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arXiv:2003.09423 · Physical review. D/Physical review. D.

Fractional and integer vortex dynamics in strongly coupled two-component Bose-Einstein condensates from AdS/CFT correspondence

Wei-Can Yang, Chuan-Yin Xia, Muneto Nitta, Hua-Bi Zeng

Published Aug 17, 2020• 8 citations
arXivHTMLPDF

Abstract

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 $U(1)$ 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.

DOI
10.1103/physrevd.102.046012

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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 \ensuremathη\ensuremath{\eta}\ensuremathη and internal coherent coupling \ensuremathϵ\ensuremath{\epsilon}\ensuremathϵ 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 \ensuremathη\ensuremath{\eta}\ensuremathη 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 \ensuremathϵ\ensuremath{\epsilon}\ensuremathϵ, we find that two fractional vortices in different components constitute dimers, and when \ensuremathη\ensuremath{\eta}\ensuremathη transcends a critical value, multidimer like hexamer or tetramer made up of two and three dimers appears. As \ensuremathϵ\ensuremath{\epsilon}\ensuremathϵ 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 study the effects of the internal coherent (Rabi) coupling in vortex lattices in two-component BECs under rotation. We find how the vortex lattices without the Rabi coupling known before are connected to the Abrikosov lattice of integer vortices with increasing the Rabi coupling. We find that (1) for small Rabi couplings, fractional vortices in a triangular or square lattice for small or large intercomponent coupling constitute hexamers or tetramers, namely multidimer bound states made of six or four vortices, respectively, (2) these bound states are broken into a set of dimers at intermediate Rabi couplings, and (3) vortices change their partners in various ways depending on the intercomponent coupling, to organize themselves for constituting the Abrikosov lattice of integer vortices at strong Rabi couplings.
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 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.
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 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 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.