orbit-coupled spin-2 spinor Bose-Einstein condensates. Using mean-field theory and adopting the multiscale perturbation method, the original five-component Gross-Pitaevskii spin-orbit-coupled spin-2 spinor Bose-Einstein condensate model can be reduced to a single effective nonlinear Schrödinger equation, which allows us to find analytical soliton solutions of this system. In this way, for different regimes of the spin-orbit coupling, Raman coupling, and interatomic interactions, we find approximate bright and dark soliton solutions. Particularly, the type of solitons depends on the dispersion properties of the system. When the lowest-energy band has a single-well structure, we find there only exist positive mass bright or dark solitons due to the dispersion coefficient of effective nonlinear Shrödinger equation always positive. However, when the lowest-energy band has a double-well structure, there will appear positive (negative) mass bright or dark solitons because the sign of the dispersion coefficient can be positive (negative) under different momentum. We employ direct numerical simulation of the original five-component Gross-Pitaevskii equations to confirm the analytical results.
We consider solitary wave excitations above the ground state of F=1F=1F=1 spin-orbit-coupled Bose-Einstein condensates (SOBECs). The low-energy properties of SOBECs in any of the three branches of the single-particle dispersion relation can be described by suitable scalar nonlinear Schr\"odinger (NLS) equations which we obtain using multiple-scale expansions. This enables us to examine a variety of different configurations, such as dark solitary waves associated with higher energy branches, as well as dark and bright structures in the lowest branch. The lowest branch can also exhibit a ``superstripe'' phase that supports solitary waves. In all cases, we provide explicit expressions for the NLS coefficients, and confirm their validity with full numerical simulations of the SOBEC system, including a harmonic confining potential.