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 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.
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.
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 investigate the dynamics of rotating pseudo-spin-1/2 Bose–Einstein condensates (BECs) with Rashba spin–orbit coupling (SOC) in a quasicrystalline optical lattice (QOL). For given parameters, the system evolves from an initial heliciform-stripe phase into a final visible vortex necklace with a giant vortex and a hidden vortex necklace. Simultaneously, the corresponding spin texture undergoes a transition from a meron–antimeron pair to a half-antiskyrmion necklace. During the dynamic evolution process, the angular momentum increases gradually, and then approaches to a convergent value. Furthermore, typical quantum phases of rotating two-component BECs with SOC in different external potentials are summarized.
Two-component Bose-Einstein condensate offers an ideal platform for investigating many intriguing topological defects due to the interplay between intraspecies and interspecies interactions. The recent realization of spin-orbit coupling in two-component Bose-Einstein condensate, owing to coupling between the spin and the centre-of-mass motion of the atom, provides possibly new opportunities to search for novel quantum states. In particular, the gradient magnetic field in the Bose-Einstein condensate has brought a new way to create topologically nontrivial structures including Dirac monopoles and quantum knots. Previous studies of the gradient magnetic field effect in the Bose-Einstein condensate mainly focused on the three-component case. However, it remains unclear how the gradient magnetic field affects the ground state configuration in the rotating two-component Bose-Einstein condensate with spin-orbit coupling. In this work, by using quasi two-dimensional Gross-Pitaevskii equations, we study the ground state structure of a rotating two-component Bose-Einstein condensate with spin-orbit coupling and gradient magnetic field. We concentrate on the effects of the spin-orbit coupling and the gradient magnetic field on the ground state. The numerical results show that increasing the strength of the spin-orbit coupling can induce a phase transition from skyrmion lattice to skyrmion chain in the presence of the gradient magnetic field. Unlike the study of skyrmion in rotating two-component Bose-Einstein condensate with only spin-orbit coupling, the skyrmion chain can occur under the isotropic spin-orbit coupling when the gradient magnetic field is considered. It is worth noting that the skyrmion chain here is arrayed along the diagonal direction. Next we examine the effect of the gradient magnetic field on spin-orbit coupled two-component Bose-Einstein condensate. For the case of weak spin-orbit coupling and the slow rotation, a phase transition from a single plane-wave to half-skyrmion is found through increasing magnetic field gradient strength. For the case of strong spin-orbit coupling and the fast rotation, the nature of the ground state is shown to support the formation of a hidden vortex as the gradient magnetic field is enhanced. These hidden vortices have no visible cores in density distributions but have phase singularities in phase distributions, which are arrayed along the diagonal direction. This result confirms a new method of creating the hidden vortices in the two-component Bose-Einstein condensate. These topological structures can be detected by using the time-of-flight absorption imaging technique. Our results illustrate that the gradient magnetic field not only provides an opportunity to explore the exotic topological structures in spin-orbit coupled spinor Bose-Einstein condensate, but also is crucial for realizing the phase transitions among different ground states. This work paves the way for the future exploring of topological defect and the corresponding dynamical stability in quantum systems subjected to a gradient magnetic field.
Abstract We study the ground-state phases of two-dimensional rotating spin–orbit coupled spin-1/2 Bose–Einstein condensates (BECs) in a gradient magnetic field. The competition between gradient magnetic field, spin–orbit coupling and rotation leads to a variety of ground-state phase structures. In the weakly rotation regime, as the increase of gradient magnetic field strength, the BECs experiences a phase transition from the unstable phase to the single vortex-line phase. The unstable phase presents the vortex lines structures along the off-diagonal direction. With magnetic field gradient strength increasing, the number of vortex lines changes accordingly. As the magnetic field gradient strength increases further, the single vortex-line phase with a single vortex line along the diagonal direction is formed. The phase diagram shows that the boundary between the two phases is linear with the relative repulsion λ ≥ 1 and is nonlinear with λ < 1. In the relatively strong rotation regime, in addition to the unstable phase and the single vortex-line phase, the vortex-ring phase is formed for the strong magnetic field gradient and rapid rotation. The vortex-ring phase shows the giant and hidden vortex structures at the center of ring. The strong magnetic field gradient makes the number of the vortices around the ring unchanged.
We investigate the ground states and rich dynamics of vortices in spin-orbit coupled Bose-Einstein condensates (BEC) subject to position-dependent detuning. Such a detuning plays the role of an effective rotational frequency, causing the generation of a synthetic magnetic field. Through scanning the detuning gradient, we numerically obtain static vortex lattice structures containing 1 to 6 vortices using the coupled Gross-Pitaevskii equations. When quenching detuning gradient below its initial value, the vortex lattices exhibit interesting periodic rotation motion, and their dynamical stability can persist for up to 1000ms. In particular, depending on the detuning gradient, the twin vortices exhibit either a scissors-like rotational oscillation or a clockwise periodic rotation, reflecting the response to the magnetic field gradient experienced by the condensates. We fit the numerical results to quantitatively analyze the relation between rotation dynamics and magnetic field gradients. When quenching the detuning gradient beyond its initial value, additional vortices appear. Our findings may motivate further experimental studies of vortex dynamics in synthetic magnetic fields and offer insights for engineering a BEC-based magnetic field gradiometer.