We consider a dipolar spin-1 Bose gas with SU(3) spin−orbit coupling trapped in a two-dimensional toroidal trap. Due to the combined effects of SU(3) spin−orbit coupling, dipole−dipole interaction, and spin−exchange interaction, the system exhibits a rich variety of ground-state phases and topological defects, including modified stripe, azimuthal distributed petal and triangular lattice, double-quantum spin vortices, and so on. In particular, by studying the spin texture of such a system, it is found that the formation and transformation between meron and skyrmion topological spin textures can be realized by a choice of dipole−dipole interaction, SU(3) spin−orbit coupling, and spin−exchange interaction. We also give an experimental protocol to observe such novel states within current experimental capacity.
Dipolar Bose gas with lt;igt;SUlt;/igt;(3) spin−orbit coupling held under a toroidal trap
We consider a dipolar spin-1 Bose gas with SU(3) spin−orbit coupling trapped in a two-dimensional toroidal trap. Due to the combined effects of SU(3) spin−orbit coupling, dipole−dipole interaction, and spin−exchange interaction, the system exhibits a rich variety of ground-state phases and topological defects, including modified stripe, azimuthal distributed petal and triangular lattice, double-quantum spin vortices, and so on. In particular, by studying the spin texture of such a system, it is found that the formation and transformation between meron and skyrmion topological spin textures can be realized by a choice of dipole−dipole interaction, SU(3) spin−orbit coupling, and spin−exchange interaction. We also give an experimental protocol to observe such novel states within current experimental capacity.
We investigate the ground-state structures of dipolar spin-orbit-coupled Bose-Einstein condensates in a toroidal trap. Combined effects of dipole-dipole interaction (DDI) and spin-orbit coupling (SOC) on the ground states of the system are discussed. A ground-state phase diagram is obtained as a function of the SOC and DDI strengths. As two new degrees of freedom, the DDI and SOC can be used to obtain the desired ground-state phases and to control the phase transition between various ground states. In particular, the system displays exotic topological structures and spin textures, such as half-quantum vortex, vortex string, vortex necklace, complex vortex lattice including giant vortex and hidden antivortex chains, different skyrmions, meron (half-skyrmion)-antimeron (half-antiskyrmion) necklace, and composite meron-antimeron lattice.
We investigate the ground-state phases and spin textures of spin–orbit-coupled dipolar pseudo-spin-1/2 Bose–Einstein condensates in a rotating two-dimensional toroidal potential. The combined effects of dipole–dipole interaction (DDI), spin–orbit coupling (SOC), rotation, and interatomic interactions on the ground-state structures and topological defects of the system are analyzed systematically. For fixed SOC strength and rotation frequency, we provide a set of phase diagrams as a function of the DDI strength and the ratio between inter- and intra-species interactions. The system can show rich quantum phases including a half-quantum vortex, symmetrical (asymmetrical) phase with quantum droplets (QDs), asymmetrical segregated phase with hidden vortices (ASH phase), annular condensates with giant vortices, triangular (square) vortex lattice with QDs, and criss-cross vortex string lattice, depending on the competition between DDI and contact interaction. For given DDI strength and rotation frequency, the increase of the SOC strength leads to a structural phase transition from an ASH phase to a tetragonal vortex lattice then to a pentagonal vortex lattice and finally to a vortex necklace, which is also demonstrated by the momentum distributions. Without rotation, the interplay of DDI and SOC may result in the formation of a unique trumpet-shaped Bloch domain wall. In addition, the rotation effect is discussed. Furthermore, the system supports exotic topological excitations, such as a half-skyrmion (meron) string, triangular skyrmion lattice, skyrmion–half-skyrmion lattice, skyrmion–meron cluster, skyrmion–meron layered necklace, skyrmion–giant-skyrmion necklace lattice, and half-skyrmion–half-antiskyrmion necklace.
Abstract We consider the topological defects and spin structures of spin-1 Bose–Einstein condensates with spin–orbit coupling (SOC) and dipole–dipole interaction (DDI) in a rotating harmonic plus quartic trap. The combined effects of SOC, DDI and rotation on the ground-state phases of the system are analyzed. Our results show that for fixed rotation frequency structural phase transitions can be achieved by adjusting the magnitudes of the SOC and DDI. A ground-state phase diagram is given as a function of the SOC and DDI strengths. It is shown that the system exhibits rich quantum phases including vortex string phase with isolated density peaks (DPs), triangular (square) vortex lattice phase with DPs, checkerboard phase, and stripe phase with hidden vortices and antivortices. For given SOC and DDI strengths, the system can display pentagonal vortex lattice with DPs, vortex necklace with DPs, and exotic topological structure composed of multi-layer visible vortex necklaces, a hidden giant vortex and hidden vortex necklaces, depending on the rotation frequency. In addition, the system sustains fascinating novel spin textures and skyrmion excitations, such as an antiskyrmion pair, antiskyrmion-half-antiskyrmion (antiskyrmion–antimeron) cluster, skyrmion–antiskyrmion lattice, skyrmion–antiskyrmion cluster, skyrmion–antiskyrmion–meron–antimeron lattice, double-layer half-antiskyrmion necklaces, and composite giant-antiskyrmion–antimeron necklaces.
Realization of spinor Bose-Einstein condensate in an optical trap has made it possible to create a variety of topological nontrivial structures, due to the vector character of the order parameter. Recently, artificial spin-orbit coupling in the spinor Bose-Einstein condensate, owing to coupling between the spin and the center-of-mass motion of the atom, provides an unprecedented opportunity to search for novel quantum states. As is well known, the potential well in the Bose-Einstein condensate is adjustable. The toroidal trap is an important model potential because of its simplicity and richness in physics. In particular, the spinor Bose-Einstein condensate under the toroidal trap has brought an ideal platform for studying fascinating properties of a superfluid, such as persistent flow and symmetry-breaking localization. For the case of the spin-orbit-coupled Bose-Einstein condensate, the previous studies of the toroidal trap mainly focused on the two-component or antiferromagnetic case. However, in the presence of a toroidal trap, there remains an open question whether the combined effects of the spin-orbit coupling and rotation can produce previously unknown types of topological excitations in the ferromagnetic Bose-Einstein condensate. In this work, by using quasi two-dimensional Gross-Pitaevskii equations, we study the ground state structure of spin-orbit coupled rotating ferromagnetic Bose-Einstein condensate in the toroidal trap. We concentrate on the effects of the spin-orbit coupling and the rotation on the ground states. The numerical results show that in the presence of a toroidal trap, the ground state structure is displayed as half-skyrmion chain with circular distribution. Adjusting the strength of spin-orbit coupling not only changes the number of half-skyrmion in the system, but also controls the symmetry of half-skyrmion with circular distribution. As the rotation frequency increases, the system undergoes the transitions from the plane wave to the half-skyrmion chain with circular distribution, and eventually developing the half-skyrmion phase of triangular lattice. Next, we examine the effect of spin-independent interaction on spin-orbit coupled rotating spinor Bose-Einstein condensate. As the spin-independent interaction increases, the topological defects in the condensate increase due to the variation of the local magnetic order. We also discuss the influence of well shape on the ground state structure. These topological structures can be detected via the time-of-flight absorption imaging technique. The spin-orbit coupled spinor Bose-Einstein condensate in the toroidal trap is an important quantum platform, which not only opens up a new avenue for exploring the exotic topological structures, but also is crucial for realizing the transitions among different ground states. This work paves the way for futureexploring the topological defects and the corresponding dynamical stability in quantum system subjected to the toroidal trap.
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.