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Dynamics of Vortices and their Interactions in Bose-Einstein Condensates

Simone Serafini

Published Jan 1, 2017• 0 citations
Publisher

Abstract

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.

DOI
10.15168/11572_368004

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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.
Reconnections and interactions of filamentary coherent structures play a fundamental role in the dynamics of fluids,redistributing energy and helicity among the length scales and inducing fine-scale turbulent mixing. Unlike ordinary fluids, where vorticity is a continuous field, in quantum fluids vorticity is concentrated into discrete (quantized) vortex lines turning vortex reconnections into isolated events, conceptually easier to study. Here we report experimental and numerical observations of three-dimensional quantum vortex interactions in a cigar-shaped atomic Bose--Einstein Condensate. In addition to standard reconnections, already numerically and experimentally observed in homogeneous systems away from boundaries, we show that double reconnections, rebounds and ejections can also occur as a consequence of the non-homogeneous, confined nature of the system.
We study the real-time dynamics of vortices in a large elongated Bose-Einstein condensate (BEC) of sodium atoms using a stroboscopic technique. Vortices are produced via the Kibble-Zurek mechanism in a quench across the BEC transition and they slowly precess keeping their orientation perpendicular to the long axis of the trap as expected for solitonic vortices in a highly anisotropic condensate. Good agreement with theoretical predictions is found for the precession period as a function of the orbit amplitude and the number of condensed atoms. In configurations with two or more vortices, we see signatures of vortex-vortex interaction in the shape and visibility of the orbits. In addition, when more than two vortices are present, their decay is faster than the thermal decay observed for one or two vortices. The possible role of vortex reconnection processes is discussed.
Reconnections of coherent filamentary structures play a key role in the dynamics of fluids, redistributing energy and helicity among the length scales, triggering dissipative effects, and inducing fine-scale mixing. Unlike ordinary (classical) fluids where vorticity is a continuous field, in superfluid helium and in atomic Bose-Einstein condensates (BECs) vorticity takes the form of isolated quantized vortex lines, which are conceptually easier to study. New experimental techniques now allow visualization of individual vortex reconnections in helium and condensates. It has long being suspected that reconnections obey universal laws, particularly a universal scaling with time of the minimum distance between vortices δ. Here we perform a comprehensive analysis of this scaling across a range of scenarios relevant to superfluid helium and trapped condensates, combining our own numerical simulations with the previous results in the literature. We reveal that the scaling exhibits two distinct fundamental regimes: a [Formula: see text] scaling arising from the mutual interaction of the reconnecting strands and a [Formula: see text] scaling when extrinsic factors drive the individual vortices.
The experimental realization of quantum-degenerate Bose gases made of atoms with sizeable magnetic dipole moments has created a new type of fluid, known as a quantum ferrofluid, which combines the extraordinary properties of superfluidity and ferrofluidity. A hallmark of superfluids is that they are constrained to rotate through vortices with quantized circulation. In quantum ferrofluids the long-range dipolar interactions add new ingredients by inducing magnetostriction and instabilities, and also affect the structural properties of vortices and vortex lattices. Here we give a review of the theory of vortices in dipolar Bose-Einstein condensates, exploring the interplay of magnetism with vorticity and contrasting this with the established behaviour in non-dipolar condensates. We cover single vortex solutions, including structure, energy and stability, vortex pairs, including interactions and dynamics, and also vortex lattices. Our discussion is founded on the mean-field theory provided by the dipolar Gross-Pitaevskii equation, ranging from analytic treatments based on the Thomas-Fermi (hydrodynamic) and variational approaches to full numerical simulations. Routes for generating vortices in dipolar condensates are discussed, with particular attention paid to rotating condensates, where surface instabilities drive the nucleation of vortices, and lead to the emergence of rich and varied vortex lattice structures. We also present an outlook, including potential extensions to degenerate Fermi gases, quantum Hall physics, toroidal systems and the Berezinskii-Kosterlitz-Thouless transition.
Interactions and reconnections of vortices are fundamental in many areas of physics, including classical and quantum fluids where they are central to understanding phenomena such as turbulence. In three-dimensional (3D) superfluids, quantum vortices are one-dimensional filaments that can intersect, reconnect, and recoil with irreversible dynamics described by near-universal scaling laws. We explore quantum-vortex reconnections in a four-dimensional superfluid, where a vortex is a two-dimensional surface. Using real-time numerical simulations, we find much richer behavior than in 3D, including stable intersecting vortex surfaces which do not reconnect, and unusual vortex reconnections which occur without significant energy dissipation, which may indicate quasireversible dynamics. Our work raises many interesting questions about vortex physics in extradimensional systems and may be further extended to look at vortex dynamics and turbulence in higher-dimensional spaces.