Non-Hermitian Topological Quantum Sensors

本项目致力于探索非厄米(NH)拓扑相在量子传感中的应用潜力。NH矩阵的复能谱的极端敏感性，在封闭的厄米系统中在数学上是不可能的，这是这一努力的主要起点。在前述NH拓扑学阶段的背景下，通常在系统边界条件的微小变化时遇到这种异常敏感性。为了将这一有趣的现象学应用于新型量子传感器件，被称为非厄米拓扑量子传感器(NTOQS)，将采取以下主要步骤：(I)首先，使用NH哈密顿量对开放量子系统进行有效描述，将识别和分析具有上述边界敏感性的最小复杂性的具体拓扑格模型，从而作为NTOQS候选模型。对传感器观测到的被测对象的耦合通常通过隧道耦合(晶格模型中的弱连接)发生，这种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转化为完全微观的开放量子系统描述。这使得可以在量子噪声理论的框架下分析和评估NTOQS的基本量子噪声有限精度。(Iii)与上述理论方面相平行，本项目的一个主要目标是设计出在量子光学系统和超冷原子气体中实现NTOQS的实验可行的蓝图。除了实际实施相关的NTOQS晶格模型外，主要重点将是确定建议的传感设备要探测的适当可观测对象，并从微观上模拟它们与代表NTOQS的NH拓扑晶格模型的边界条件的耦合。最后，目标是数值模拟NTOQS设备的动态操作，考虑到所建议的各个实验平台最相关的缺陷，从而为未来的实验做出明确的预测。

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.