Abstract We explore the spin texture dynamics of a harmonically trapped spin-1 Bose–Einstein condensate with Rashba spin–orbit coupling and ferromagnetic spin-exchange interactions under a sinusoidally varying magnetic field along the x-direction. This interplay yields an intrinsic spin texture in the ground state, forming a linear chain of alternating skyrmions at the saddle points of the magnetic field. Our study analyzes the spin-mixing dynamics for both a freely evolving and a controlled longitudinal magnetization. The spin-1 system exhibits the Einstein–de Haas effect for the first case, for which an exchange between the total orbital angular momentum and the spin angular momentum is observed, resulting in minimal oscillations about the initial position of the skyrmion chain. However, for the fixed magnetization dynamics, the skyrmion chain exhibits ample angular oscillations about the equilibrium position, with the temporary formation of new skyrmions to facilitate the oscillatory motion. For the case of fixed magnetization, this contrast now stems from the exchange between the canonical and spin-dependent contribution to the orbital angular momentum. The variation in canonical angular momentum is linked to the angular oscillations, while the spin-dependent angular momentum accounts for the creation or annihilation of skyrmions. We confirm the presence of scissors mode excitations in the spin texture due to the angular skyrmion oscillations.
Abstract We explore the spin texture dynamics of a harmonically trapped spin-1 Bose–Einstein condensate with Rashba spin–orbit coupling and ferromagnetic spin-exchange interactions under a sinusoidally varying magnetic field along the x-direction. This interplay yields an intrinsic spin texture in the ground state, forming a linear chain of alternating skyrmions at the saddle points of the magnetic field. Our study analyzes the spin-mixing dynamics for both a freely evolving and a controlled longitudinal magnetization. The spin-1 system exhibits the Einstein–de Haas effect for the first case, for which an exchange between the total orbital angular momentum and the spin angular momentum is observed, resulting in minimal oscillations about the initial position of the skyrmion chain. However, for the fixed magnetization dynamics, the skyrmion chain exhibits ample angular oscillations about the equilibrium position, with the temporary formation of new skyrmions to facilitate the oscillatory motion. For the case of fixed magnetization, this contrast now stems from the exchange between the canonical and spin-dependent contribution to the orbital angular momentum. The variation in canonical angular momentum is linked to the angular oscillations, while the spin-dependent angular momentum accounts for the creation or annihilation of skyrmions. We confirm the presence of scissors mode excitations in the spin texture due to the angular skyrmion oscillations.
We explore topological excitations in a spin-1 Bose-Einstein condensate subjected to an in-plane sinusoidally varying magnetic field and Rashba spin-orbit coupling (SOC). In the absence of SOC, the periodic magnetic field induces vortex-antivortex structures in the $|F=1,{m}_{F}=\ifmmode\pm\else\textpm\fi{}1\ensuremath{\rangle}$ condensates at saddle points such that the net topological charge remains zero. The introduction of Rashba SOC breaks the system's symmetry, leading to nonconservation of overall angular momentum in the spin-1 condensate. This anisotropy results in the emergence of certain skyrmion spin textures. We provide a comparative study for various in-plane magnetic-field configurations while keeping the SOC strength constant. Our numerical simulations within the mean-field framework reveal the potential to engineer diverse topological excitations controlled by the interplay between the spin-orbit coupling and in-plane magnetic field in a spinor condensate.
Abstract We consider the ground-state properties of Rashba spin–orbit-coupled pseudo-spin-1/2 Bose–Einstein condensates (BECs) in a rotating two-dimensional (2D) toroidal trap. In the absence of spin–orbit coupling (SOC), the increasing rotation frequency enhances the creation of giant vortices for the initially miscible BECs, while it can lead to the formation of semiring density patterns with irregular hidden vortex structures for the initially immiscible BECs. Without rotation, strong 2D isotropic SOC yields a heliciform-stripe phase for the initially immiscible BECs. Combined effects of rotation, SOC, and interatomic interactions on the vortex structures and typical spin textures of the ground state of the system are discussed systematically. In particular, for a fixed rotation frequency above the critical value, the increasing isotropic SOC favors a visible vortex necklace in each component which is accompanied by a hidden giant vortex plus a (several) hidden vortex necklace(s) in the central region. In the case of one-dimensional anisotropic SOC, large SOC strength results in the generation of hidden linear vortex string and the transition from initial component separation (component mixing) to component mixing (component separation). Furthermore, the peculiar spin textures including skyrmion lattice, skyrmion pair and skyrmion string are revealed in this system.
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.
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 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.
For a spin-carrying particle moving in a spatially varying magnetic field, effective electromagnetic forces can arise due to the geometric phase associated with adiabatic spin rotation of the particle. We report the observation of a geometric Hall effect in a spinor Bose-Einstein condensate with a Skyrmion spin texture. Under translational oscillations of the spin texture, the condensate resonantly develops a circular motion in a harmonic trap, demonstrating the existence of an effective Lorentz force. When the condensate circulates, quantized vortices are nucleated in the boundary region of the condensate and the vortex number increases over 100 without significant heating. We attribute the vortex nucleation to the shearing effect of the effective Lorentz force from the inhomogeneous effective magnetic field.