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arXiv:1310.2082 · Physical Review A

Counter-rotating vortices in miscible two-component Bose-Einstein condensates

Shungo Ishino, Makoto Tsubota, Hiromitsu Takeuchi

Published Dec 10, 2013• 24 citations
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Abstract

Counter-rotating vortices in miscible two-component Bose-Einstein condensates, in which superflows counter-rotate between the two components around the overlapped vortex cores, are studied theoretically in a pancake-shaped potential. In a linear stability analysis with the Bogoliubov--de Gennes model, we show that counter-rotating vortices are dynamically unstable against splitting into multiple vortices. The instability shows characteristic behaviors as a result of counter-superflow instability, which causes relaxation of relative flows between the two components in binary condensates. The characteristic behaviors are completely different from those of multiquantum vortices in single-component Bose-Einstein condensates; the number of vortices generated by the instability can become larger than the initial winding number of the counter-rotating vortex. We also investigate the nonlinear dynamics of the instability by numerically solving the Gross-Pitaevskii equations. The nonlinear dynamics drastically changes when the winding number of counter-rotating vortices becomes larger, which lead to nucleation of vortex pairs outside of the vortex core. The instability eventually develops into turbulence after the relaxation of the relative rotation between the two components.

DOI
10.1103/physreva.88.063617

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Counter-rotating vortices in miscible two-component Bose-Einstein condensates, in which superflows counter-rotate between the two components around the overlapped vortex cores, are studied theoretically in a pancake-shaped potential. In a linear stability analysis with the Bogoliubov--de Gennes model, we show that counter-rotating vortices are dynamically unstable against splitting into multiple vortices. The instability shows characteristic behaviors as a result of counter-superflow instability, which causes relaxation of relative flows between the two components in binary condensates. The characteristic behaviors are completely different from those of multiquantum vortices in single-component Bose-Einstein condensates; the number of vortices generated by the instability can become larger than the initial winding number of the counter-rotating vortex. We also investigate the nonlinear dynamics of the instability by numerically solving the Gross-Pitaevskii equations. The nonlinear dynamics drastically changes when the winding number of counter-rotating vortices becomes larger, which lead to nucleation of vortex pairs outside of the vortex core. The instability eventually develops into turbulence after the relaxation of the relative rotation between the two components.
We study theoretically the instability of countersuperflow, i.e., two counterpropagating miscible superflows, in uniform two-component Bose-Einstein condensates. Countersuperflow instability causes mutual friction between the superfluids, causing a momentum exchange between the two condensates, when the relative velocity of the counterflow exceeds a critical value. The momentum exchange leads to nucleation of vortex rings from characteristic density patterns due to the nonlinear development of the instability. Expansion of the vortex rings drastically accelerates the momentum exchange, leading to a highly nonlinear regime caused by intervortex interaction and vortex reconnection between the rings. For a sufficiently large interaction between the two components, rapid expansion of the vortex rings causes isotropic turbulence and the global relative motion of the two condensates relaxes. The maximum vortex line density in the turbulence is proportional to the square of the relative velocity.
We theoretically study the instability of countersuperflow, i.e. , two counter-propagating miscible superflows, in uniform two-component Bose-Einstein condensates. When the relative velocity of the counterflow exceeds a critical value, the instability causes the nucleation and expansion of vortex rings. A lot of vortex reconnections are caused and lead to binary quantum turbulence, where both components become turbulent. Then we introduce the unique velocity in two-component Bose-Einstein condensates and investigate the probability distribution of the velocity in the binary quantum turbulence to obtain the probability distribution whose tail in the high-velocity region is considerably suppressed compared to single-component quantum turbulence.
This study aims to research on dynamics of two quantized vortices in miscible two-component Bose--Einstein condensates, trapped by a circular box potential by using the Gross--Pitaevskii equation. We consider a situation in which two vortices belong to different components and they are initially close. Their dynamics are significantly different from those of a vortex pair in a single-component condensate. When two vortices are initially co-located, they are split by dynamical instability or remain co-located depending on their intercomponent interaction. If the two split vortices have the same sign of circulation, they rotate around each other. Then, the angular velocity can be given as a function of the distance between two vortices, which is understood through the equations of motion and their interaction. If the circulations of two close vortices have different signs, however, they move in the same direction initially, then overlap during the dynamics. This subsequent overlap can be categorized into two types based on the initial distance between them. The mechanism of this overlapping can be understood from the interaction between the vortex and its image vortex, which makes the two vortices close to each other even if the intrinsic interaction between them is repulsive.
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.
Binary Bose-Einstein condensates of two distinct atomic species are studied, with interesting effects being verified due to the imbalance of atomic masses. We study the formation of vortices and associated turbulence flows created by stirring two mass-imbalanced coupled Bose-Einstein condensates in the miscible regime. We consider the mixture in the laboratory frame, confined in a pancake-like harmonic trap slightly perturbed elliptically by a time-dependent periodic potential, which introduces turbulent dynamics with final stable patterns of vortices, induced by the periodicity of the perturbation. Derived rotational frequencies are shown to be associated with the observed vortex patterns in the asymptotic regime, with a correspondence between the stirring procedure and a direct time-independent approach being indicated. It was also confirmed that a larger pattern of vortices is supported by the higher mass condensed species at the same frequency. For the experimentally accessible mixtures $^{85}\mathrm{Rb}\text{\ensuremath{-}}^{133}\mathrm{Cs}$ and $^{85}\mathrm{Rb}\text{\ensuremath{-}}^{87}\mathrm{Rb}$, we numerically solve the equations of motion and analyze the system dynamics using a range of measures including energy spectra. In the transient turbulent regime, spectral analysis shows evidence for the characteristic ${k}^{\ensuremath{-}5/3}$ Kolmogorov classical law associated with turbulence, modified by the universal ${k}^{\ensuremath{-}3}$ vortex core scaling in the ultraviolet regime.