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arXiv:cond-mat/9609145 · Physical review. B, Condensed matter

Dynamical vortices in superfluid films

Daniel P. Arovas, José A. Freire

Published Jan 1, 1997• 60 citations
arXivHTMLPDF

Abstract

The coupling of superfluid film to a moving vortex is a gauge coupling entirely dictated by topology. From the definition of a linking number, one can define a gauge field ${\mathrm{A}}^{\mathrm{\ensuremath{\mu}}}$ , whose (2+1)-dimensional curl is the vortex three-current ${\mathrm{J}}^{\mathrm{\ensuremath{\mu}}}$ , and to which the superfluid is minimally coupled. We compute the superfluid density and current response to a moving vortex. Exploiting the analogy to (2+1)-dimensional electrodynamics, we compute the effective vortex mass M(\ensuremath{\omega}) and find that it is logarithmically divergent in the \ensuremath{\omega}\ensuremath{\rightarrow}0 limit, with a constant imaginary part, yielding a super-Ohmic dissipation in the presence of an oscillating superflow. Numerical integration of the nonlinear Schr\"odinger equation supports these conclusions. The interaction of vortices with impurities coupling to the density also is discussed.

DOI
10.1103/physrevb.55.1068

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The coupling of superfluid film to a moving vortex is a gauge coupling entirely dictated by topology. From the definition of a linking number, one can define a gauge field A\ensuremathμ{\mathrm{A}}^{\mathrm{\ensuremath{\mu}}}A\ensuremathμ , whose (2+1)-dimensional curl is the vortex three-current J\ensuremathμ{\mathrm{J}}^{\mathrm{\ensuremath{\mu}}}J\ensuremathμ , and to which the superfluid is minimally coupled. We compute the superfluid density and current response to a moving vortex. Exploiting the analogy to (2+1)-dimensional electrodynamics, we compute the effective vortex mass M(\ensuremath{\omega}) and find that it is logarithmically divergent in the \ensuremath{\omega}\ensuremath{\rightarrow}0 limit, with a constant imaginary part, yielding a super-Ohmic dissipation in the presence of an oscillating superflow. Numerical integration of the nonlinear Schr"odinger equation supports these conclusions. The interaction of vortices with impurities coupling to the density also is discussed.
Abstract Vorticity in two-dimensional superfluids is subject to intense research efforts due to its role in quantum turbulence, dissipation and the BKT phase transition. Interaction of sound and vortices is of broad importance in Bose–Einstein condensates and superfluid helium. However, both the modelling of the vortex flow field and of its interaction with sound are complicated hydrodynamic problems, with analytic solutions only available in special cases. In this work, we develop methods to compute both the vortex and sound flow fields in an arbitrary two-dimensional domain. Further, we analyse the dispersive interaction of vortices with sound modes in a two-dimensional superfluid and develop a model that quantifies this interaction for any vortex distribution on any two-dimensional bounded domain, possibly non-simply connected, exploiting analogies with fluid dynamics of an ideal gas and electrostatics. As an example application we use this technique to propose an experiment that should be able to unambiguously detect single circulation quanta in a helium thin film.
We give a general review of recent developments in the theory of vortices in superfluids and superconductors, discussing why the dynamics of vortices is important, and why some key results are still controversial. We discuss work that we have done on the dynamics of quantized vortices in a superfluid. Despite the fact that this problem has been recognized as important for forty years, there is still a lot of controversy about the forces on and masses of quantized vortices. We think that one can get unambiguous answers by considering a broken symmetry state that consists of one vortex in an infinite ideal system. We argue for a Magnus force that is proportional to the superfluid density, and we find that the effective mass density of a vortex in a neutral superfluid is divergent at low frequencies. We have generalized some of the results for a neutral superfluid to a charged system.
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.
We carry out extensive direct numerical simulations to investigate the interaction of active particles and fields in the two-dimensional Gross-Pitaevskii superfluid, in both simple and turbulent flows. The particles are active in the sense that they affect the superfluid even as they are affected by it. We tune the mass of the particles, which is an important control parameter. At the one-particle level, we show how light, neutral, and heavy particles move in the superfluid, when a constant external force acts on them; in particular, beyond a critical velocity, at which a vortex-antivortex pair is emitted, particle motion can be periodic or chaotic. We demonstrate that the interaction of a particle with vortices leads to dynamics that depends sensitively on the particle characteristics. We also demonstrate that assemblies of particles and vortices can have rich, and often turbulent, spatiotemporal evolution. In particular, we consider the dynamics of the following illustrative initial configurations: (a) one particle placed in front of a translating vortex-antivortex pair; (b) two particles placed in front of a translating vortex-antivortex pair; (c) a single particle moving in the presence of counter-rotating vortex clusters; (d) four particles in the presence of counter-rotating vortex clusters. We compare our work with earlier studies and examine its implications for recent experimental studies in superfluid helium and Bose-Einstein condensates.