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 under 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 universal in the form of 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 of expanding vortex clusters 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∼11 vortices. Our theoretical, numerical, and experimental results establish the validity of the vortex fluid theory for superfluid systems.
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 under 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 universal in the form of 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 of expanding vortex clusters 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∼11 vortices. Our theoretical, numerical, and experimental results establish the validity of the vortex fluid theory for superfluid systems.
In this thesis, we analytically and numerically study two different scenarios of vortex dynamics in a two-dimensional superfluid. The first system we explore is an expanding cluster of like-sign vortices, which recently suggested it could explain observations in a superfluid optomechanics experiment. We employ a recent theoretical model that approximates large collections of vortices as a fluid and present an analytic solution for its dynamics. Analysis suggests that as a cluster expands due to thermal friction, it forms a Rankine vortex (i.e., a top-hat distribution) that expands self-similarly in time regardless of initial vorticity distribution. Numerical simulations of point vortices confirm this universal expanding regime and further demonstrates vortex lattice formation that goes beyond the vortex fluid theory. We analyse correlations that emerge in the resulting lattices and observe decaying disorder as the cluster expands. Furthermore, we analyse experimental data from a quasi-two-dimensional 87Rb Bose-Einstein condensate, which supports the vortex fluid theory’s predictions.The second scenario considers the dynamics of a scattering event where a single quantum vortex interacts with a uniform, circular pinning potential in a steady two-dimensional superfluid flow. We first develop an approximate hydrodynamical model to understand the interaction between the vortex and the pinning potential in the conservative regime and find it is in good agreement with the mean-field Gross-Pitaevskii equation in the low-velocity limit. We further solve the Gross-Pitaevskii equation for higher background velocities to study how the vortex moves around pinning sites, interacts with it, and ultimately becomes pinned. We uncover four different regimes of vortex pinning, each marked with a characteristic emission of sound energy. Finally, we study how vortices become unpinned from a pinning site, revealing large vortex dipoles form to stabilise the system.Our work in this thesis takes significant steps towards advancing knowledge of both the collective dynamics of vortices and their individual interaction with defects upon surface substrates. Our numerical and analytical results opens up new avenues of exploration be it further understanding dissipation mechanisms in two-dimensional superfluids, or elucidating the nature of vortex pinning in systems such as neutron stars.
Dissipation of quantum vortex motion is fundamental to superfluid dynamics and quantum turbulence, yet there is currently a large gap between theory and experiments with ultracold atoms. Here we present a microscopic open quantum systems theory of thermally damped vortex motion in oblate atomic superfluids that includes previously neglected energy-damping interactions between superfluid and thermal atoms. This mechanism couples strongly to vortex core motion and causes dissipation of vortex energy due to mutual friction, as well as Brownian motion of vortices due to thermal fluctuations. We derive an analytic expression for the dimensionless mutual friction coefficient that gives excellent quantitative agreement with experimentally measured values, without any fitted parameters. Our work closes an existing two orders of magnitude gap between dissipation theory and experiments, previously bridged by fitted parameters, and provides a microscopic origin for the mutual friction and diffusion of quantized vortices in two-dimensional atomic superfluids.
We show that in two dimensional superfluids a large number of quantum vortices with positive and negative circulations behave as an inviscid fluid on large scales. Two hydrodynamical velocities are introduced to describe this emergent binary vortex fluid, via vortex number current and vortex change current. The velocity field associated with the vortex number current evolves according to a hydrodynamic equation, subject to an anomalous stress absent from Euler's equation. In contrast to the chiral vortex fluid containing only like-sign vortices, the binary vortex fluid is compressible and the orbital angular momentum is not conserved, as characterized by an asymmetric Cauchy stress tensor. Dissipation effects due to thermal friction and vortex-sound interactions induce an effective damping rate, an anomalous viscous stress tensor, and a coefficient of second viscosity.
The two-dimensional point vortex model was first introduced in the nineteenth century by Helmholtz and Kirchhoff. The methods of statistical physics were used to apply it to the problem of two-dimensional fluid flow and turbulence by Onsager in the 1940s, and it has provided many qualitative insights into the emergence of large scale vortices from turbulence. However, until recently there has been no quantitative comparison of its predictions with experimental measurements. Here we present the results of two sets of superfluid dynamics experiments for which the point vortex model provides quantitative insights. The first is in a planar quasi-two-dimensional atomic gas Bose-Einstein condensate cooled to nanokelvin temperatures [1]. The superfluid is confined and manipulated in a potential formed by laser light reflected from a Digital Micromirror Device (DMD) identical to those found in digital video projectors. Two different stirring procedures inject vortices into the gas. For the first stirring method the vortex number decays relatively quickly. However, the second stirring method leads to the formation of two macroscopic vortex clusters of opposite signs. The system quickly relaxes into a deeply negative temperature Onsager vortex state that persists in quasi-equilibrium for more than fifty cluster turnover times. The second experiment is in a superfluid helium thin film [2]. Optical stirring generates a macroscopic superfluid flow in the system that lifts the degeneracy in frequency of a number of third sound modes. These frequency splitting are subsequently observed to decay. Modelling the system using the point vortex model with a small amount of dissipation leads to a consistent interpretation of the measurements. We infer that a pinned persistent current slowly decays as a cluster of opposite sign vortices slowly annihilate the central charge. Improvements in the experimental apparatus are expected to lead to the capability of tracking the dynamics of a single vortex in real time. [1] Negative-Temperature Onsager Vortex Clusters in a Quantum Fluid, G. Gauthier, M. T. Reeves, X. Yu, A. S. Bradley, M. Baker, T. A. Bell, H. Rubinsztein-Dunlop, M. J. Davis, T. W. Neely, to appear in Science (2019). arXiv:1801.06951 [2] Coherent vortex dynamics in a strongly-interacting superfluid on a silicon chip, Yauhen P. Sachkou, Christopher G. Baker, Glen I. Harris, Oliver R. Stockdale, Stefan Forstner, Matthew T. Reeves, Xin He, David L. McAuslan, Ashton S. Bradley, Matthew J. Davis, Warwick P. Bowen. arXiv:1902.04409
We study the emergence of distinctly subdiffusive scaling in the vicinity of an anomalous nonthermal fixed point, which reflects spatio-temporally self-similar scaling dynamics, in a quasi-two-dimensional Bose gas in the superfluid phase. In this regime, the far-from-equilibrium dynamics is governed by ensembles of quantum vortices. Mutual annihilation of vortices and antivortices drives coarsening, leading to the observed scaling behavior and an algebraically growing mean inter-defect distance over time. Introducing dipolar interactions provides additional control over the anisotropy and long-range character of the interactions. This control, combined with various parameter regimes and initial conditions, allows us to explore the universality of the subdiffusive scaling near the anomalous nonthermal fixed point. Scaling exponents are extracted from occupation-number spectra, the temporal evolution of inter-defect distances, and the decay of the total vortex number. At late times, compressible excitations of the background condensate grow due to ongoing vortex-antivortex annihilation, resulting in a crossover toward diffusion-type scaling near the Gaussian nonthermal fixed point. The observed temporal scaling depends only weakly on the strength and anisotropy of the dipolar interactions, demonstrating the universality of both anomalous and diffusion-type nonthermal fixed points. Nevertheless, the dipolar case exhibits qualitatively distinct vortex-clustering behavior. In contrast to non-dipolar gases, roton excitations in anisotropic, dipolar interactions appear to suppress same-sign vortex clustering, favoring the formation of vortex dipoles and maximizing the separation between vortices of equal sign. For pure contact interaction, we additionally observe spatial scaling characteristics consistent with Kraichnan--Kolmogorov turbulence. During a universal interval, in which the characteristic length scale associated with the inter-defect distance exhibits subdiffusive power-law growth, the moments of the superfluid velocity circulation around a square contour scale as predicted from classical turbulence theory. Higher-order moments of the velocity circulation reveal intermittent deviations, which are found to be consistent with values measured in fully developed classical turbulence. Notably, the subdiffusive coarsening clearly deviates from values known in classical systems. Collectively, these results provide strong evidence for the universality of the subdiffusive scaling near the anomalous nonthermal fixed point and establish a direct connection to decaying quantum turbulence cascades, highlighting the relevance of nonthermal fixed points in turbulence theory.