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.
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.
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.
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
Fluid turbulence remains an open problem in contemporary physics. In gases or liquids encountered in daily life, turbulence is comprised of swirling vortices of varying sizes, shapes and strengths. The impossibility of making detailed predictions of turbulent flows comes, in part, from the complicated nature of these vortices. Turbulence in quantum mechanical superfluids, on the other hand, is comparatively simple. When stirred, a superfluid produces well-defined, discretised vortex lines, and hence turbulence in these fluids is much more straightforward to interpret. As such, there is hope that the study of vortices in superfluids may hold the key to unlocking the mysteries of turbulence.
We review turbulence in ultracold quantum gases, using the scalar contact-interaction Bose-Einstein condensate as the reference system for quantized circulation, compressibility, vortices, sound, and cascades. We focus on the quantitative diagnostics that connect helium and classical phenomenology to microscopic wave-function dynamics: incompressible and compressible kinetic-energy spectra, wave-occupation spectra, spectral fluxes, vortex-resolved correlations, and velocity statistics. These diagnostics distinguish equilibrium vortex organization, decaying turbulent relaxation, forced cascade dynamics, and weak-wave turbulence, and show why power laws alone are insufficient evidence for a cascade. We survey experiments on two-dimensional Onsager clustering, three-dimensional vortex-line turbulence, box-trap wave cascades, engineered dissipation, and turbulent equations of state. We close by briefly placing the contact-interaction scalar superfluid system in a broader landscape of nonlocal, multicomponent, fermionic, and driven-dissipative quantum fluids, where turbulence concepts can be tested for universality.
We investigate wave-vortex interaction emerging from an expanding compact vortex cluster in a two-dimensional Bose-Einstein condensate. We adapt techniques developed for compact gravitational objects to derive the characteristic modes of the wave-vortex interaction perturbatively around an effective vortex flow field. We demonstrate the existence of orbits or sound rings, in analogy to gravitational light rings, and compute the characteristic spectrum for the out-of-equilibrium vortex cluster. The spectrum obtained from numerical simulations of a stochastic Gross-Pitaevskii equation exhibiting an expanding vortex cluster is in excellent agreement with analytical predictions. Our findings are relevant for two-dimensional quantum turbulence, the semiclassical limit around fluid flows, and rotating compact objects exhibiting discrete circulation.
Vortex reconnections and interactions play a fundamental role in the dynamics of fluids and turbulent flows, both in the classical and quantum regime. Studying vortices in a clean system like ultracold gases can therefore help, as a bottom-up approach, to understand the physics in a wider context, including superfluid helium, polariton condensates, fluid dynamics and turbulence, neutron stars and cosmological models. So far vortex-vortex interaction was studied in Bose-Einstein condensates either in rotating systems with the observation of regular Abrikosov lattices or in flat condensates across the Berezinskii-Kosterlitz-Thouless transition. In both cases the geometrical constraints allowed to study just a planar interaction among aligned or anti-aligned vortices. The present study instead is carried out in an axisymmetric cigar-shaped Bose-Einstein condensate. Vortices in prolate structures are also known as solitonic vortices. This geometry is especially suitable for investigating vortex interactions. Indeed vortices are oriented perpendicularly to the condensate axis to minimize their length, hence energy, and, because of the cylindrical symmetry, the orientation of a vortex in the radial plane has no constraints. These facts permit interactions to occur with different incoming relative angles between the vortex lines and with different relative velocities. The strong confinement, acting along the radial axis, enhances also interesting effects due to the boundaries.