Abstract
A large ensemble of quantum vortices in a superfluid may itself be treated as a novel kind of fluid that exhibits anomalous hydrodynamics. Here we consider the dynamics of vortex clusters with thermal friction, and present an analytic solution that uncovers a new universality class in the out-of-equilibrium dynamics of dissipative superfluids. We find that the long-time dynamics of the vorticity distribution is an expanding Rankine vortex (i.e.~top-hat distribution) independent of initial conditions. This highlights a fundamentally different decay process to classical fluids, where the Rankine vortex is forbidden by viscous diffusion. Numerical simulations of large ensembles of point vortices confirm the universal expansion dynamics, and further reveal the emergence of a frustrated lattice structure marked by strong correlations. We present experimental results in a quasi-two-dimensional Bose-Einstein condensate that are in excellent agreement with the vortex fluid theory predictions, demonstrating that the signatures of vortex fluid theory can be observed with as few as $N\sim 11$ vortices. Our theoretical, numerical, and experimental results establish the validity of the vortex fluid theory for superfluid systems.
Highlights
A defining feature of quantum fluids is that they exhibit quantized vortices
We further demonstrate the universality of the Rankine vortex by numerically simulating large ensembles of vortex clusters
We have analytically shown within dissipative vortex fluid theory that any dense vortex cluster in a finite-temperature quantum fluid evolves to form a Rankine vortex, confirming a new universality class in dissipative superfluids
Summary
A defining feature of quantum fluids is that they exhibit quantized vortices. These stable topological defects have a circulation that is quantized in units of = h/m, where h is Planck’s constant and m is the mass of a fluid particle. Recent theoretical work has shown that a dense system of chiral (i.e., same sign) quantum vortices at large scales may be treated as a kind of fluid in its own right [22] In such a vortex fluid, the dynamics are governed by a hydrodynamic equation that contains anomalous stress terms absent in the standard Euler equation, allowing for phenomena such as analog edge states of the fractional quantum Hall effect [23]. This theory was recently extended to describe dissipative effects [24], accounting for mutual friction due to the interaction between the superfluid and a stationary thermal component present in experiments. Through our numerical and experimental results, we demonstrate a platform for further experiments investigating the vortex fluid theory
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