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arXiv:1907.01918 · The European Physical Journal C

Phase separation and exotic vortex phases in a two-species holographic superfluid

Wei-Can Yang, Chuan-Yin Xia, Hua-Bi Zeng, Hai-Qing Zhang

Published Jan 1, 2021• 14 citations
arXivHTMLPDF

Abstract

Abstract At finite temperature, the stable equilibrium states of coupled two-component Bose Einstein condensations (BECs) with the same conformal mass in both non-rotating and rotating condition can be obtained by studying its real dynamics via holography. The equilibrium state is the state where the free energy reaches the minimum and does not change any more. In the case of no rotation, the spatial phase separated states of the two components become more stable than the miscible condensates state when the direct repulsive inter-component coupling constant $$\eta>\eta _c>0$$ η > η c > 0 . Under rotation, the quantum fluid reveals four equilibrium structures of vortex states by varying the $$\eta $$ η from the miscible region to the phase separated region. Among the four structures, the vortex sheet solution is the most exotic one that appears in the phase separated region.

DOI
10.1140/epjc/s10052-021-08838-x

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Abstract At finite temperature, the stable equilibrium states of coupled two-component Bose Einstein condensations (BECs) with the same conformal mass in both non-rotating and rotating condition can be obtained by studying its real dynamics via holography. The equilibrium state is the state where the free energy reaches the minimum and does not change any more. In the case of no rotation, the spatial phase separated states of the two components become more stable than the miscible condensates state when the direct repulsive inter-component coupling constant η>ηc>0\eta>\eta _c>0η>ηc​>0 η > η c > 0 . Under rotation, the quantum fluid reveals four equilibrium structures of vortex states by varying the η\eta η η from the miscible region to the phase separated region. Among the four structures, the vortex sheet solution is the most exotic one that appears in the phase separated region.
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 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.
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.
The combination of multi-component Bose–Einstein condensates (BECs) and phase imprinting techniques provides an ideal platform for exploring nonlinear dynamics and investigating the quantum transport properties of superfluids. In this paper, we study abundant density structures and corresponding dynamics of phase-separated binary Bose–Einstein condensates with phase-imprinted single vortex or vortex dipole. By adjusting the ratio between the inter-species and intra-species interactions, and the locations of the phase singularities, the typical density profiles such as ball-shell structures, crescent-gibbous structures, Matryoshka-like structures, sector-sector structures and sandwich-type structures appear, and the phase diagrams are obtained. The dynamics of these structures exhibit diverse properties, including the penetration of vortex dipoles, emergence of halfvortex dipoles, co-rotation of sectors, and oscillation between sectors. The pinning effects induced by a potential defect are also discussed, which is useful for controlling and manipulating individual quantum states.
Equilibrium vortex formation in rotating binary Bose gases with a rotating frequency higher than the harmonic trapping frequency is investigated theoretically. We consider the system being evaporatively cooled to form condensates and a combined numerical scheme is applied to ensure the binary system being in an authentic equilibrium state. To keep the system stable against the large centrifugal force of ultrafast rotation, a quartic trapping potential is added to the existing harmonic part. Using the Thomas-Fermi approximation, a critical rotating frequency ${\ensuremath{\Omega}}_{c}$ is derived, which characterizes the structure with or without a central density hole. Vortex structures are studied in detail with rotation frequency both above and below ${\ensuremath{\Omega}}_{c}$ and with respect to the miscible, symmetrically separated, and asymmetrically separated phases in their nonrotating ground-state counterparts.
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.