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arXiv:2409.07076 · Physica Scripta

Josephson effect and self-trapping in helicoidal spin-orbit coupled Bose–Einstein condensates with optical lattices

Sumaita Sultana, Golam Ali Sekh

Published Jul 10, 2025• 1 citation
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Abstract

Abstract We consider matter-wave bright solitons in helicoidal spin-orbit coupled Bose–Einstein condensates in optical lattices with a view to study Josephson-type oscillation and self-trapping of population imbalance between two pseudo-spin states. For fixed values of nonlinear interaction and lattice parameters, the population imbalance executes Josephson-type oscillation and the frequency of oscillation decreases with the increase of helicoidal gauge potential. The frequency of oscillation, however, increases in presence of nonlinear optical lattices. We find that the population imbalance can oscillate about a non-zero value and result self-trapping for proper choices of parameters of the system. The self-trapping can be enhanced by the increase of helicoidal gauge potential and by properly tuning the lattice parameters.

DOI
10.1088/1402-4896/adee6c

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Abstract We consider matter-wave bright solitons in helicoidal spin-orbit coupled Bose–Einstein condensates in optical lattices with a view to study Josephson-type oscillation and self-trapping of population imbalance between two pseudo-spin states. For fixed values of nonlinear interaction and lattice parameters, the population imbalance executes Josephson-type oscillation and the frequency of oscillation decreases with the increase of helicoidal gauge potential. The frequency of oscillation, however, increases in presence of nonlinear optical lattices. We find that the population imbalance can oscillate about a non-zero value and result self-trapping for proper choices of parameters of the system. The self-trapping can be enhanced by the increase of helicoidal gauge potential and by properly tuning the lattice parameters.
Abstract We consider matter–wave solitons in spin–orbit coupled Bose–Einstein condensates embedded in an optical lattice and study the dynamics of the soliton within the framework of Gross–Pitaevskii equations. We express spin components of the soliton pair in terms of nonlinear Bloch equations and investigate the effective spin dynamics. It is seen that the effective magnetic field that appears in the Bloch equation is affected by optical lattices, and thus the optical lattice influences the precessional frequency of the spin components. We make use of numerical approaches to investigate the dynamical behavior of density profiles and center-of-mass of the soliton pair in the presence of the optical lattice. It is shown that the spin density is periodically varying due to flipping of spinors between the two states. The amplitude of spin-flipping oscillation increases with lattice strength. We find that the system can also exhibit interesting nonlinear behavior for chosen values of parameters. We present a fixed point analysis to study the effects of optical lattices on the nonlinear dynamics of the spin components. It is seen that the optical lattice can act as a control parameter to change the dynamical behavior of the spin components from periodic to chaotic.
Abstract We investigate ground-state phase diagram of helicoidal spin-orbit coupled Bose-Einstein condensates in a harmonic trap when the intraspecies interaction ggg and the interspecies interaction g↑↓g_{\uparrow\downarrow}g↑↓​ are unequal. In the case of g>g↑↓g>g_{\uparrow\downarrow}g>g↑↓​, increasing the strength of the helicoidal spin-orbit coupling can induce a multiple-peak matter-wave structure with small oscillation amplitude. In the case of g＜g↑↓g＜g_{\uparrow\downarrow}g＜g↑↓​, increasing the strength of the helicoidal spin-orbit coupling can induce a multiple-peak matter-wave structure with large oscillation amplitude. Our findings show that the helicoidal spin-orbit coupling plays a crucial role in inducing multiple-peak matter waves. Adjusting the spin-orbit coupling strength and the gauge potential can control the number of wave peaks. Finally, we also discuss the ground-state properties under different Zeeman splitting parameters when the helicoidal spin-orbit coupling strength and the gauge potential are fixed.
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.
We investigate families of soliton solutions in a spin-orbit-coupled Bose-Einstein condensate embedded in an optical lattice, which bifurcate from the nearly flat lowest band. Unlike the conventional gap solitons, the obtained solutions have the shape well approximated by a Wannier function (or a few Wannier functions) of the underlying linear Hamiltonian with amplitudes varying along the family and with nearly constant widths. The Wannier solitons sharing all symmetries of the system Hamiltonian are found to be stable. Such solutions allow for the construction of Wannier breathers that can be viewed as nonlinearly coupled one-hump solitons. The breathers are well described by a few-mode model and manifest stable behavior either in an oscillatory regime with balanced average populations or in a self-trapping regime characterized by unbalanced atomic populations of the local potential minima (similarly to the conventional boson Josephson junction), with the frequencies controlled by the interatomic interactions.
The stationary bright solitons that appear in the ground state of the spin-orbit coupled Bose-Einstein condensate (SOC-BEC) exhibit nodes. We consider SOC-BEC in combined linear and nonlinear optical lattices and study their effects on the matter-wave bright soliton and find that the parameters of the nonlinear lattice or atomic scattering length can be judiciously manipulated to have useful control over the nodes of the soliton. It is seen that the soliton with large number of nodes is less stable compared to one having fewer number of nodes. We infer that that the synthetic spin-orbit coupling induces instability in the ordinary matter-wave soliton.
The existence and dynamics of solitons in quasi-one-dimensional Bose-Einstein condensates with spin-orbit coupling (SOC) and attractive two-body interactions are described for two coupled atomic pseudospin components with slowly and rapidly varying time-dependent Raman frequency. By varying the Raman frequency linearly in time, it was shown that ordinary nonlinear Schr\"odinger-type bright solitons can be converted to striped bright solitons, and vice versa. The internal Josephson oscillations between atom number of the coupled soliton components and the corresponding center-of-mass motion are studied for different parameter configurations. In this case, a mechanism to control the soliton parameters is proposed by considering parametric resonances, which can emerge when using time-varying Raman frequencies. Full-numerical simulations confirm variational analysis predictions when applied to the region where regular solitons are expected. In the limit of high frequencies, the system is described by a time-averaged Gross-Pitaevskii formalism with renormalized nonlinear and SOC parameters and modified phase-dependent nonlinearities. By comparing full-numerical simulations with averaged results, we have also studied the lower limits for the frequency of Raman oscillations in order to obtain stable soliton solutions.