The ground-state phases of a spin-orbit (SO)-coupled atomic spin-2 Bose-Einstein condensate are studied. Interesting density patterns forme spontaneously are widespread due to the competition between SO coupling and spin-dependent interactions as in an SO-coupled spin-1 condensate. Unlike the case of spin-1 condensates, which are characterized by either a ferromagnetic or a polar phase in the absence of SO, spin-2 condensates can take a cyclic phase, where we find that the patterns formed due to SO are square or triangular in their spin-component densities for axial symmetric SO interaction. Both patterns are found to evolve continuously into striped forms with increased asymmetry of the SO coupling.
The ground-state phases of a spin-orbit (SO)-coupled atomic spin-2 Bose-Einstein condensate are studied. Interesting density patterns forme spontaneously are widespread due to the competition between SO coupling and spin-dependent interactions as in an SO-coupled spin-1 condensate. Unlike the case of spin-1 condensates, which are characterized by either a ferromagnetic or a polar phase in the absence of SO, spin-2 condensates can take a cyclic phase, where we find that the patterns formed due to SO are square or triangular in their spin-component densities for axial symmetric SO interaction. Both patterns are found to evolve continuously into striped forms with increased asymmetry of the SO coupling.
We study supersolid-like crystalline structures emerging in the stationary states of a quasi-two-dimensional spin-orbit (SO)-coupled spin-2 condensate in the ferromagnetic, cyclic, and antiferromagnetic phases by solving a mean-field model. Interplay of different strengths of SO coupling and interatomic interactions gives rise to a variety of nontrivial density patterns in the emergent solutions. For small SO-coupling strengths $\ensuremath{\gamma}$ $(\ensuremath{\gamma}\ensuremath{\approx}0.5)$, the ground state is an axisymmetric multiring soliton for polar, cyclic, and weakly ferromagnetic interactions, whereas for stronger ferromagnetic interactions a circularly asymmetric soliton emerges as the ground state. Depending on the values of interaction parameters, with an increase in SO-coupling strength, a stripe phase may also emerge as the ground state for polar and cyclic interactions. For intermediate values of SO-coupling strength $(\ensuremath{\gamma}\ensuremath{\approx}1)$, in addition to these solitons, one could have a quasidegenerate triangular-lattice soliton in all magnetic phases. On further increasing the SO-coupling strength $(\ensuremath{\gamma}⪆4)$, a square-lattice and a superstripe soliton emerge as quasidegenerate states. The emergence of all these solitons can be inferred from a study of solutions of the single-particle Hamiltonian.
The recent experimental realization of spin-orbit (SO) coupling for spin-1 ultracold atoms opens an interesting avenue for exploring SO-coupling-related physics in large-spin systems, which is generally unattainable in electronic materials. In this paper, we study the effects of interactions between atoms on the ground states and collective excitations of SO-coupled spin-1 Bose-Einstein condensates (BECs) in the presence of a spin-tensor potential. We find that ferromagnetic interaction between atoms can induce a stripe phase exhibiting in-phase or out-of-phase modulating patterns between spin-tensor and zero-spin-component density waves. We characterize the phase transitions between different phases using the spin-tensor density as well as the collective dipole motion of the BEC. We show that there exists a double maxon-roton structure in the Bogoliubov-excitation spectrum, attributed to the three band minima of the SO-coupled spin-1 BEC.
We numerically investigate the ground state phases and quench dynamics of spin-orbit coupled spin-1 Bose-Einstein condensates with ferromagnetic and antiferromagnetic interactions. For finite Rabi coupling, the system exhibits zero-momentum, elongated zero-momentum, and stripe phases, while in the limit Ω→0, the superstripe wave phases emerge. Varying the attractive density-density (c0) and spin-exchange (c2) interactions induces the transition from stripe and superstripe phases to the elongated zero-momentum phase, characterized by miscibility and polarization. The condensate remains miscible in the zero-momentum phase and partially miscible for the elongated, stripe, and superstripe phases. Quenching in Rabi coupling stabilizes the condensate, while spin-orbit coupling quenching leads to fluctuations or the formation of complex patterns, with the stripe phase exhibiting the vanishing of the zeroth spin component over time. Our results may offer valuable insights into engineering exotic quantum phases in ultracold atomic gases.
We consider the spin-1 Bose-Einstein condensates with the isotropic Rashba spin-orbit coupling in a two-dimensional toroidal trap. Three types of striped phases are found in a nonrotational system, i.e., the stripe phase with the periodic density modulation along the azimuthal direction, the stripe phase with the periodic density modulation along both the azimuthal and the radial directions, and the stripe phase with the periodic density modulation along the radial direction. By adding the rotation, the condensates occupy the mF=0 component for small rotational frequency, while they occupy both the mF=1 and ${m}_{F}=\ensuremath{-}1$ components for large rotational frequency when both the relative interaction and the spin-orbit coupling are weak. For the stronger relative interaction and spin-orbit coupling, the vortices of the system are elongated along the radial direction and linked one after another. As the rotational frequency further increases, the density evolves from the elongated effect of the vortices into a laminar vortex ring.
In this paper, we consider the ground state properties of a spin-orbit coupled binary Bose-Einstein condensates with dipole-dipole interaction.Our results are obtained by numerically solving the Gross-Pitaevskii equation in the mean field.It is shown that the density structures are greatly affected by spin-orbit coupled strength and dipole strength.With the increase of spin-orbit coupled strength, we find that a stripe phase and phase separation of two components appear, and the number of stripes increases.In addition, concentric circularity stripes with spatial symmetry appear.We also verify that the phase separation can be broken as the dipole strength increases.However, the stripe phase is still kept in this process.As a result, there are no regions of zero density inside the cloud and the nonfragmented density BEC is exhibited.Also, the critical dipole strength decreases with increasing the SOC strength for the non-fragmented state.This result reflects a competition in which the spin-orbit coupling dominates the dipole-dipole interaction.
Abstract We investigate the ground-state properties of spin–orbit (SO)-coupled Bose–Einstein condensates confined in a spin-dependent asymmetric potential composed of harmonic and quartic contributions. The combined effect of the two potentials gives rise to an effective spatially inhomogeneous Zeeman field along the z -direction, and the complex competition among SO coupling, interatomic interactions, and this effective field leads to the emergence of nontrivial topological phases and complex spin textures in the system. For weak interatomic interactions, as the SO coupling strength increases, the system undergoes a series of transitions between ground-state phases: from a spin-polarized state, to an Anderson–Toulouse (AT) vortex state, a high-order radial dark soliton state, and finally to a domain structure. For strong interatomic interactions, the condensate evolves from a spin-polarized state to an AT vortex state, and then to a spatially coexisting state of AT and Mermin–Ho vortices, which corresponds to a novel topological excitation in pseudospin space: a skyrmion-dominated texture embedded with circular-hyperbolic antimeron pairs, realizing the coexistence and nesting of multiple topological defects. For sufficiently strong SO coupling, both components eventually evolve into similar multiring-shaped higher-order radial dark soliton states, with the number of soliton rings increasing as the SO coupling strength increases. Our results enrich the ground-state phases and topological excitations of cold atomic systems and provide new insights for exploring and manipulating nontrivial topological excitations in such systems.