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arXiv:1106.0884 · Physical Review A

Countersuperflow instability in miscible two-component Bose-Einstein condensates

Shungo Ishino, Makoto Tsubota, Hiromitsu Takeuchi

Published Jun 3, 2011• 54 citations
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Abstract

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.

DOI
10.1103/physreva.83.063602

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•Jul 28, 2010•0 citations
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.
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 investigate the dynamics of two miscible superfluids experiencing fast counterflow in a narrow channel. The superfluids are formed by two distinguishable components of a trapped dilute-gas Bose-Einstein condensate (BEC). The onset of counterflow-induced modulational instability throughout the cloud is observed and shown to lead to the proliferation of dark-dark vector solitons. These solitons do not exist in single-component systems, exhibit intriguing beating dynamics, and can experience a transverse instability leading to vortex line structures. Experimental results and multidimensional numerical simulations are presented.
We explore instabilities in binary superfluids with a nonvanishing relative superflow, particularly focusing on counterflow and coflow instabilities. We extend recent results on the thermodynamic origin of finite superflow instabilities in single-component superfluids to binary systems and derive a criterion for the onset of instability through a hydrodynamic analysis, which applies to interacting many-body systems at finite temperature. We find that the onset of these instabilities is signaled by the determinant of the Hessian of the thermal free energy diverging and changing sign. We verify this hydrodynamic prediction in a holographic binary superfluid modeled with gauge/gravity duality, which naturally incorporates strong coupling, finite temperature, and dissipation. We also compare to results obtained using the Gross-Pitaevskii equation for weakly interacting Bose-Einstein condensates and find that the same criterion continues to apply at zero temperature, where it reduces to evaluating derivatives of the supercurrents with respect to the superfluid velocities. We observe that the critical velocities of these instabilities follow a general scaling law related to the interaction strength between superfluid components. Finally, the nonlinear stages of the instabilities are studied by full time evolution using gauge/gravity duality, where vortex annihilation leads to a decrease of superfluid velocity back to a value where the binary superfluid phase is stable.
Washington State University, Department of Physics and Astronomy, Pullman, Washington 99164, USA(Dated: July 29, 2010)Modulational instability (MI) due to relative motion of two superfluids is found for a miscible,binary Bose-Einstein condensate (BEC). For sufficiently large relative speeds of the BEC compo-nents, we experimentally observe the onset of counterflow induced MI leading to the proliferationof dark-dark vector solitons which can experience a transverse (snake) instability. This is in con-trast to nonlinear self-steepening and intercomponent shock formation previously observed at lowcounterflow speeds. Our experimental results are complemented by a linear stability analysis andby multi-dimensional numerical simulations that reveal an intriguing dynamical richness of the su-perfluid counterflow.