Dynamics of phase transitions to gapped and ungapped quantum states

自1995年第一个玻色-爱因斯坦凝聚态产生以来，超冷原子气体的基础多体物理研究取得了巨大成功。它们极大地增加了对量子流体的了解，并解决了几十年来一直在思考的问题。它们的适用性，以更好地了解真实的材料将促进可控设计的新功能材料在未来。到目前为止，这方面的研究主要集中在平衡系统，但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）可以通过外部手段（如激光或磁场）在真实的时间内控制哈密顿参数;（ii）与环境近乎完美的隔离使它们成为研究内在量子动力学的理想选择;（iii）相关的时间尺度通常有利于时间分辨研究（毫秒尺度）。这些独特的功能允许实验实现量子淬火实验，在此期间，哈密尔顿参数，如相互作用强度，有效地瞬间（“瞬时淬火”）或缓慢（“缓慢淬火”）改变。这使得系统处于一种不是哈密顿量本征态的状态，并且随后通过多体量子干涉效应时间演化和弛豫到一个新的（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，因为它们在概念上非常清晰，并且在瞬时猝灭的情况下，理论上最好描述（即使通常仍然无法解决）。例如，考虑一个孤立的多体量子系统通过相变淬灭--有许多问题还远没有得到回答：是什么决定了量子系统是否会平衡？量子系统如何平衡？平衡总是导致热化吗？温度和能隙在光谱中的作用是什么？密度有序化和非对角长程有序的建立等不同过程是如何竞争的？当然，形式上孤立量子力学态的幺正时间演化是已知的。然而，强相互作用和/或长的进化时间使问题在理论上难以解决。此外，耗散的存在使问题复杂化，即使对于弱耗散，也只有很少的特殊情况，如马尔可夫耗散或谐振子浴，得到了彻底的研究。为了将经典相变转变为有序相，缺陷形成的动力学已经被预测为服从根据Kibble-Zurek机制的普遍行为，但是该机制对量子系统的适用性存在很大争议。因此，使用控制良好的超冷原子模型系统来回答上述相当普遍的问题，将为建立可能的平衡和热化的一般定律提供关键的基准，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淬火通过BEC相变以及费米气体淬火到赝隙或超流相。对于玻色子的一部分，建立非对角长程秩序后，淬火将是主要的焦点，以建立一个坚实的和一般的物理图片，这一过程。在费米的情况下，我们将探讨本地（对形成）和全球（非对角长程）秩序之间的关系。在预先形成的局部对（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对玻色气体的测量结果进行比较。然后，这将提供一个很好的基准，用于逐渐（通过调整相互作用）向非局部库珀对的更卷积极限移动。

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.