We study matter-wave bright solitons in spin-orbit coupled Bose-Einstein condensates with attractive interactions. We use a multiscale expansion method to identify solution families for chemical potentials in the semi-infinite gap of the linear energy spectrum. Depending on the linear and spin-orbit coupling strengths, the solitons may present either a sech2-shaped or a modulated density profile reminiscent of the stripe phase of spin-orbit coupled repulsive Bose-Einstein condensates. Our numerical results are in excellent agreement with our analytical findings and demonstrate the potential robustness of solitons for experimentally relevant conditions.
We study matter-wave bright solitons in spin-orbit coupled Bose-Einstein condensates with attractive interactions. We use a multiscale expansion method to identify solution families for chemical potentials in the semi-infinite gap of the linear energy spectrum. Depending on the linear and spin-orbit coupling strengths, the solitons may present either a sech2-shaped or a modulated density profile reminiscent of the stripe phase of spin-orbit coupled repulsive Bose-Einstein condensates. Our numerical results are in excellent agreement with our analytical findings and demonstrate the potential robustness of solitons for experimentally relevant conditions.
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.
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 present a unified description of different types of matter-wave solitons that can emerge in quasi one-dimensional spin-orbit coupled (SOC) Bose-Einstein condensates (BECs). This description relies on the reduction of the original two-component Gross-Pitaevskii SOC-BEC model to a single nonlinear Schrödinger equation, via a multiscale expansion method. This way, we find approximate bright and dark soliton solutions, for attractive and repulsive interatomic interactions respectively, for different regimes of the SOC interactions. Beyond this, our approach also reveals "negative mass" regimes, where corresponding "negative mass" bright or dark solitons can exist for repulsive or attractive interactions, respectively. Such a unique opportunity stems from the structure of the excitation spectrum of the SOC-BEC. Numerical results are found to be in excellent agreement with our analytical predictions.
We present three types of dark solitons in quasi–one-dimensional spin-orbit coupled repulsive Bose-Einstein condensates. Among these families, two are always stable, while the third one is only stable sufficiently close to the linear regime. The solitons' excitation spectra reveal the potential existence of a second anomalous mode. While the first such mode describes the soliton oscillatory motion in a parabolic trap, the second, when present, reflects the double-well structure of the underlying single-particle spectrum. This novel mode results in moving density stripes in the vicinity of the soliton core, or in an out-of-phase oscillation of the constituent components, with little effect on the nearly stationary striped total density of the composite soliton.
We present families of beating dark-dark solitons in spin-orbit (SO) -coupled Bose-Einstein condensates. These families consist of solitons residing simultaneously in the two bands of the energy spectrum. The soliton components are characterized by two different spatial and temporal scales, which are identified by a multiscale expansion method. The solitons are ``beating'' ones, as they perform density oscillations. The characteristic frequency of the latter is relevant to Zitterbewegung (ZB) oscillations, which were recently observed in experiments with SO-coupled condensates [C. Qu et al., Phys. Rev. A 88, 021604(R) (2013); L. J. LeBlanc et al., New J. Phys. 15, 073011 (2013)]. We find that spin oscillations may occur, depending on the parity of each soliton branch, which consequently lead to ZB oscillations of the beating dark solitons. Analytical results are corroborated by numerical simulations, illustrating the robustness of the solitons.
We investigate the moving matter-wave solitons in spin—orbit coupled Bose—Einstein condensates (BECs) by a perturbation method. Starting with the one-dimensional Gross—Pitaevskii equations, we derive a new KdV-like equation to which an approximate solution is obtained by assuming weak Raman coupling and strong spin—orbit coupling. The derivation of the KdV-like equation may be useful to understand the properties of solitons excitation in spin—orbit coupled BECs. We find different types of moving solitons: dark—bright, bright—bright and dark—dark solitons. Interestingly, moving dark—dark soliton for attractive intra- and inter-species interactions is found, which depends on the Raman coupling. The amplitude and velocity of the moving solitons strongly depend on the Raman coupling and spin—orbit coupling.