Turbulence in quantum gases: setting the framework

在极低的温度下，物质的行为与我们所习惯的不同：它的组成粒子不是独立的，而是作为一个实体集体行为，称为玻色-爱因斯坦凝聚体（BEC）。冷凝物以固体、液体或气体的形式出现，导致一些最基本的物理现象。历史上，冷凝物在液氦中被广泛研究。在极低的温度下，氦表现出奇怪的性质，我们可以通过将氦描述为一种普通液体（“正常流体”）和一种新的“量子”液体（称为“超流体”）的组合来理解，这种液体可以在没有正常流体所经历的摩擦的情况下流动。每个人都熟悉飞机的抖动运动，这是由于它所飞行的湍流空气的不规则运动。湍流是自然界最普遍的现象之一：从主动脉血流到水管和气管，再到大气中的风，流动中都出现湍流涡流和漩涡。超流氦中的湍流有一个新的功能：它由离散的涡旋组成，所有涡旋都具有相同的环流和核心结构，而不像普通流体的涡旋具有任意的形状和强度。这种区别的出现是因为超流体由许多原子的凝聚体组成，并且在数学上由单个波函数描述：超流体的任何旋转运动都被限制在被量子化的涡旋中，也就是说，它们周围的流动受到量子力学定律的限制。最近对超流氦的实验突出了许多显著的相似之处（例如能量谱）和普通湍流与超流湍流（也称为量子湍流）之间的差异（例如速度统计）。实验学家已经报道了不同的量子湍流状态（例如随机与结构）的存在，其特征在于不同的时间演化（衰变定律）;理论家已经提出了能量转移和衰变的新机制（例如开尔文波级联）。自然的大问题是，在某种意义上，普通湍流是否是量子湍流的经典极限：湍流中漩涡和漩涡的复杂性是否可以通过大量离散涡丝的动力学来更好地理解，每个涡丝携带一个单位的环流？与此同时，在过去的15年里，出现了新的物理系统，用于在宏观尺度上研究量子效应。实验学家们现在没有使用液氦，因为液氦的组成粒子相互作用很强，而是创造了弱相互作用的气体中原子的被困凝聚物，称为量子气体。这样的系统为量子湍流的研究提供了一个理想的背景，因为它们允许对大量参数进行前所未有的实验控制，例如系统的几何形状和有效维度，以及相互作用的强度和类型（可以调整，而不是像氦那样由自然界给定）。BEC超冷气体中湍流的第一个实验证据仅在去年公布。该方案及时地结合了上述概念，以研究量子气体中的湍流。我们认为，通过促进对更可控的原子气体的研究，可以更好地理解经典和量子系统中出现的不同形式的湍流，特别是因为量子气体在理论上可以非常精确地描述。我们计划建立研究原子凝聚体中湍流的框架，并解决这一新兴领域的关键问题，例如：我们如何以可控的方式在量子气体中产生湍流？产生的湍流结构的主要特征是什么？哪些实验方案可能产生最佳结果？

At extremely low temperatures, matter behaves differently to what we are used to: its constituent particles are not independent but behave collectively as one entity, known as the Bose-Einstein Condensate (BEC). The condensate appears in solids, liquids, or gases, leading to some of the most fundamental physical phenomena. Historically the condensate has been studied extensively in liquid helium. At very low temperatures helium exhibits strange properties, which we can understand by describing helium as a combination of a usual liquid (the 'normal fluid') and a new 'quantum' liquid, called the 'superfluid', which can flow without the friction which a normal fluid would experience.Everybody is familiar with the jittery motion of an aeroplane due to the irregular motion of the turbulent air through which it flies. Turbulence is one of nature's most ubiquitous phenomenon: turbulent eddies and swirls occur in flows ranging from the aortic blood stream, to water and gas pipes, to winds in the atmosphere. Turbulence in superfluid helium has a new feature: it consists of discrete vortices, all with the same circulation and core structures, unlike the eddies of arbitrary shapes and strengths of ordinary fluids. This distinction arises because the superfluid consists of a condensate of many atoms, and is mathematically described by a single wavefunction: any rotational motion of the superfluid is constrained to vortices which are quantised, i.e. the flow around them is restricted by the laws of quantum mechanics.Recent experiments with superfluid helium have highlighted many remarkable similarities (e.g. energy spectra) and differences (e.g. velocity statistics) between ordinary turbulence and superfluid turbulence (also called quantum turbulence). Experimentalists have reported the existence of different regimes of quantum turbulence (e.g. random vs. structured), characterised by different temporal evolution (decay laws); theoreticians have proposed new mechanisms (e.g. the Kelvin wave cascade) for energy transfer and decay. The natural big question is whether ordinary turbulence is, in some sense, the classical limit of quantum turbulence: can the complexity of eddies and swirls in a turbulent stream be better understood in terms of the dynamics of a large number of discrete vortex filaments, each carrying one unit of circulation ?Parallel to this development, the last 15 years have seen the emergence of new physical systems for studying quantum effects on a macroscopic scale. Instead of working with liquid helium, whose constituent particles interact strongly, experimentalists have now created weakly-interacting trapped condensates of atoms in gases, known as quantum gases. Such systems provide an ideal context for the study of quantum turbulence, because they allow unprecedented experimental control of a vast range of parameters, such as the geometry and the effective dimensionality of the system, and the strength and the type of interactions (which can be tuned, rather than be given by nature as for helium). The first experimental evidence of turbulence in BEC ultracold gases was announced only last year. This proposal timely combines the above concepts in order to investigate turbulence in quantum gases. We think that, by promoting the study of more controllable atomic gases, the different forms of turbulence arising in classical and quantum systems can be better understood, particularly since quantum gases can be theoretically described very precisely. We plan to establish the framework for studying turbulence in atomic condensates, and address crucial questions in this new emerging field such as: how can we produce turbulence in a quantum gas in a controlled way ? what are the main features classifying the produced turbulent structure ? which experimental schemes are likely to produce the optimal results?