Non-equilibrium dynamics of long-range interacting quantum systems and their applications to quantum metrology

量子计量学使用量子效应，如干涉、纠缠，或者非常普遍的非经典量子态，来提高物理量测量的灵敏度。相互作用发挥着核心作用，因为一方面，它们是创建非经典态所必需的，另一方面，它们可以自己测量，其精度与粒子的数量成正比。该项目针对这第二个迄今鲜有探索的可能性，将研究具有长程相互作用的动态驱动开放量子系统中不同的非平衡态，并探索它们在量子计量学中的作用。从理论上，我们将研究相互作用多体系统的绝热和非绝热(猝灭)动力学，并检验它们对于提高外部参数(如电磁场)测量的灵敏度的作用。我们将阐明潜在的相空间结构对灵敏度的作用，并开发和实现高效的量子算法来模拟开放的复杂量子系统。在实验上，我们将使用二维冷原子云，通过共振激光耦合到存在受控电场的高激发里德堡态。电场的小而快的变化允许相应的长程偶极-偶极相互作用强度的动态调节。这将使我们能够实现不同类型的动态驾驶方案，并调整松弛和电离率。利用具有高时空分辨率的离子显微镜，我们将对这一相互作用量子系统的时空动力学和关联进行精确测量。将进行长程相互作用里德堡原子电场测量的原理验证实验。

Quantum metrology uses quantum effects such as interference, entanglement, or very generally non-classical quantum states to increase the sensitivity of the measurement of physical quantities. Interactions play a central role, as on the one hand they are needed to create the non-classical states, and on the other hand they can be measured themselves with a precision that scales favorably with the number of particles. The project aims at this second, so far little explored possibility and will investigate different non-equilibrium states in dynamically driven open quantum systems with long-range interactions and explore their usefulness for quantum metrology.Theoretically, we will study adiabatic and non-adiabatic (quenched) dynamics of the interacting many-body systems and examine their utility for increasing the sensitivity of measurements of external parameters, such as electromagnetic fields. We will elucidate the role of underlying phase-space structures for the sensitivity and develop and implement efficient quantum algorithms for simulating open complex quantum systems. Experimentally, we will employ two-dimensional clouds of cold trapped atoms coupled by resonant lasers to the highly excited Rydberg states in the presence of controlled electric fields. Small and fast changes of the electrical field permit dynamical tuning of the corresponding long-range dipole-dipole interaction strength. This will allow us to realise different kinds of dynamical driving schemes and to tune the relaxation and ionisation rates. Using an ion microscope with high spatiotemporal resolution, we will perform precise measurements of the spatial and temporal dynamics and correlations in this driven interacting quantum system. A proof-of-principle experiment for measuring the electric field with long-range interacting Rydberg atoms will be performed.