We study rotating two-component Bose–Einstein condensates with equal particle numbers and strong intercomponent repulsion located in a harmonic potential by numerically solving two-dimensional coupled Gross–Pitaevskii equations. The condensates are observed as a dramatic departure, forming a pair of shells located symmetrically in the trap with a small spatial overlap. Projecting the system into a pseudospin space, a spin domain wall is formed at the interface of the two components. The complex and spatial periodic spin texture is formed on the domain-wall region. We discuss the dependence of the spin texture of the domain wall on the angular velocity in detail. The relation among the number of the vortices, the topological charge and the angular momentum, as an extension of Feynman's rule in the two-component Bose–Einstein condensates, is given, based on the spin texture carrying the angular momentum of the condensates.
We study rotating two-component Bose–Einstein condensates with equal particle numbers and strong intercomponent repulsion located in a harmonic potential by numerically solving two-dimensional coupled Gross–Pitaevskii equations. The condensates are observed as a dramatic departure, forming a pair of shells located symmetrically in the trap with a small spatial overlap. Projecting the system into a pseudospin space, a spin domain wall is formed at the interface of the two components. The complex and spatial periodic spin texture is formed on the domain-wall region. We discuss the dependence of the spin texture of the domain wall on the angular velocity in detail. The relation among the number of the vortices, the topological charge and the angular momentum, as an extension of Feynman's rule in the two-component Bose–Einstein condensates, is given, based on the spin texture carrying the angular momentum of the condensates.
We investigate half-vortex sheets and domain-wall trains of rotating two-component Bose-Einstein condensates in spin-dependent optical lattices. The two-component condensates undergo phase separation in the form of stripes arranged alternately. The vortices of one component are aligned in lines in the low-density regions and filled with the other component, which results in a stable vortex configuration, straight half-vortex sheets. A train of domain walls, with spatially periodic eyebrowlike spin textures embedded on them, are formed at the interfaces of the two components. We reveal that these spatially periodic textures on the domain walls result from the linear gradient of the relative phase, which is induced by the alternating arrangement of the vortex sheets in the two components. An accurate manipulation of the textures can be realized by adjusting the intercomponent interaction strength, the rotating angular frequency, and the period of the optical lattices. Under external disturbances, some interesting phenomena, including collective movement of vortices along the sheets and spin-wave propagation along the domain walls, as well as local spin precession, are observed.
We investigate vortex states of immiscible two-component Bose-Einstein condensates under rotation through numerical simulations of the coupled Gross-Pitaevskii equations. For strong intercomponent repulsion, the two components undergo phase separation to form several density domains of the same component. In the presence of the rotation, the nucleated vortices are aligned between the domains to make up winding chains of singly quantized vortices, a vortex sheet, instead of periodic vortex lattices. The vortices of one component are located at the region of the density domains of the other component, which results in the serpentine domain structure. The sheet configuration is stable as long as the imbalance of the intracomponent parameter is small. We employ a planar sheet model to estimate the distance between neighboring sheets, determined by the competition between the surface tension of the domain wall and the kinetic energy of the superflow via quantized vortices. By comparing the several length scales in this system, the phase diagram of the vortex state is obtained.
We investigate two kinds of coreless vortices with axisymmetric and nonaxisymmetric configurations in rotating two-component Bose-Einstein condensates. Starting from the Gross-Pitaevskii energy functional in a rotating frame, we derive a nonlinear sigma model generalized to the two-component condensates. In terms of a pseudospin representation, an axisymmetric vortex and a nonaxisymmetric one correspond to spin textures referred to as a ``skyrmion'' and a ``meron-pair,'' respectively. A variational method is used to investigate the dependence of the sizes of the stable spin textures on system parameters, and the optimized variational function is found to reproduce well the numerical solution. In the SU(2) symmetric case, the optimal skyrmion and meron-pair are degenerate and transform to each other by a rotation of the pseudospin. An external rf field that couples coherently the hyperfine states of two components breaks the degeneracy in favor of the meron-pair texture due to an effective transverse pseudomagnetic field. The difference between the intracomponent and intercomponent interactions yields a longitudinal pseudomagnetic field and a ferromagnetic or an antiferromagnetic pseudospin interaction, leading to a meron-pair texture with an anisotropic distribution of vorticity.
We investigate the ground-state structures and vortex configurations in a two-component Bose-Einstein condensate under the influence of spin-orbital-angular-momentum coupling (SOAMC) with a high spatial inhomogeneity and high characteristic orbital angular momentum. By modulating the coupling strength, we uncover two distinct quantum phases: a stripe phase at low coupling strengths and a new vortex-necklace phase at higher coupling intensities. The latter is characterized by vortices forming a ring-shaped structure that acts as a domain wall, a unique phase boundary between a central stripe phase and an outer single-momentum phase. For a better understanding of this new mixed phase of the system, we develop an analytical model to describe the domain-wall radius as a function of coupling strength, which aligns well with numerical simulations. Our findings contribute to the understanding of SOAMC-driven quantum phase transitions and domain-wall formation, offering new insights into topological phenomena in ultracold atomic systems.
We investigate the ground state of rotating two-component Bose-Einstein condensates in the combined potential well of one-dimensional spin-dependent optical lattice potential and harmonic potential. The density distribution of the condensate is striped. By defining the generalized momentum operator, we derive the velocity distribution of the condensate. The velocity contours are concentric circles for each stripe, with different centers for different stripes. This velocity distribution corresponds to a specific spin texture structure. In this texture, the azimuthal angle of the magnetic moments varies along the y-direction, while the z-component of the magnetic moments varies along the x-direction. When the lattice period [Formula: see text], the texture is divided into two regions. The magnetic moments reverse in a counterclockwise direction and in a clockwise direction as y increases in regions I and II, respectively. Furthermore, when the lattice period [Formula: see text], the texture is divided into three regions. The magnetic moments reverse in a counterclockwise direction, do not reverse, and reverse in a clockwise direction as y increases in regions I, II, and III, respectively. Accurate manipulation of the texture can be achieved by adjusting the optical lattice periods [Formula: see text] and [Formula: see text], the relative phase φ, and the rotational angular frequency Ω.
We investigate the ground states and spin textures of rotating two-component Bose–Einstein condensates (BECs) confined in an annular potential. For the two-component miscible BECs, we analytically give the critical angular velocity of each component with the Thomas–Fermi approximation (TFA), at which the density profile changes from a disc shape into an annulus shape, forming a giant vortex. We present a phase diagram showing three kinds of density profiles of the ground states that are two disc shaped, one disc and another annulus shaped, and two annulus shaped. For the two-component immiscible BECs with particle number grave imbalance, we also discuss their ground states using the TFA, and three kinds of symmetrical structures of the density profiles are classified analytically. The spin textures of the two-component immiscible BECs have been studied and we find three kinds of symmetrical structures of the spin textures in the annular trap. One of these textures is an annular skyrmion which has been observed in harmonic potentials. Both of the other spin textures contain a new structure composed of concentric double-annulus skyrmion whose topological charge is the sum of the ones of two annular skyrmions, and the topological charge of each annular skyrmion is equal to the absolute value of the difference between the quantum numbers of circulation of two components inside this annular skyrmion. We also prove that these new textures are robust by investigating the dynamical behaviours of the system under external disturbances.