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arXiv:1210.7993 · Physical Review A

Observable vortex properties in finite-temperature Bose gases

A. Joy Allen, E. Zaremba, Carlo F. Barenghi, Nick P. Proukakis

Published Jan 25, 2013• 39 citations
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Abstract

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.

DOI
10.1103/physreva.87.013630

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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.
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.
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.
In this thesis we study the dynamics of dark solitons, vortices and Josephson effects, in trapped atomic Bose-Einstein condensates. We firstly demonstrate a novel, sound mediated, long-range interaction mechanism between dark solitons using the Gross-Pitaevskii equation. Then we present the effect of finite temperatures on the dynamics of vortices and Josephson effects using a generalised form of this equation, which additionally includes a source term modelling the coupling of the condensate to a fully dynamical thermal cloud, described by a quantum Boltzmann equation. The latter formalism is known as the Zaremba-Nikuni-Griffin scheme (ZNG). The sound-mediated interaction between dark solitons is such that the speed and trajectory of one soliton in a condensate confined by a harmonic trap can be significantly modified by the presence of a second soliton in the same trap. By confining the two solitons to spatially separated subregions of a double well trap, we show how this effect can be magnified. In particular we find it can be large, and therefore detectable, in experimentally relevant geometries, including high-periodicity optical lattices in which the ability of solitons to act as both absorbers and emitters of energy becomes apparent. At finite temperatures, we model the dynamics via the ZNG scheme. Firstly, we give a detailed description of the scheme for numerically solving these coupled equations including all collisional terms. Then we study the effect of a dynamical thermal cloud on vortex dynamics, in particular, focussing on the experimentally-relevant quantities of precession frequencies, decay rates and vortex core brightness. The changes in these are found to increase with increasing temperature for a pancake-shaped geometry, in particular for trapping parameters of a recent experiment of Freilich et al. (Science 329, 1182 (2010)). Particle exchanging collisions between the condensate and thermal cloud are found to be crucial in determining the rate of decay of a precessing vortex. We further show that, rotation of the thermal cloud can be a mechanism for radially translating the position of a vortex, a scenario under current investigation. Finally, we analyse the effect of finite temperatures on population dynamics in a double well atom chip experiment by LeBlanc et al. (Phys. Rev. Lett. 106, 025302 (2011)). Focussing on the coupled evolution in the absence of collisions, we find that it generates significant damping which is, however, less than that observed in the experiment. A detailed comparison in the presence of collisions is beyond the scope of this thesis.
We study the dynamics of a single vortex and a pair of vortices in quasi two-dimensional Bose-Einstein condensates at finite temperatures. To this end, we use the stochastic Gross--Pitaevskii equation, which is the Langevin equation for the Bose--Einstein condensate. For a pair of vortices, we study the dynamics of both the vortex-vortex and vortex-antivortex pairs, which are generated by rotating the trap and moving the Gaussian obstacle potential, respectively. Due to thermal fluctuations, the constituent vortices are not symmetrically generated with respect to each other at finite temperatures. This initial asymmetry coupled with the presence of random thermal fluctuations in the system can lead to different decay rates for the component vortices of the pair, especially in the case of two corotating vortices.