We study the topological defects and spin structures of rotating SU(3) spin–orbit-coupled spin F=1 Bose–Einstein condensates (BECs) in an in-plane quadrupole field with ferromagnetic spin interaction, and the BECs is confined by a harmonic trap. Without rotation, as the quadrupole field strength is increased, the spin F=1 BECs with SU(3) spin–orbit coupling (SOC) evolves from the initial Thomas–Fermi phase into the stripe phase; then, it enters a vortex–antivortex cluster state and eventually a polar-core vortex state. In the absence of rotation with the given quadrupole field, the enhancing SU(3) SOC strength can cause a phase transition from a central Mermin–Ho vortex to a vortex–antivortex cluster, subsequently converting to a bending vortex–antivortex chain. In addition, when considering rotation, it is found that this system generates the following five typical quantum phases: a three-vortex-chain cluster structure with mutual angles of approximately 2π3, a tree-fork-like vortex chain cluster, a rotationally symmetric vortex necklace, a diagonal vortex chain cluster, and a density hole vortex cluster. Particularly, the system exhibits unusual topological structures and spin textures, such as a bending half-skyrmion–half-antiskyrmion (meron–antimeron) chain, three half-skyrmion (meron) chains with mutual angles of an approximately 2π3, slightly curved diagonal half-skyrmion (meron) cluster lattice, a skyrmion–half-skyrmion (skyrmion-meron) necklace, and a tree-fork-like half-skyrmion (meron) chain cluster lattice.
We study the topological defects and spin structures of rotating SU(3) spin–orbit-coupled spin F=1 Bose–Einstein condensates (BECs) in an in-plane quadrupole field with ferromagnetic spin interaction, and the BECs is confined by a harmonic trap. Without rotation, as the quadrupole field strength is increased, the spin F=1 BECs with SU(3) spin–orbit coupling (SOC) evolves from the initial Thomas–Fermi phase into the stripe phase; then, it enters a vortex–antivortex cluster state and eventually a polar-core vortex state. In the absence of rotation with the given quadrupole field, the enhancing SU(3) SOC strength can cause a phase transition from a central Mermin–Ho vortex to a vortex–antivortex cluster, subsequently converting to a bending vortex–antivortex chain. In addition, when considering rotation, it is found that this system generates the following five typical quantum phases: a three-vortex-chain cluster structure with mutual angles of approximately 2π3, a tree-fork-like vortex chain cluster, a rotationally symmetric vortex necklace, a diagonal vortex chain cluster, and a density hole vortex cluster. Particularly, the system exhibits unusual topological structures and spin textures, such as a bending half-skyrmion–half-antiskyrmion (meron–antimeron) chain, three half-skyrmion (meron) chains with mutual angles of an approximately 2π3, slightly curved diagonal half-skyrmion (meron) cluster lattice, a skyrmion–half-skyrmion (skyrmion-meron) necklace, and a tree-fork-like half-skyrmion (meron) chain cluster lattice.
Abstract We investigate the topological excitations of rotating spin-1 ferromagnetic Bose–Einstein condensates with spin–orbit coupling (SOC) in an in-plane quadrupole field. Such a system sustains a rich variety of exotic vortex structures due to the spinor order parameter and the interplay among in-plane quadrupole field, SOC, rotation, and interatomic interaction. For the nonrotating case, with the increase of the quadrupole field strength, the system experiences a transition from a coreless polar-core vortex with a bright soliton to a singular polar-core vortex with a density hole. Without rotation but with a fixed quadrupole field, when the SOC strength increases, the system transforms from a central Mermin–Ho vortex into a criss-crossed vortex–antivortex string lattice. For the rotating case, we give a phase diagram with respect to the quadrupole field strength and the SOC strength. It is shown that the rotating system supports four typical quantum phases: vortex necklace, diagonal vortex chain cluster, single diagonal vortex chain, and few vortex states. Furthermore, the system favors novel spin textures and skyrmion excitations including an antiskyrmion, a criss-crossed half-skyrmion–half-antiskyrmion lattice, a skyrmion-meron necklace, a symmetric half-skyrmion lattice, and an asymmetric skyrmion-meron lattice.
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.
Abstract We investigate the ground-state properties of spin–orbit-coupled pseudo-spin-1/2 dipolar Bose–Einstein condensates in a two-dimensional harmonic trap and an in-plane quadrupole field. The effects of spin–orbit coupling (SOC), dipole–dipole interaction (DDI) and the in-plane quadrupole field on the ground-state structures and spin textures of the system are systematically analyzed and discussed. For fixed SOC and DDI strengths, the system shows a quadrupole stripe phase with a half-quantum vortex, or a quadrupole Thomas–Fermi phase with a half-quantum antivortex for small quadrupole field strength, depending on the ratio between inter- and intraspecies interaction. As the quadrupole field strength enhances, the system realizes a ring mixed phase with a hidden vortex–antivortex cluster rather than an ordinary giant vortex in each component. Of particular interest, when the strengths of DDI and quadrupole field are fixed, strong SOC leads to the formation of criss-crossed vortex string structure. For given SOC and quadrupole field, the system for strong DDI displays a sandwich-like structure, or a special delaminated structure with a prolate antivortex in the spin-up component. In addition, typical spin textures for the ground states of the system are analyzed. It is shown that the system sustains exotic topological structures, such as a hyperbolic spin domain wall, skyrmion-half-antiskyrmion-antiskyrmion lattice, half-skyrmion-skyrmion-half-antiskyrmion lattice, and a drum-shaped antimeron.
We investigate the dynamics of rotating spin-orbit-coupled spin-1 Bose–Einstein condensates (BECs) in an in-plane gradient magnetic field, which is confined in an anharmonic trap. In the case of rotating spin-orbit-coupled spin-1 BECs with given parameters, the system evolves from initial disk-shaped condensates into drastic turbulent oscillations and ghost vortices on the surface of the component densities due to surface wave excitations and then into two final vortex necklaces along the azimuthal direction with an irregular density hole, in which the vortices differ by one quantum number in turn. For the case of rotating spin-orbit-coupled spin-1 BECs with in-plane gradient magnetic field, with the dynamic evolution, the system undergoes a transition from an initial central polar-core vortex to violent turbulent oscillations and then to a final vortex chain along the diagonal of BECs, with the remaining vortices symmetrically distributed on both sides in the individual component. In addition, the corresponding spin texture undergoes a transition from plane-wave phase to double half-antiskyrmion necklaces for the former case and a transition from a structure similar to a quadrupole magnetic field to a half-antiskyrmion chain with the rest of the half-antiskyrmions on both sides. During the dynamic evolution process, the angular momentum increases gradually and then approaches a convergent value.
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.
The ground state properties of the rotating Bose–Einstein condensates (BECs) with SU(3) spin–orbit coupling (SOC) in a two-dimensional harmonic trap are studied. The results show that the ferromagnetic and antiferromagnetic systems present three half-skyrmion chains at an angle of 120° to each other along the coupling directions. With the enhancement of isotropic SU(3) SOC strength, the position of the three chains remains unchanged, in which the number of half-skyrmions increases gradually. With the increase of rotation frequency and atomic density–density interaction, the number of half-skyrmions on the three chains and in the regions between two chains increases gradually. The relationships of the total number of half-skyrmions on the three chains with the increase of SU(3) SOC strength, rotation frequency and atomic density–density interaction are also given. In addition, changing the anisotropic SU(3) SOC strength can regulate the number and morphology of the half-skyrmion chains.