Jack Dodd Centre for Quantum Technology, Department of Physics, University of Otago, Dunedin 9016, New Zealand.
College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA.
Phys Rev Lett. 2014 Apr 11;112(14):145301. doi: 10.1103/PhysRevLett.112.145301.
Despite the prominence of Onsager's point-vortex model as a statistical description of 2D classical turbulence, a first-principles development of the model for a realistic superfluid has remained an open problem. Here we develop a mapping of a system of quantum vortices described by the homogeneous 2D Gross-Pitaevskii equation (GPE) to the point-vortex model, enabling Monte Carlo sampling of the vortex microcanonical ensemble. We use this approach to survey the full range of vortex states in a 2D superfluid, from the vortex-dipole gas at positive temperature to negative-temperature states exhibiting both macroscopic vortex clustering and kinetic energy condensation, which we term an Onsager-Kraichnan condensate (OKC). Damped GPE simulations reveal that such OKC states can emerge dynamically, via aggregation of small-scale clusters into giant OKC clusters, as the end states of decaying 2D quantum turbulence in a compressible, finite-temperature superfluid. These statistical equilibrium states should be accessible in atomic Bose-Einstein condensate experiments.
尽管 Onsager 的点涡模型作为二维经典湍流的统计描述而备受关注，但为现实超流建立该模型的第一性原理方法仍然是一个悬而未决的问题。在这里，我们开发了一种将由均匀二维 Gross-Pitaevskii 方程 (GPE) 描述的量子涡旋系统映射到点涡模型的方法，从而能够对涡旋微正则系综进行蒙特卡罗采样。我们使用这种方法调查了二维超流中涡旋状态的全范围，从正温度下的涡旋偶极气体到表现出宏观涡旋聚集和动能凝聚的负温度状态，我们称之为 Onsager-Kraichnan 凝聚态 (OKC)。阻尼 GPE 模拟表明，通过小尺度团簇聚集成大 OKC 团簇，这种 OKC 状态可以作为可压缩、有限温度超流中二维量子湍流的衰减终结态而动态出现。这些统计平衡态应该可以在原子玻色-爱因斯坦凝聚实验中实现。
