Under suitable forcing a fluid exhibits turbulence, with characteristics strongly affected by the fluid's confining geometry. Here we study two-dimensional quantum turbulence in a highly oblate Bose-Einstein condensate in an annular trap. As a compressible quantum fluid, this system affords a rich phenomenology, allowing coupling between vortex and acoustic energy. Small-scale stirring generates an experimentally observed disordered vortex distribution that evolves into large-scale flow in the form of a persistent current. Numerical simulation of the experiment reveals additional characteristics of two-dimensional quantum turbulence: spontaneous clustering of same-circulation vortices, and an incompressible energy spectrum with k −5/3 dependence for low wavenumbers k and k −3 dependence for high k.A critical distinction between hydrodynamic turbulence in a bulk fluid [1] and in one whose flows are restricted to two dimensions is that energy dissipation at small length scales is generally inhibited in the latter. In two-dimensional (2D) flows subject to small-scale forcing, energy flux is blocked through the small length scales and, instead, energy is transferred towards larger scales, comprising the inverse energy cascade of 2D turbulence [2,3]. Small-scale forcing may thus generate large-scale flows, as seen for instance in dispersal of atmospheric and oceanic particulates [4], flows of soap films [5,6] and plasmas [7], and Jupiter's Great Red Spot [8,9]. However, the nature of 2D turbulence in quantum fluids is less clear. Progress in 2D quantum turbulence (2DQT) may offer innovative routes to understanding quantum fluid dynamics [10,11] and aspects of the universality of 2D turbulence. Here we describe an experimental and numerical study of forced and decaying 2DQT in a dilute-gas Bose-Einstein condensate (BEC). Our primary result is the first clear evidence that three key characteristics of 2D turbulence may also simultaneously appear in systems exhibiting 2DQT: (i) emergence of large-scale flow from small-scale forcing, seen experimentally and numerically, (ii) numerical observation of the formation of coherent vortex structures accompanying approximate enstrophy conservation [12], and (iii) numerical observation of an incompressible kinetic energy spectrum with k −5/3 dependence for low wavenumbers k and k −3 dependence for high k. Our observations are consistent with the notion that an inverse energy cascade can exist in this system. Concepts of significance for 2D turbulence and quantum fluids share a common origin. Analyzing point vortex motion in a bounded domain, Onsager proposed in 1949 that longlived vortices may develop via mergers of smaller vortices in turbulent flows of a 2D fluid, enabling the remaining vortices to move more freely and thereby maximize system entropy [13,14]. He also proposed that vortices in superfluids have quantized circulation, and implied that turbulent 2D vortex dynamics might be ideally studied in superfluids. However, experimental demonstration of 2DQT has not been repo...
The decay of a vortex from a non-rotating high temperature Bose-Einstein condensate (BEC) is modeled using the stochastic projected Gross-Pitaevskii equation (SPGPE). In order to exploit the tunability of temperature in SPGPE theory while maintaining the total atom number constant, we develop a simple and accurate Hartree-Fock method to estimate the SPGPE parameters for systems close to thermal equilibrium. We then calculate the lifetime of a vortex using three classical field theories that describe vortex decay in different levels of approximation. The SPGPE theory is shown to give the most complete description of the decay process, predicting significantly shorter vortex lifetimes than the alternative theories. Using the SPGPE theory to simulate vortex decay for a trapped gas of 5 × 10 5 87 Rb atoms, we calculate a vortex lifetimet that decreases linearly with temperature, falling in the range 20s>t >1.5s corresponding to the temperature range 0.78Tc ≤ T ≤ 0.93Tc. The vortex lifetimes calculated provide a lower bound for the lifetime of a persistent current with unit winding number in our chosen trap geometry, in the limit of vanishing vortex pinning potential. arXiv:0912.3300v1 [cond-mat.quant-gas]
We have achieved the first full implementation of the stochastic projected Gross-Pitaevskii equation for a three-dimensional trapped Bose gas at finite temperature. Our work advances previous applications of this theory, which have only included growth processes, by implementing number-conserving scattering processes. We evaluate an analytic expression for the coefficient of the scattering term and compare it to that of the growth term in the experimental regime, showing the two coefficients are comparable in size. We give an overview of the numerical implementation of the deterministic and stochastic terms for the scattering process, and use simulations of a condensate excited into a large amplitude breathing mode oscillation to characterize the importance of scattering and growth processes in an experimentally accessible regime. We find that in such non-equilibrium regimes the scattering can dominate over the growth, leading to qualitatively different system dynamics. In particular, the scattering causes the system to rapidly reach thermal equilibrium without greatly depleting the condensate, suggesting that it provides a highly coherent energy transfer mechanism.
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