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arXiv:cond-mat/0301397 · Physical Review A

Zero-temperature damping of Bose-Einstein condensate oscillations by vortex-antivortex pair creation

Peter O. Fedichev, Uwe R. Fischer, Alessio Recati

Published Jul 22, 2003• 8 citations
arXivHTMLPDF

Abstract

We investigate vortex-antivortex pair creation in a supersonically expanding and contracting quasi-two-dimensional Bose-Einstein condensate at zero temperature. For sufficiently large-amplitude condensate oscillations, pair production provides the leading dissipation mechanism. The condensate oscillations decay in a nonexponential manner, and the dissipation rate depends strongly on the oscillation amplitude. These features allow one to distinguish the decay due to pair creation from other possible damping mechanisms. An experimental observation of the predicted oscillation behavior of the superfluid gas provides a direct confirmation of the hydrodynamical analogy of quantum electrodynamics and quantum vortex dynamics in two spatial dimensions.

DOI
10.1103/physreva.68.011602

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We investigate vortex-antivortex pair creation in a supersonically expanding and contracting quasi-two-dimensional Bose-Einstein condensate at zero temperature. For sufficiently large-amplitude condensate oscillations, pair production provides the leading dissipation mechanism. The condensate oscillations decay in a nonexponential manner, and the dissipation rate depends strongly on the oscillation amplitude. These features allow one to distinguish the decay due to pair creation from other possible damping mechanisms. An experimental observation of the predicted oscillation behavior of the superfluid gas provides a direct confirmation of the hydrodynamical analogy of quantum electrodynamics and quantum vortex dynamics in two spatial dimensions.
Understanding the elementary mechanism for the dissipation of vortex energy in quantum liquids is one central issue in quantum hydrodynamics, such as quantum turbulence in systems ranging from neutron stars to atomic condensates. In a two-dimensional (2D) Bose-Einstein condensate (BEC) at zero temperature, besides the vortex drift-out process from the boundary, vortex-antivortex pair can annihilate in the bulk, but controversy remains on the number of vortices involved in the annihilation process. We find there exists a dynamical transition from four-body to three-body vortex annihilation processes with the time evolution in a boundary-less uniform quasi-2D BEC. Such dynamical transition depends on the initial vortex pair density, and occurs when the sound waves generated in the vortex annihilation process surpass a critical energy. With the confinement along the third direction is relaxed in a quasi-2D BEC, the critical sound wave energy decreases due to the 3D vortex line curve and reconnection, shifting the dynamical transition to the early time. Our work reveals an elementary mechanism for the dissipation of vortex energy that may help understand exotic matter and dynamics in quantum liquids.
Abstract In a two-dimensional (2D) classical fluid, a large-scale flow structure emerges out of turbulence, which is known as the inverse energy cascade where energy flows from small to large length scales. An interesting question is whether this phenomenon can occur in a superfluid, which is inviscid and irrotational by nature. Atomic Bose-Einstein condensates (BECs) of highly oblate geometry provide an experimental venue for studying 2D superfluid turbulence, but their full investigation has been hindered due to a lack of the circulation sign information of individual quantum vortices in a turbulent sample. Here, we demonstrate a vortex sign detection method by using Bragg scattering, and we investigate decaying turbulence in a highly oblate BEC at low temperatures, with our lowest being ~0.5T c , where T c is the superfluid critical temperature. We observe that weak spatial pairing between vortices and antivortices develops in the turbulent BEC, which corresponds to the vortex-dipole gas regime predicted for high dissipation. Our results provide a direct quantitative marker for the survey of various 2D turbulence regimes in the BEC system.
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.
We study the relaxation dynamics of an isolated zero temperature quasi-two-dimensional superfluid Bose-Einstein condensate that is imprinted with a spatially random distribution of quantum vortices. Following a period of vortex annihilation the remaining vortices self-organize into two macroscopic coherent "Onsager vortex" clusters that are stable indefinitely--despite the absence of driving or external dissipation in the dynamics. We demonstrate that this occurs due to a novel physical mechanism--the evaporative heating of the vortices--that results in a negative-temperature phase transition in the vortex degrees of freedom. At the end of our simulations the system is trapped in a nonthermal state. Our computational results provide a pathway to observing Onsager vortex states in a superfluid Bose gas.
Two-dimensional flow past an infinitely long cylinder of nanoscopic radius in superfluid 4He^{4}\mathrm{He}4He at zero temperature is studied using time-dependent density-functional theory. The calculations reveal two distinct critical phenomena for the onset of dissipation: (i) vortex-antivortex pair shedding from the periphery of the moving cylinder, and (ii) the appearance of cavitation in the wake, which possesses similar geometry to that observed experimentally for fast-moving micrometer-scale particles in superfluid 4He^{4}\mathrm{He}4He. The formation of cavitation bubbles behind the cylinder is accompanied by a sudden jump in the drag exerted on the moving cylinder by the fluid. Vortex pairs with the same circulation are occasionally emitted in the form of dimers, which constitute the building blocks for the Benard--von Karman vortex street structure observed in classical turbulent fluids and Bose-Einstein condensates. The cavitation-induced dissipation mechanism should be common to all superfluids that are self-bound and have a finite surface tension, which include the recently discovered self-bound droplets in ultracold Bose gases. These systems would provide an ideal testing ground for further exploration of this mechanism experimentally.