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arXiv:1304.4375 · Physical Review A

Vortex lattices in three-component Bose-Einstein condensates under rotation: Simulating colorful vortex lattices in a color superconductor

M. Cipriani, Muneto Nitta

Published Jul 29, 2013• 28 citations
arXivHTMLPDF

Abstract

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 $g$. 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.

DOI
10.1103/physreva.88.013634

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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′{g}^{\ensuremath{'}}g\ensuremath′ is less than the intracomponent coupling ggg. When g>g\ensuremath′g>{g}^{\ensuremath{'}}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′g={g}^{\ensuremath{'}}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 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.
When a two-component Bose-Einstein condensate is placed into rotation, a lattice of vortices and cores appear. The geometry of this lattice (triangular or square) varies according to the rotational value and the intercomponent coupling strengths. In this paper, assuming a Thomas-Fermi regime, we derive a point energy that allows us to determine for which values of the parameters the lattice goes from triangular to square. It turns out that the separating curve in the phase diagram agrees fully with the complete numerical simulations of the Gross-Pitaevskii equations. We also derive a formula for the critical velocity of appearance of the first vortex and prove that the first vortex always appears first in the component with largest support in the case of two disks, and we give a criterion in the case of disk and annulus.
In order to study the rotating strongly coupled Bose-Einstein condensations (BEC), a holographic model defined in an anti--de Sitter black hole that duals to a coupled two-component condensations in global U(1)U(1)U(1) symmetry broken phase with intercomponent coupling $\ensuremath{\eta}$ and internal coherent coupling $\ensuremath{\epsilon}$ is proposed. By solving the dynamics of the model, we study the process of vortex formation and also the crossover from fractional to integer vortex phases. With changing only $\ensuremath{\eta}$ from zero to a finite value, fractional vortex lattices undergo a transition from hexagon to square lattice and finally to vortex sheets. By continuing to turn on $\ensuremath{\epsilon}$, we find that two fractional vortices in different components constitute dimers, and when $\ensuremath{\eta}$ transcends a critical value, multidimer like hexamer or tetramer made up of two and three dimers appears. As $\ensuremath{\epsilon}$ keeps increasing, some dimers rotate to adjust themselves and then constitute the lattice of integer vortices. Under an initial condition similar to a spinor BEC vortices dynamics experiment, the appearance of disordered turbulence is found in the process of fractional vortex generation, which matches the experimental observation. While in the formation process of integer vortices, the appearance of grooves is predicted.
We observe interlaced square vortex lattices in rotating dilute-gas spinor Bose-Einstein condensates (BEC). After preparing a hexagonal vortex lattice in a one-component BEC in an internal atomic state |1, we coherently transfer a fraction of the superfluid to a different state |2. The subsequent evolution of this pseudo-spin-1/2 superfluid towards a state of offset square lattices involves an intriguing interplay of phase-separation and -mixing dynamics, both macroscopically and on the length scale of the vortex cores, and a stage of vortex turbulence. The stability of the square structure is proved by its response to applied shear perturbations. An interference technique shows the spatial offset between the two vortex lattices. Vortex cores in either component are filled by fluid of the other component, such that the spin-1/2 order parameter forms a Skyrmion lattice.
We review the topic of quantized vortices in multicomponent Bose–Einstein condensates of dilute atomic gases, with an emphasis on the two-component condensates. First, we review the fundamental structure, stability and dynamics of a single vortex state in a slowly rotating two-component condensates. To understand recent experimental results, we use the coupled Gross–Pitaevskii equations and the generalized nonlinear sigma model. An axisymmetric vortex state, which was observed by the JILA group, can be regarded as a topologically trivial skyrmion in the pseudospin representation. The internal, coherent coupling between the two components breaks the axisymmetry of the vortex state, resulting in a stable vortex molecule (a meron pair). We also mention unconventional vortex states and monopole excitations in a spin-1 Bose–Einstein condensate. Next, we discuss a rich variety of vortex states realized in rapidly rotating two-component Bose–Einstein condensates. We introduce a phase diagram with axes of rotation frequency and the intercomponent coupling strength. This phase diagram reveals unconventional vortex states such as a square lattice, a double-core lattice, vortex stripes and vortex sheets, all of which are in an experimentally accessible parameter regime. The coherent coupling leads to an effective attractive interaction between two components, providing not only a promising candidate to tune the intercomponent interaction to study the rich vortex phases but also a new regime to explore vortex states consisting of vortex molecules characterized by anisotropic vorticity. A recent experiment by the JILA group vindicated the formation of a square vortex lattice in this system.
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.