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Science

Real-Time Dynamics of Single Vortex Lines and Vortex Dipoles in a Bose-Einstein Condensate

Daniel V. Freilich, Dylan Bianchi, Adam M. Kaufman, Thomas Langin, David S. Hall

Published Sep 2, 2010• 262 citations
Publisher

Abstract

Understanding the behavior of quantized vortices is essential to gaining insight into diverse superfluid phenomena, from critical-current densities in superconductors to quantum turbulence in superfluids. We observe the real-time dynamics of quantized vortices in trapped dilute-gas Bose-Einstein condensates by repeatedly imaging the vortex cores. The precession frequency of a single vortex is measured by explicitly observing its time dependence and is found to be in good agreement with theory. We further characterize the dynamics of vortex dipoles in two distinct configurations: (i) an asymmetric configuration, in which the vortex trajectories are dynamic and nontrivial, and (ii) a stable, symmetric configuration, in which the dipole is stationary.

DOI
10.1126/science.1191224

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When a vessel containing a superfluid is set in rotational motion, the superfluid does not rotate uniformly with it; instead, quantized vortices develop. Vortices have been observed in a range of superfluids, including helium, atomic Bose-Einstein condensates, and type II superconductors in a magnetic field. Freilich et al. (p. [1182][1]) visualized real-time vortex dynamics in the most tunable of superfluid systems, an atomic Bose-Einstein condensate. A small section of condensate was displaced from the trap and imaged as it fell in the gravitational field. The technique is applicable to exploring other complex dynamic systems, such as vortex reconnections and the role of vortices in quantum turbulence. [1]: /lookup/doi/10.1126/science.1191224

Science•Sep 2, 2010•0 citations
Understanding the behavior of quantized vortices is essential to gaining insight into diverse superfluid phenomena, from critical-current densities in superconductors to quantum turbulence in superfluids. We observe the real-time dynamics of quantized vortices in trapped dilute-gas Bose-Einstein condensates by repeatedly imaging the vortex cores. The precession frequency of a single vortex is measured by explicitly observing its time dependence and is found to be in good agreement with theory. We further characterize the dynamics of vortex dipoles in two distinct configurations: (i) an asymmetric configuration, in which the vortex trajectories are dynamic and nontrivial, and (ii) a stable, symmetric configuration, in which the dipole is stationary.
A quantized vortex dipole is the simplest vortex molecule, comprising two countercirculating vortex lines in a superfluid. Although vortex dipoles are endemic in two-dimensional superfluids, the precise details of their dynamics have remained largely unexplored. We present here several striking observations of vortex dipoles in dilute-gas Bose-Einstein condensates, and develop a vortex-particle model that generates vortex line trajectories that are in good agreement with the experimental data. Interestingly, these diverse trajectories exhibit essentially identical quasiperiodic behavior, in which the vortex lines undergo stable epicyclic orbits.
Recently, Freilich et al. [Science 329, 1182 (2010)] experimentally discovered stationary states of vortex dipoles, pairs of vortices of opposite circulation, in dilute Bose-Einstein condensates. To explain their observations, we perform simulations based on the Gross-Pitaevskii equation and obtain excellent quantitative agreement on the size of the stationary dipole. We also investigate how their imaging method, in which atoms are repeatedly extracted from a single condensate, affects the vortex dynamics. We find that it mainly induces isotropic size oscillations of the condensate without otherwise disturbing the vortex trajectories. Thus, the imaging technique appears to be a promising tool for studying real-time superfluid dynamics.
In this review, we give an overview of the experimental and theoretical advances in the physics of quantized vortices in dilute atomic-gas Bose--Einstein condensates in a trapping potential, especially focusing on experimental research activities and their theoretical interpretations. Making good use of the atom optical technique, the experiments have revealed many novel structural and dynamic properties of quantized vortices by directly visualizing vortex cores from an image of the density profiles. These results lead to a deep understanding of superfluid hydrodynamics of such systems. Typically, vortices are stabilized by a rotating potential created by a laser beam, magnetic field, and thermal gas. Finite size effects and inhomogeneity of the system, originating from the confinement by the trapping potential, yield unique vortex dynamics coupled with the collective excitations of the condensate. Measuring the frequencies of the collective modes is an accurate tool for clarifying the character of the vortex state. The topics included in this review are the mechanism of vortex formation, equilibrium properties, and dynamics of a single vortex and those of a vortex lattice in a rapidly rotating condensate.
We have observed and characterized the dynamics of singly quantized vortices in dilute-gas Bose-Einstein condensates. Our condensates are produced in a superposition of two internal states of 87Rb, with one state supporting a vortex and the other filling the vortex core. Subsequently, the state filling the core can be partially or completely removed, reducing the radius of the core by as much as a factor of 13, all the way down to its bare value of the healing length. The corresponding superfluid rotation rates, evaluated at the core radius, vary by a factor of 150, but the precession frequency of the vortex core about the condensate axis changes by only a factor of 2.
We report experimental observations and numerical simulations of the formation, dynamics, and lifetimes of single and multiply charged quantized vortex dipoles in highly oblate dilute-gas Bose-Einstein condensates (BECs). We nucleate pairs of vortices of opposite charge (vortex dipoles) by forcing superfluid flow around a repulsive Gaussian obstacle within the BEC. By controlling the flow velocity we determine the critical velocity for the nucleation of a single vortex dipole, with excellent agreement between experimental and numerical results. We present measurements of vortex dipole dynamics, finding that the vortex cores of opposite charge can exist for many seconds and that annihilation is inhibited in our trap geometry. For sufficiently rapid flow velocities, clusters of like-charge vortices aggregate into long-lived multiply charged dipolar flow structures.
When a vessel containing a superfluid is set in rotational motion, the superfluid does not rotate uniformly with it; instead, quantized vortices develop. Vortices have been observed in a range of superfluids, including helium, atomic Bose-Einstein condensates, and type II superconductors in a magnetic field. Freilich et al. (p. [1182][1]) visualized real-time vortex dynamics in the most tunable of superfluid systems, an atomic Bose-Einstein condensate. A small section of condensate was displaced from the trap and imaged as it fell in the gravitational field. The technique is applicable to exploring other complex dynamic systems, such as vortex reconnections and the role of vortices in quantum turbulence. [1]: /lookup/doi/10.1126/science.1191224