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arXiv:0809.4400 · Physical Review A

Finite-temperature vortex dynamics in Bose-Einstein condensates

B. Jackson, Nick P. Proukakis, Carlo F. Barenghi, E. Zaremba

Published May 12, 2009• 87 citations
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Abstract

We study the dynamics of a vortex in an atomic Bose-condensed gas at finite temperature within the Zaremba-Nikuni-Griffin formalism. In a harmonically trapped pancake-shaped condensate, an off-centered vortex is known to decay by spiraling out toward the edge of the condensate. We quantify the dependence of this decay on temperature, atomic collisions, and thermal cloud rotation. Near the trap center where the density varies slowly, we show that our numerical results agree with the predictions of the Hall-Vinen phenomenological friction force model used to describe quantized vorticity in superfluid systems. Our result thus clarifies the microscopic origin of the friction and provides an ab initio determination of its value.

DOI
10.1103/physreva.79.053615

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We study the dynamics of a vortex in an atomic Bose-condensed gas at finite temperature within the Zaremba-Nikuni-Griffin formalism. In a harmonically trapped pancake-shaped condensate, an off-centered vortex is known to decay by spiraling out toward the edge of the condensate. We quantify the dependence of this decay on temperature, atomic collisions, and thermal cloud rotation. Near the trap center where the density varies slowly, we show that our numerical results agree with the predictions of the Hall-Vinen phenomenological friction force model used to describe quantized vorticity in superfluid systems. Our result thus clarifies the microscopic origin of the friction and provides an ab initio determination of its value.
We study the dynamics of vortices in finite temperature atomic Bose-Einstein condensates, focusing on decay rates, precession frequencies, and core brightness, motivated by a recent experiment [Science 329, 1182 (2010)] in which real-time dynamics of a single vortex was observed. Using the Zaremba, Nikuni, and Griffin (ZNG) formalism based on a dissipative Gross-Pitaevskii equation for the condensate coupled to a semiclassical Boltzmann equation for the thermal cloud, we find a rapid nonlinear increase of both the decay rate and precession frequency with increasing temperatures. The increase, which is dominated by the dynamical condensate-thermal coupling is also dependent on the intrinsic thermal cloud collisional dynamics; the precession frequency also varies with the initial radial coordinate. The integrated thermal cloud density in the vortex core is for the most part independent of the position of the vortex (except when it is near the condensate edge), with its value increasing with temperature. This could potentially be used as a variant to the method of Coddington et al. [Phys. Rev. A 70, 063607 (2004)] for experimentally determining the temperature.
At finite temperatures, the motion of topological defects (such as solitons or vortices) in trapped atomic Bose-Einstein condensates is affected by the presence of an inhomogeneous cloud of thermal atoms. Recent interest in quantum turbulence leads us to investigate the temperature dependence of vortex reconnections - events which are essential ingredients of turbulence. Using the Zaremba-Nikuni-Griffin (ZNG) formalism based on a dissipative Gross-Pitaevskii equation for the condensate coupled to a semiclassical Boltzmann equation for the thermal cloud, we find that, on the typical length scales and time scales of atomic condensates, vortex reconnections are temperature independent. Furthermore, comparison to vortex reconnections in homogeneous condensates show reconnections to be insensitive to inhomogeneity in the background density.
The study of vortex reconnections is an essential ingredient of understanding superfluid turbulence, a phenomenon recently also reported in trapped atomic Bose-Einstein condensates. In this work we show that, despite the established dependence of vortex motion on temperature in such systems, vortex reconnections are actually temperature independent on the typical length and time scales of atomic condensates. Our work is based on a dissipative Gross-Pitaevskii equation for the condensate, coupled to a semiclassical Boltzmann equation for the thermal cloud (the Zaremba-Nikuni-Griffin formalism). Comparison to vortex reconnections in homogeneous condensates further shows reconnections to be insensitive to the inhomogeneity in the background density.
The study of vortex reconnections is an essential ingredient of understanding superfluid turbulence, a phenomenon recently also reported in trapped atomic Bose-Einstein condensates. In this work we show that, despite the established dependence of vortex motion on temperature in such systems, vortex reconnections are actually temperature independent on the typical length and time scales of atomic condensates. Our work is based on a dissipative Gross-Pitaevskii equation for the condensate, coupled to a semiclassical Boltzmann equation for the thermal cloud (the Zaremba-Nikuni-Griffin formalism). Comparison to vortex reconnections in homogeneous condensates further shows reconnections to be insensitive to the inhomogeneity in the background density.
The dynamics of Bose-Einstein condensate (BEC) is studied at nonzero temperatures using our variational time-dependent-Hartree-Fock-Bogoliubov formalism. We have shown that this approach is an efficient tool to study the expansion and collective excitations of the condensate, the thermal cloud, and the anomalous correlation function at nonzero temperatures. We have found that the condensate and the anomalous density have the same breathing oscillations. We have investigated, on the other hand, the behavior of a single quantized vortex in a harmonically trapped BEC at nonzero temperatures. Generalized expressions for vortex excitations, vortex core size, and Kelvin modes have been derived. An important and somehow surprising result is that the numerical solution of our equations predicts that the vortex core is partially filled by the thermal atoms at nonzero temperatures. We have shown that the effect of thermal fluctuations is important and it may lead to enhancing the size of the vortex core. The behavior of the singly anomalous vortex has also been studied at nonzero temperatures.
We derive the finite-temperature oscillation modes of a harmonically confined Bose-Einstein condensed gas undergoing rigid body rotation supported by a vortex lattice in the condensate. The hydrodynamic modes separate into two classes corresponding to center of mass and relative oscillations of the thermal cloud and the condensate. These classes are independent of each other in the case where the thermal cloud is inviscid for all modes studied, except the radial pulsations which couple them because the pressure perturbations of the condensate and the thermal cloud are governed by different adiabatic indices. If the thermal cloud is viscous, the two classes of oscillations are coupled, i.e., each type of motion involves simultaneously mass and entropy currents. The relative oscillations are damped by the mutual friction between the condensate and the thermal cloud mediated by the vortex lattice. The damping is large for the values of the drag-to-lift ratio of the order of unity and becomes increasingly ineffective in either limit of small or large friction. An experimental measurement of a subset of these oscillation modes and their damping can provide information on the values of the phenomenological mutual friction coefficients and the quasiparticle-vortex scattering processes in dilute atomic Bose gases.