Single Spin Resolved Quantum Metrology in Optical Lattices

本课题旨在实现二维光学晶格中超冷原子的单自旋分辨探测及其在量子计量中的应用。探测技术的核心将是一个量子自旋泵，提供两个相关自旋态的鲁棒（拓扑保护）空间分离。这将使二维原子阵列的全局部量子位读出成为可能，这是量子模拟和量子信息的基本要求，迄今为止尚未得到证明。重要的是，该技术将普遍适用于包括碱土原子在内的二维超冷晶格系统。后者在该项目提案的更广泛背景下是重要的，该项目提案伴随着<s:1>宾根大学的海森堡教授提案。在与日本研究伙伴密切合作的情况下，在<s:1>宾根量子科学中心正在进行的研究工作之一是实现紧凑连续的碱土原子光学晶格时钟。在更长的时间尺度上，在提议的项目中开发的技术将使我们能够在这个光学时钟中实现量子增强测量。单自旋分辨读出，因此，检测宇称的磁化，需要利用量子计量的最大纠缠态，这保证了最终的测量精度在海森堡极限。单轴扭转动力学在较短的演化时间内产生自旋压缩，在较长时间内确实会导致最大程度的正午态纠缠。这个时间是整体磁化恢复时间的一半，即逆相互作用强度所设定的时间。在这两者之间产生了复杂的非高斯状态，通常难以表征。在这里，局部单自旋分辨探测承诺了新的见解，因为它允许人们不仅通过全局可观察性而且通过局部多点相关性来表征系统。我们建议在二维光学晶格中使用10到100个原子之间的远程相互作用来实现像量子动力学一样的单轴扭曲。这种相互作用是由近共振激光耦合到里德堡态（又名里德堡修饰）引起的。在这样的设置下，我们最近证明了相干时间长达100次逆相互作用，而该系统中自旋压缩的时间尺度是逆相互作用时间的十分之一。因此，完全相干的进化甚至到产生正午态的时间似乎是可以实现的。我们还将探索实现洛施密特回波序列的可行方案，在此基础上，更一般的纠缠态可以用于量子计量。

This project aims at the realization of single spin resolved detection of ultracold atoms in two dimensional optical lattices and its application to quantum metrology. At the heart of the detection technique will be a quantum spin pump, providing robust (topologically protected) spatial separation of the two involved spin states. This will enable full local qubit readout in two-dimensional atomic arrays, a fundamental requirement for quantum simulation and quantum information, which has not yet been demonstrated so far. Importantly, the technique will be generally applicable to two-dimensional ultracold lattice systems including alkaline-earth like atoms. The latter is important in the wider context of this project proposal, which is accompanying a Heisenberg professorship proposal at the University of Tübingen. One of the ongoing research efforts at the Center for Quantum Science in Tübingen - in close collaboration with Japanese research partners - is the realization of a compact and continuous alkaline-earth atom based optical lattice clock. On longer time scale, the techniques developed within the proposed project will allow us to realize quantum enhanced measurements in this optical clock.Single spin resolved readout and, hence, the detection of the parity of the magnetization, is required to make use of maximally entangled states for quantum metrology, which promise ultimate measurement precision at the Heisenberg limit. One-axis twisting dynamics, producing spin squeezing on short evolution times, indeed results in maximally entangled NOON states at longer times. This time is half-way to the revival time of the global magnetization, i.e. the time set by the inverse interaction strength. In between complicated non-gaussian states are produced that are in general difficult to characterize. Here local single spin resolved detection promises new insight as it allows one to characterize the system not only by global observable but also by local multi-point correlations.We propose to use long-range interactions between ten to hundred atoms in a two-dimensional optical lattice to implement one-axis twisting like quantum dynamics. The interaction is induced by near-resonant laser coupling to Rydberg states (aka Rydberg dressing). With such a setting, we recently demonstrated coherence times as long as 100 inverse interaction times, while the time scale for spin squeezing in this system is one tenth of the inverse interaction time. Thus, fully coherent evolution even to the time to produce NOON states seems within reach. We will additionally explore feasible schemes to realize a Loschmidt echo sequence, based on which much more general entangled states can be used for quantum metrology.