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

过去15年的深入研究表明，通过适当使用磁铁和光，可以将气体中的原子冷却到绝对零度以上的一小部分，绝对零度是所有运动都冻结的温度。在如此低的温度下，原子突然经历了“身份危机”，并被迫采取相同的行为-科学上称为“一致性”。由于这些“超冷”原子几乎是静止的，它们实际上可以成为敏感的“测量设备”，测量它们本来感觉不到的效应，如重力或磁场。已经建造了合适的设备来利用这一点，并被称为“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离的位置被分成两个大小近似相等的较小的组，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关于它们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引力强度的变化）。这种“测量装置”基本上有两种变体，这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。为了充分利用这些设备，人们应该对这些系统中发生的物理过程有详细的了解，而这个项目打算在这一领域取得重大进展。对这些系统的详细描述是复杂的，因为在大多数当前实验发生的典型温度下，只有一些原子表现出“相干”，其余的原子以随机的方式运动，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似乎在细长几何中得到增强，但这种显著的好处部分地被这种几何破坏系统的“相干”性质的趋势所抵消;后者是由于波动（在系统的相位中），这是量子力学的基本结果，描述微观世界的理论。任何试图精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设备精度的基本物理机制。(ii)其次，该项目解决了一个关键问题，即以受控的方式产生一束原子，即使它们实际上在移动，也能保持它们的一致性，这是一个当前非常感兴趣的话题。虽然在文献中有许多相关的理论研究，这项工作是独一无二的，因为它结合了迄今为止只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，其中只有一些原子的行为是一致的，包括“相干”和“随机”原子及其相互作用的全部动力学。(ii)此外，额外的并发症（相位波动）所产生的事实，这些系统是非常薄和长的，也处理先进的（随机）技术，这是自然'内置'的方法，上面提到的，这样一个广义的理论解决数值第一次在本工作。最近的开拓性实验的动机，仍然只有部分理解，我们利用计算机研究原子的性质如何在改变系统的各种参数，如几何形状，大小和温度时受到影响，并进一步研究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.