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arXiv:1112.5161 · Physical Review A

Half-vortex sheets and domain-wall trains of rotating two-component Bose-Einstein condensates in spin-dependent optical lattices

Wei Han, Suying Zhang, Jingjing Jin, Wu‐Ming Liu

Published Apr 30, 2012• 22 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.85.043626

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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 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 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 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 consider the ground state of vortices in a rotating Bose-Einstein condensate that is loaded in a corotating two-dimensional optical lattice. Due to the competition between vortex interactions and their potential energy, the vortices arrange themselves in various patterns, depending on the strength of the optical potential and the vortex density. We outline a method to determine the phase diagram for arbitrary vortex filling factor. Using this method, we discuss several filling factors explicitly. For increasing strength of the optical lattice, the system exhibits a transition from the unpinned hexagonal lattice to a lattice structure where all the vortices are pinned by the optical lattice. The geometry of this fully pinned vortex lattice depends on the filling factor and is either square or triangular. For some filling factors there is an intermediate half-pinned phase where only half of the vortices is pinned. We also consider the case of a two-component Bose-Einstein condensate, where the possible coexistence of the above-mentioned phases further enriches the phase diagram. In addition, we calculate the dispersion of the low-lying collective modes of the vortex lattice and find that, depending on the structure of the ground state, they can be gapped or gapless. Moreover, in the half-pinned and fully pinned phases, the collective mode dispersion is anisotropic. Possible experiments to probe the collective mode spectrum, and in particular the gap, are suggested.
This report addresses our recent study on pattern formation in two-component Bose-Einstein condensates(BECs), focusing on the dynamics of multiple-domain formation and the structure of vortex states in rotating condensates. Cross-phase modulation instability gives rise to formation of multiple domains that alternate two components, which are consistent with the experimental observation by the MIT group. Rotating two-component BECs exhibit a rich variety of vortex states such as square lattices and vortex sheets, which depend on the strength of intercomponent interaction and rotation frequency.
We investigate the structure of vortex states in rotating two-component Bose-Einstein condensates with equal intracomponent but varying intercomponent-coupling constants. A phase diagram in the intercomponent-coupling versus rotation-frequency plane reveals rich equilibrium structures of vortex states. As the ratio of intercomponent to intracomponent couplings increases, the interlocked vortex lattices undergo phase transitions from triangular to square, to double-core lattices, and eventually develop interwoven "serpentine" vortex sheets with each component made up of chains of singly quantized vortices.