Abstract
We stir vortices into a trapped quasi two-dimensional atomic Bose-Einstein condensate by moving three laser stirrers. We apply stirring protocols introduced by Boyland et al. (2000), that efficiently build in topological chaos in classical fluids and are classified as Pseudo-Anosov stirring protocols. These are compared to their inefficient mixing counterparts, finite-order stirring protocols. We investigate if inefficient stirring protocols result in a more clustered distribution of vortices. The efficiency with which vortices are 'mixed' or distributed in a condensate is important for investigating dynamics of continuously forced quantum turbulence and the existence of the inverse cascade in turbulent two-dimensional superfluids.
Highlights
Jupiter’s Great Red Spot is a beautiful demonstration of a large spot of vorticity, one of the defining features of two dimensional (2D) classical turbulence, arising from the inverse cascade process (Sommeria et al (1988); Marcus (1988))
After a few stirring operations, the vortices appear randomly distributed, independent of stirring protocol. This result is an indication of the potential nature of quantum fluids
One might expect underlying chaotic dynamics would result in a vortex distribution that is less clustered than underlying regular dynamics
Summary
Jupiter’s Great Red Spot is a beautiful demonstration of a large spot of vorticity, one of the defining features of two dimensional (2D) classical turbulence, arising from the inverse cascade process (Sommeria et al (1988); Marcus (1988)). For stokes flow (characterised by Reynolds number, Re 1), chaotic advection of fluid particles is built into the flow faster by stirring schemes that build in topological chaos Such protocols are classified as pseudo-Anosov stirring protocols and it is established that stirring a fluid in such a way results in exponential stretching of material lines. In the remainder of this paper we present numerical simulations of three laser stirrers in an atomic BEC tracing out the finite-order and pseudo-Anosov stirring schemes A and B, presented above. We choose the velocity of the laser stirrers to be larger than the critical velocity for vortex nucleation in order to determine if a pseudo-Anosov stirring protocol (B) results in a more random distribution of vortices than a finite-order stirring scheme (A). Snap-shots of time-evolution of the condensate density profile is depicted in figure 3
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