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arXiv:cond-mat/0606684 · Journal of the Physical Society of Japan

Boojums in Rotating Two-Component Bose–Einstein Condensates

Hiromitsu Takeuchi, Makoto Tsubota

Published Jun 8, 2006• 18 citations
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Abstract

A boojum is a topological defect that can form only on the surface of an ordered medium such as superfluid $^3$He and liquid crystals. We study theoretically boojums appearing between two phases with different vortex structures in two-component BECs where the intracomponent interaction is repulsive in one phase and attractive in the other. The detailed structure of the boojums is revealed by investigating its density distribution, effective superflow vorticity and pseudospin texture.

DOI
10.1143/jpsj.75.063601

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A boojum is a topological defect that can form only on the surface of an ordered medium such as superfluid 3^33He and liquid crystals. We study theoretically boojums appearing between two phases with different vortex structures in two-component BECs where the intracomponent interaction is repulsive in one phase and attractive in the other. The detailed structure of the boojums is revealed by investigating its density distribution, effective superflow vorticity and pseudospin texture.
We study vortex lattices in three-component Bose-Einstein condensates (BECs) under rotation, where three kinds of fractional vortices winding one of three components are present. Unlike the cases of two-component BECs where the phases of square and triangular lattices are present depending on the intercomponent coupling constant and the rotation speed, we find triangular ordered ``colorful'' vortex lattices where three kinds of fractional vortices are placed in order without defects, in all parameter regions where the intercomponent coupling ${g}^{\ensuremath{'}}$ is less than the intracomponent coupling ggg. When $g>{g}^{\ensuremath{'}}$ on the other hand, we find the phase separation: In a region where one component is present, the other two components must vanish, where we find ghost vortices in these two components whose positions are separated. In the boundary $g={g}^{\ensuremath{'}}$, the accidental U(3) symmetry is present, in which case two vortices in different components are close to each other in some regions.
We investigate the phase structure of two-component Bose-Einstein condensates (BECs) with repulsive intra- and interspecies interactions in the presence of respective vortex-antivortex superposition states (VAVSSs). We show that different winding numbers of the vortex and antivortex and different intra- and interspecies interaction strengths may lead to different phase configurations, such as fully separated phases, inlaid separated phases, asymmetric separated phases, and partially mixed phases, where the density profile of each component displays a petal-like (or modulated petal-like) structure. A phase diagram is given for the case of equal unit winding numbers of the vortex and antivortex in the respective components, and it is shown that the conventional criterion for phase separation of two-component BECs is not applicable for the present system due to the VAVSSs. In addition, our nonlinear stability analysis indicates that the typical phase structures of two-component BECs with VAVSSs allow them to be detected in experiments. Moreover, for the case of unequal winding numbers of the vortex and antivortex in the respective components, we find that each component in any of the possible phase structures is in a cluster state of vortices and antivortices, where the topological defects appear in the form of a singly quantized visible vortex, or a hidden vortex, or a ghost vortex, depending on the specific parameters of the system. Finally, a general relationship between the vortex-antivortex cluster state and the winding numbers of vortex and antivortex is revealed.
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 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.
Abstract In contrast to one-component Bose-Einstein condensate case, the vortices in two-component condensate can have various complicated structures. The vortices in a space-homogeneous Bose-Einstein condensate have been studied in this paper. It is shown that the vortex structure is described by three dimensionless parameters. This is totally different from the usual one-component condensate case,where an isolated vortex is described by a parameterless dimensionless equation. The two-component vortex structure strongly depends on the sign of “interaction” constant of the components. A few types of vortices with different qualitative structure are explored. We show that the “super-density vortices” can exist, when the “interaction” constant is positive. The “super-density vortices” have the near-axis density greater than the equilibrium density of a homogeneous space Bose-Einstein condensate. We also show that the vortices with opposite direction of the condensate component rotation near the axis and far off the axis can exist.
The vortex structure in a space-homogeneous Bose-Einstein condensate of two particle species with different masses has been studied. It is shown that the vortex structure in the two-component condensate is described by three dimensionless parameters, which define the system. That is different from the usual one-component condensate, where the vortex is described by a parameter-less dimensionless equation with a fixed structure. A few types of vortices with different qualitative structure are explored. In particular, it is shown, that the vortex structure strongly depends on the sign of “interaction” constant of the components. There can exist the super-density vortices, when the “interaction” constant is positive. These vortices have the near-axis density greater than the equilibrium density of a homogeneous space Bose-Einstein condensate. We show that there can exist the vortices with opposite direction of the condensate rotation near the axis and far off the axis.