Ultracold Gases far from Equilibrium: Fluctuations in time-dependent Geometries

过去15年的密集研究表明，人们可以通过适当使用磁铁和光将气体中的原子冷却到绝对零度以上的微小比例，绝对零度是所有运动冻结的温度。在如此低的温度下，原子突然经历了一场“身份危机”，被迫表现出相同的行为--科学上称之为“一致”。因为这些“超冷”原子几乎是静止的，它们实际上可以成为敏感的“测量装置”，测量它们原本根本感觉不到的影响，比如重力或磁场。人们已经建造了合适的装置来利用这一点，并将其称为“原子干涉仪”。在这样的装置中，一组被捕获的非常冷的原子在物理上分开的位置被分成两个大小大致相等的较小的组，然后随后再次结合在一起。对原子结合后的性质的研究揭示了有关原子分离时发生的现象变化的重要信息(例如，两个分离位置之间重力强度的变化)。这种“测量设备”基本上有两种变种，取决于原子最初是静止的还是运动的，每种方案都有自己的优点和缺点。为了充分利用这种装置，人们应该对这种系统中发生的物理过程有一个详细的了解，这个项目打算在这一领域取得重大进展。由于这样一个事实，使得对这种系统的详细描述变得复杂，因为在目前大多数实验进行的典型温度下，只有一些原子的行为是一致的，其余原子的行为是随机的，就像我们周围空气中的原子一样。此外，我们控制原子运动的能力在细长的几何图形中似乎得到了增强，但这种显著的好处部分被这种几何图形破坏系统的‘连贯’性质的倾向所抵消；后者是由于(系统相中的)波动，这是作为描述微观世界的量子力学的基本结果而出现的。任何试图准确描述这类实验的理论模型都应该考虑到这些问题。本项目的主要目的有两个：(I)首先，深入研究可能限制这类装置精度的基本物理机制。(Ii)其次，该项目解决了一个关键问题，即以受控方式产生原子束的可行性有多大，尽管原子束实际上在运动，但它仍然保持着它们的连贯性，这是目前非常感兴趣的一个专题。尽管文献中有许多相关的理论研究，但这项工作的独特之处在于，它结合了迄今为止仅在独立研究中实施的基本特征：(I)首先，这项研究是在现实条件下进行的，在现实条件下，只有一些原子的行为是一致的，并且包括“相干”和“随机”原子及其相互作用的全部动力学。(Ii)此外，由于这些系统非常薄和很长的事实而产生的额外的复杂性(相位波动)也被先进的(随机)技术处理，这些技术自然地‘内置’到上面提到的方法中，这样的普遍理论在本工作中第一次得到了数值解决。在最近仍然只有部分了解的开创性实验的激励下，我们使用计算机来研究原子的性质如何随着系统的各种参数的变化而受到影响，如几何形状、大小和温度，我们进一步研究了原子运动中的相关问题。

Intensive research over the last 15 years has shown that one can cool atoms in a gas by suitable use of magnets and light to a tiny fraction above absolute zero, the temperature at which all motion freezes. At such a low temperature, atoms suddenly experience an 'identity crisis', and are coerced into behaving identically - what is scientifically termed 'coherently'. Because these 'ultracold' atoms are almost stationary, they can actually become sensitive 'measuring devices' of effects they would otherwise essentially not feel, such as gravity, or magnetic fields. Suitable devices have been constructed to take advantage of this, and are known as 'atom interferometers'. In such devices, a group of trapped, very cold atoms is split into two smaller groups of approximately equal size in physically-separated locations, and then subsequently joined together again. A study of the properties of the atoms after they are joined reveals important information about changes in phenomena taking place when they were separated (e.g. changes in the strength of gravity between the two separated locations). Such a 'measuring device' has essentially two variants, depending on whether the atoms were originally stationary or moving, with each scheme having its own benefits and shortcomings. In order to take full advantage of such devices, one should develop a detailed understanding of the physical processes that take place in such systems, and this project intends to make significant advances in this area.A detailed description of such systems is complicated by the fact that at the typical temperatures where most current experiments take place, only some of the atoms behave 'coherently', with the rest of the atoms behaving in a random fashion, just like atoms in the air around us. Moreover, our ability to control the motion of atoms appears to be enhanced in thin long geometries, but this significant benefit is partly counterbalanced by the tendency of such geometries to destroy the 'coherent' nature of the system; the latter is due to fluctuations (in the phase of the system) which arise as a fundamental consequence of quantum mechanics, the theory which describes the microscopic world. Any theoretical model attempting to describe such experiments accurately should take account of these issues.The main aims of this project are two-fold: (i) firstly, to perform an in-depth study of fundamental physical mechanisms which may restrict the accuracy of such devices. (ii) Secondly, this project addresses the crucial question of how feasible it is to produce in a controlled manner a beam of atoms which maintain their coherence, even though they are actually moving, a topic of great current interest. Although there are numerous related theoretical studies in the literature, this work is unique in that it combines essential features that have to date only been implemented in independent studies: (i) firstly, this study is performed under realistic conditions, in which only some of the atoms behave coherently, and includes the full dynamics of both 'coherent' and 'random' atoms and their interactions. (ii) Moreover, additional complications (phase fluctuations) arising from the fact that these systems are very thin and long are also treated by advanced (stochastic) techniques, which are naturally 'built into' the approach mentioned above, with such a generalised theory solved numerically for the first time in the present work.Motivated by recent pioneering experiments which remain only partly understood, we use computers to study how the properties of the atoms are affected upon changing various parameters of the system, such as geometry, size and temperature, and we further investigate related issues in moving atoms.