Spin-1 spin-orbit-coupled spinor Bose-Einstein condensates have been realized in experiment. We study spin-orbit-coupled spinor gap solitons in this experimentally realizable system with an optical lattice. The spin-dependent parity symmetry of the spin-orbit coupling plays an important role in the properties of gap solitons. Two families of solitons with opposite spin-dependent parity are found. Using an approximate model by replacing the optical lattice with a harmonic trap, we demonstrate the physical origin of the two families. For the zero effective quadratic Zeeman shift, we also find a type of gap soliton that spontaneously breaks the spin-dependent parity symmetry.
Spin-1 spin-orbit-coupled spinor Bose-Einstein condensates have been realized in experiment. We study spin-orbit-coupled spinor gap solitons in this experimentally realizable system with an optical lattice. The spin-dependent parity symmetry of the spin-orbit coupling plays an important role in the properties of gap solitons. Two families of solitons with opposite spin-dependent parity are found. Using an approximate model by replacing the optical lattice with a harmonic trap, we demonstrate the physical origin of the two families. For the zero effective quadratic Zeeman shift, we also find a type of gap soliton that spontaneously breaks the spin-dependent parity symmetry.
While different ways to realize spin-orbit coupling in Bose-Einstein condensates exist, not all are currently experimentally implementable. Here we present a detailed study of gap solitons in a Bose-Einstein condensate with experimentally realizable spin-orbit coupling and discuss two cases relating to a spin-dependent parity symmetry. In the parity symmetric case, two families of fundamental gap solitons in the second linear energy gap are demonstrated with the opposite sign of the parity, with one family having single-humped densities and the other double-humped ones. In the case of broken parity symmetry, the fundamental modes manifest spin polarization. Both families possess an opposite sign of the spin polarization.
We report a diversity of stable gap solitons in a spin-orbit-coupled Bose-Einstein condensate subject to a spatially periodic Zeeman field. It is shown that the solitons can be classified by the main physical symmetries they obey, i.e., symmetries with respect to parity (P), time (T), and internal degree of freedom, i.e., spin (C), inversions. The conventional gap and gap-stripe solitons are obtained in lattices with different parameters. It is shown that solitons of the same type but obeying different symmetries can exist in the same lattice at different spatial locations. PT and CPT symmetric solitons have antiferromagnetic structure and are characterized, respectively, by nonzero and zero total magnetizations.
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.
We present gap solitons (GSs) that can be created in free nearly two-dimensional (2D) space in dipolar spinor Bose-Einstein condensates with the spin-orbit coupling (SOC), subject to tight confinement, with size ${a}_{\ensuremath{\perp}}$, in the third direction. For quasi-2D patterns, with lateral sizes $l\ensuremath{\gg}{a}_{\ensuremath{\perp}}$, the kinetic-energy terms in the respective spinor Gross-Pitaevskii equations may be neglected in comparison with SOC. This gives rise to a band gap in the system's spectrum, in the presence of the Zeeman splitting between the spinor components. While the present system with contact interactions does not produce 2D solitons, stable gap solitons (GSs), with vorticities 0 and 1 in the two components, are found, in quasianalytical and numerical forms, under the action of dipole-dipole interaction (DDI). Namely, isotropic and anisotropic 2D GSs are obtained when the dipoles are polarized, respectively, perpendicular or parallel to the 2D plane. The GS families extend, as embedded solitons (ESs), into spectral bands, a part of the ES branch being stable for isotropic solitons. The GSs remain stable if the competing contact interaction, with the sign opposite to that of the DDI, is included, while the addition of the contact term with the same sign destabilizes the GSs, at first replacing them by breathers, and eventually leading to destruction of the solitons. Mobility and collision of the GSs are studied too, revealing negative and positive effective masses of the isotropic and anisotropic solitons, respectively.
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.
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.