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Journal of Physics Conference Series

Vortex Nucleation and Transition to Turbulence in two-component Bose—Einstein condensates

Shungo Ishino, Makoto Tsubota, Hiromitsu Takeuchi

Published Dec 17, 2012• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1742-6596/400/1/012022

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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.
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 turbulence in miscible two-component Bose-Einstein condensates confined in a box potential using the coupled Gross-Pitaevskii equations. Turbulence is driven by an oscillating force, causing the components to oscillate either in-phase (co-oscillating) or out-of-phase (counter-oscillating). A parameter measuring component separation (0 for overlap, 1 for full separation) reveals two turbulent states: coupled (the parameter ∼0\sim0∼0) and decoupled (the parameter ∼0.5\sim0.5∼0.5). Co-oscillating flows transition between these states at a critical interaction strength, while counter-oscillating flows consistently show the decoupled state. A probabilistic model predicts the decoupled state's parameter as 4/π−1=0.523\sqrt{4/π- 1} = 0.5234/π−1​=0.523, consistent with simulations.
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 use classical field simulations of the homogeneous Bose gas to study the breakdown of superflow due to vortex nucleation past a cylindrical obstacle at finite temperature. Thermal fluctuations modify the vortex nucleation from the obstacle, turning antiparallel vortex lines (which would be nucleated at zero temperature) into wiggly lines, vortex rings, and even vortex tangles. We find that the critical velocity for vortex nucleation decreases with increasing temperature and scales with the speed of sound of the condensate, becoming zero at the critical temperature for condensation.