Non-Hermitian Topological Quantum Sensors

该项目致力于探索非厄米（NH）拓扑相位在量子传感中的应用前景。NH矩阵的复杂能量谱的极端敏感性，这在闭合厄米特系统中在数学上是不可能的，作为这项奋进的主要出发点。在上述的NH拓扑相位的上下文中，这种异常的敏感性一般遇到系统的边界条件的微小变化。为了利用这种有趣的现象学来制造新的量子传感器件，即所谓的非厄米拓扑量子传感器（NTOQS），我们将采取以下主要步骤。(i)首先，使用一个有效的描述的开放量子系统的NH哈密顿量，具体的拓扑晶格模型的最小复杂性，表现出上述边界敏感性，从而作为NTOQS候选模型，将被识别和分析。与传感器观察到的被测变量的耦合一般通过隧道耦合（晶格模型中的弱连接）发生，隧道耦合有效地调节了NTOQS系统的边界条件。(ii)基于NH哈密顿的直觉，NTOQS候选模型将分别在量子主方程和量子朗之万方程的框架下被转化为一个完全微观的开放量子系统描述。这允许在量子噪声理论的框架内分析和评估NTOQS的基本量子噪声限制精度。(iii)与上述理论方面平行，该项目的一个主要目标是设计实验可行的蓝图，用于在量子光学系统和超冷原子气体中实现NTOQS。除了相关的NTOQS晶格模型的实际实施，一个主要的重点将是确定合适的可观测量被检测的传感设备，并微观建模其耦合的NH拓扑晶格模型代表的NTOQS的边界条件。最后，我们的目标是数值模拟的动态操作的NTOQS设备，考虑到最相关的缺陷预期拟议的个人实验平台，从而达到明确的预测未来的实验。

This project is devoted to exploring the promising potential of non-Hermitian (NH) topological phases for applications in quantum sensing. The extreme sensitivity of the the complex energy-spectra of NH matrices, which would be mathematically impossible in closed Hermitian systems, serves as the main starting point of this endeavor. In the context of the aforementioned NH topological phases, this anomalous sensitivity is generically encountered upon small changes of the system's boundary conditions. To harness this intriguing phenomenology for novel quantum sensing devices, coined non-Hermitian topological quantum sensors (NTOQS), the following major steps will be taken.(i) First, using an effective description of open quantum systems in terms of NH Hamiltonians, concrete topological lattice models of minimal complexity that exhibit the aforementioned boundary sensitivity, and thus serve as NTOQS candidate models, will be identified and analyzed. The coupling to the measurand observed by the sensor generically happens via a tunnel coupling (weak link in the lattice model) that effectively tunes the boundary conditions of the NTOQS system.(ii) Building up on the intuition from NH Hamiltonians, the NTOQS candidate models will be translated to a fully microscopic open quantum system description in the framework of quantum master equations and quantum Langevin equations, respectively. This allows for the analysis and assessment of the fundamental quantum noise limited precision of NTOQS in the framework of quantum noise theory.(iii) In parallel to the above theoretical aspects, a major objective of this project is to devise experimentally feasible blueprints for the realization of NTOQS in both quantum optical systems and ultracold atomic gases. In addition to the practical implementation of the relevant NTOQS lattice models, a main focus will be to identify suitable observables to be detected by the proposed sensing devices, and to microscopically model their coupling to the boundary conditions of the NH topological lattice model representing the NTOQS. Finally, the goal is to numerically simulate the dynamical operation of the NTOQS devices, taking into account the most relevant imperfections expected for the proposed individual experimental platforms, thus reaching clear predictions for future experiments.