Dynamics of phase transitions to gapped and ungapped quantum states

自从1995年第一个原子玻色-爱因斯坦凝聚体产生以来，利用超冷原子气体进行的基础多体物理研究取得了巨大的成功。他们大大增加了有关量子流体的知识，并解决了几十年来一直在思考的问题。量子气体对更好地理解真实材料的适用性将有助于未来新功能材料的可控设计。到目前为止，这方面的研究大多集中在平衡系统上；然而，量子气体可能更适合于研究非平衡现象。特别是，它们具有以下优点：(I)哈密顿参数可以通过外部手段实时控制，如激光或磁场；(Ii)与环境的近乎完美的隔离使它们成为研究本征量子动力学的理想工具；(Iii)相关的时间尺度通常有利于时间分辨研究(毫秒尺度)。这些独特的特性允许在实验上实现量子猝灭实验，在此过程中，哈密顿参数，如相互作用强度，要么有效地瞬时改变(“瞬时猝灭”)，要么缓慢改变(“慢猝灭”)。这使得系统处于一种不是哈密顿本征态的状态，随后通过多体量子干涉效应随时间演化并松弛到新的(可能是静止的)状态。量子猝灭实验是科学理解非平衡现象的基石，因为它们在概念上是非常干净的，在瞬时猝灭的情况下，理论上是最好的描述(尽管通常仍然无法解决)。例如，考虑一个通过相变猝灭的孤立的多体量子系统--有许多问题仍然远未得到回答：是什么决定了量子系统是否会平衡？量子系统是如何平衡的？平衡总是会导致热敏化吗？温度和能隙在光谱中的作用是什么？密度有序和建立非对角线长程有序等不同的过程是如何竞争的？当然，形式上来说，孤立的量子力学状态的么正时间演化是已知的。然而，强相互作用和/或较长的进化时间使得这个问题在理论上难以解决。此外，耗散的存在使问题变得复杂，即使对于弱耗散，也只有很少的特殊情况，如马尔科夫耗散或谐振子浴，被深入研究。为了将经典相变转变为有序相，根据Kibble-Zurek机制，缺陷形成的动力学被预测为遵循普遍行为，但该机制对量子系统的适用性仍有很大争议。因此，使用控制良好的超冷原子模型系统回答上述相当一般的问题，将为建立可能的一般平衡和热化定律提供关键基准，这被认为是物理学的重大挑战之一。在我们的实验中，我们将研究玻色气体通过BEC相变猝灭，以及费米气体猝灭为赝隙或超流体相。对于玻色子部分，在猝灭后建立非对角线长程有序将是主要焦点，以便建立这一过程的坚定和一般的物理图景。在费米情况下，我们将探索局域(对形成)和整体(非对角线长程)有序之间的关系。在预制的局域对(分子)的限制下，我们将处于一个独特的位置，可以直接将结果与我们自己用玻色气体进行的测量进行比较。这将为逐步向更复杂的非本地Cooper对极限移动(通过调整交互)提供一个极好的基准。

Since the production of the first atomic Bose-Einstein condensate in 1995, studies of fundamental many-body physics with ultracold atomic gases have been highly successful. They have resulted in a substantial increase of knowledge about quantum fluids and have addressed questions that have been pondered for decades. Their applicability to a better understanding of real materials will facilitate the controllable design of new functional materials in the future.Up to now most of this research has focused on equilibrium systems; however quantum gases are perhaps even better suited to studying non-equilibrium phenomena. In particular, they have the following advantages: (i) Hamiltonian parameters can be controlled in real time by external means, such as laser light or magnetic fields; (ii) near perfect isolation from the environment makes them ideal for studying intrinsic quantum dynamics; (iii) the relevant timescales are generally favourable (millisecond scale) for time resolved studies. These unique features allow for experimentally realizing quantum quench experiments , during which Hamiltonian parameters, such as the interaction strength, are changed either effectively instantaneously ("instantaneous quench") or slowly ("slow quench"). This leaves the system in a state that is not an eigenstate of the Hamiltonian and which subsequently time-evolves and relaxes into a new (possibly stationary) state through many-body quantum interference effects. Quantum quench experiments are the cornerstones of the scientific understanding of non-equilibrium phenomena because they are conceptually very clean and, in the case of an instantaneous quench, best describable theoretically (even though usually still unsolvable). Consider, for example, an isolated many-body quantum system quenched through a phase transition - there are many questions that are still far from being answered: What determines whether the quantum system will equilibrate? How does the quantum system equilibrate? Does equilibration always lead to thermalisation? What are the roles of temperature and energy gaps in the spectrum? How do different processes like density ordering and the establishment of off-diagonal long-range order compete? Of course, formally the unitary time evolution of an isolated quantum mechanical state is known. However, strong interactions and/or long evolution times make the problem theoretically intractable. Additionally, the presence of dissipation complicates matters and even for weak dissipation only very few special cases, such as Markovian dissipation or harmonic oscillator baths, have been thoroughly studied. For crossing a classical phase transitions into an ordered phase, the dynamics of defect formation has been predicted to obey universal behaviour according to the Kibble-Zurek mechanism but the applicability of the mechanism to quantum systems is highly debated. Therefore, answering the above, fairly generic, questions using well-controlled model systems of ultracold atoms will provide crucial benchmarks for establishing possibly general laws of equilibration and thermalisation, which has been considered one of the Grand Challenges of Physics. In our experiments, we will investigate Bose gases quenched through the BEC phase transition as well as Fermi gases quenched into pseudogap or superfluid phases. For the bosonic part, the establishment of off-diagonal long-range order after a quench will be the prime focus in order to establish a firm and general physical picture of this process. In the Fermi case we will explore the relation between local (pair formation) and global (off-diagonal long-range) order. In the limit of preformed local pairs (molecules) we will be in a unique position to directly compare the results with our own measurements with Bose gases. This will then provide an excellent benchmark for gradually moving (by tuning the interactions) towards the more convolved limit of non-local Cooper pairs.