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arXiv:1507.01511 · Physical Review Letters

Dynamics and Interaction of Vortex Lines in an Elongated Bose-Einstein Condensate

Simone Serafini, Matteo Barbiero, M. Debortoli, Simone Donadello, F. Larcher, F. Dalfovo, Giacomo Lamporesi, G. Ferrari

Published Oct 21, 2015• 69 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.115.170402

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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.
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.
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.
We observe solitonic vortices in an atomic Bose-Einstein condensate (BEC) after free expansion. Clear signatures of the nature of such defects are the twisted planar density depletion around the vortex line, observed in absorption images, and the double dislocation in the interference pattern obtained through homodyne techniques. Both methods allow us to determine the sign of the quantized circulation. Experimental observations agree with numerical simulations. These solitonic vortices are the decay product of phase defects of the BEC order parameter spontaneously created after a rapid quench across the BEC transition in a cigar-shaped harmonic trap and are shown to have a very long lifetime.
It has been demonstrated experimentally that non-axisymmetric vortices precess around the center of a Bose-Einstein condensate. Two types of single vortex states have been observed, usually referred to as the S vortex and the U vortex. We study theoretically the single vortex excitations in spherical and elongated condensates as a function of the interaction strength. We solve numerically the Gross-Pitaevskii equation and calculate the angular momentum as a function of precession frequency. The existence of two types of vortices means that we have two different precession frequencies for each angular momentum value. As the interaction strength increases the vortex lines bend and the precession frequencies shift to lower values. We establish that for given angular momentum the S vortex has higher energy than the U vortex in a rotating elongated condensate. We show that the S vortex is related to the solitonic vortex, which is a nonlinear excitation in the nonrotating system. For small interaction strengths the S vortex is related to the dark soliton. In the dilute limit a lowest Landau level calculation provides an analytic description of these vortex modes in terms of the harmonic oscillator states.
Motivated by recent experiments, we study theoretically the dynamics of vortices in the crossover from two dimensions to one in atomic condensates in elongated traps. We explore the transition from the dynamics of a vortex to that of a dark soliton as the one-dimensional limit is approached, mapping this transition out as a function of the key system parameters. Moreover, we probe this transition dynamically through the hysteresis under time-dependent deformation of the trap at the dimensionality crossover. When the solitonic regime is probed during the hysteresis, significant angular momentum is lost from the system, but remarkably, the vortex can reemerge.
The dynamics of vortices in trapped Bose-Einstein condensates are investigated both analytically and numerically. In axially symmetric traps, the critical rotation frequency for metastability of an isolated vortex coincides with the largest vortex precession frequency (or anomalous mode) in the Bogoliubov excitation spectrum. The number of anomalous modes increases for an elongated condensate. The largest mode frequency exceeds the thermodynamic critical frequency and the nucleation frequency at which vortices are created dynamically. Thus, anomalous modes describe both vortex precession and the critical rotation frequency for creation of the first vortex in an elongated condensate.