We theoretically investigate the dynamics of polar bright soliton under the influence of spin-orbit coupling (SOC) in spin-1 three component Bose-Einstein condensate (BEC). Periodically oscillating dark-bright-dark solitons are found to be induced by the SOC with their multifrequency oscillations jointly determined by the interparticle nonlinear interaction and the SOC strength. Explicit formulas are provided to identify these frequencies, which are in good agreement with the numerical simulation results. A linear Zeeman interaction is further introduced to break the time-reversal symmetry and change the polarity of the spinor BECs, which results in the periodic transition of the system from polar state to ferromagnetic state.
We theoretically investigate the dynamics of polar bright soliton under the influence of spin-orbit coupling (SOC) in spin-1 three component Bose-Einstein condensate (BEC). Periodically oscillating dark-bright-dark solitons are found to be induced by the SOC with their multifrequency oscillations jointly determined by the interparticle nonlinear interaction and the SOC strength. Explicit formulas are provided to identify these frequencies, which are in good agreement with the numerical simulation results. A linear Zeeman interaction is further introduced to break the time-reversal symmetry and change the polarity of the spinor BECs, which results in the periodic transition of the system from polar state to ferromagnetic state.
We demonstrate that the model of a spatially nonuniform two-component Bose-Einstein condensates (BEC) featuring the helicoidal spin-orbit coupling (SOC), gives rise to dark-bright soliton complexes characterized by spatiotemporal periodic oscillations in each component. These solitons are formed by the superposition of dark and bright ones, and exhibit a beating state over time and a striped state across space, earning them the designation of beating stripe solitons. Our analysis demonstrates that helicoidal SOC significantly affects the formation and dynamical properties of these solitons, also serving as the primary driver for spin oscillations. Through the nonlinear superposition of the beating stripe solitons, a range of intricate scenarios of the interaction between multiple solitons emerges, including head-on collisions, bound states, and parallel states.
Abstract We investigate oscillatory soliton pairs including the bright–bright solitons, dark–dark solitons, bright–dark solitons and beating solitons (beating soliton refers to a type of soliton characterized by components that are each composed of both bright and dark solitons, and the overall density is equivalent to that of a single soliton) in the spin-orbit coupled spin-1/2 Bose–Einstein condensates. Two important effects that are the spin orbit coupling (SOC) and Raman detuning resonance on these solitons are studied. The results show that the intensity of SOC affects the spatial oscillation of solitons, while Raman detuning resonance affects the temporal oscillation of solitons. Moreover, the oscillatory soliton pairs and their background are affected by gain/loss. Under different gain/loss modulator, the periodic, parabolic, dromion type and line solitons are constructed for bright–bright pairs, and the periodic and parabolic background planes are presented for dark–dark soliton pairs, as well as the bound state solitons on periodic and kink type background planes are obtained for bright–dark soliton pairs. For one-beating soliton pairs, two types of beating solitons including the petal and breather-like are discovered by adjusting the wave number. For two-beating soliton pairs, the interaction between different combinations of the two types of beating solitons mentioned above, especially the X- and Y-type beating solitons, are presented by controlling two wave numbers. Furthermore, we verify the stability of soliton pairs through numerical simulation and the physics-informed neural network methods.
Abstract We investigate analytically the effects of spin–orbit coupling (SOC) for the dynamics of soliton collisions in spin-1 Bose–Einstein condensates (BECs). Applying the non-standard Hirota’s bilinear method, we derive some exact one- and two-soliton solutions for the one-dimensional system of a spin–orbit coupled spin-1 BEC, which clearly shows how the dynamics of the solitons in spinor BECs can be engineered by SOC. Under SOC, the soliton collisions of ferromagnetic-polar type, ferromagnetic-ferromagnetic type and polar-polar type are discussed in details. Comparisons for the soliton states between the systems with and without SOC are displayed, a remarkable phenomenon is that the SOC can lead to the split of a soliton.
Spin mixing induced dynamics of spinor solitons in F=1 Bose Einstein condensates
We explore soliton interactions in a homogeneous spinor F=1 Bose Einstein Condensate (BEC) in the presence of a magnetic field, focusing on dark bright dark and bright dark bright configurations. We investigate how these interactions depend on the phase differences among bright solitons and their influence during the dynamics. Our findings align with prior non spinor results, i.e., repulsion among in phase bright solitons and attraction among out of phase pairs in self repulsive atomic BECs. The potential bright soliton attraction, added to the short range repulsion of dark dark soliton interactions, can lead to bound states. However, we find that these bound states break in the presence of spinor interactions due to the particle exchange dynamics between the hyperfine states of the components. Additonally, we develop an effective classical model to describe the soliton dynamics, using a Lagrangian approach. The accuracy of the model is tested by comparing it against numerical simulations. Our results suggest that the proposed model captures the essential features of soliton behavior in the presence of spin interactions, and provides congruent soliton trajectories and interspecies particle exchange dynamics in most of the cases.
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.
We have investigated the dynamics of bright solitons in a spin–orbit coupled spin-1 Bose–Einstein condensate analytically and numerically. By using the hyperbolic sine function as the trial function to describe a plane wave bright soliton with a single finite momentum, we have derived the motion equations of soliton’s spin and center of mass, and obtained its exact analytical solutions. Our results show that the spin–orbit coupling couples the soliton’s spin with its center-of-mass motion, the spin oscillations induced by the exchange of atoms between components result in the periodical oscillation of center-of-mass, and the motion of center of mass of soliton can be viewed as a superposition of periodical and linear motions. Our analytical results have also been confirmed by the direct numerical simulations of Gross–Pitaevskii equations.