RUI: Quantum Correlations and Dynamics of Ring Sensors and Simulators

利用量子力学的奇异特性来超越经典物理学的极限，已经成为定义本世纪的技术创新的最突出主题之一。量子规则不是取代，而是准备大幅扩展现有技术的能力，最有希望的推动力是在计算，传感和模拟领域。该项目侧重于最后两个方面，因为它们的好处可以产生广泛的影响：量子效应可以显着提高对加速度和力场的灵敏度，并直接应用于计量和系统控制。人们也早就认识到，量子效应是最有效的模拟量子系统。 量子态在与人类尺度相结合时的脆弱性继续推动着对更好平台的追求。该项目研究了一种替代平台，该平台由限制在环形周期晶格中的超冷原子组成，该系统是鲁棒的，但包含与应用相关的所有量子特征。 量子力学优势的本质在于超越经典定域性概念的系统内的深层相关性。此外，应用程序需要系统随时间演化，这需要对其量子动力学有透彻的理解。 本研究将在量子过程模拟器的多个途径中的实用性和推动灵敏度极限的量子传感器阵列的开发的背景下，对环晶格系统的这两个基本方面进行彻底的分析。 在物理研究方面培训众多本科生将是一个优先事项，在先前赠款的成功基础上，利用经验将学生引导到STEM职业道路，包括许多来自代表性不足的人口。 传感器开发将优先考虑一种在先前授权下获得专利的机制，以进行旋转和磁场的高精度传感。取代了干涉测量法，一个世纪以来精密传感的主要方法，其工作原理是基于环形晶格中相干介质的局部化过渡。 它的开发和部署将取决于动力学和量子相关性如何影响灵敏度和校准。量子优势将寻求提高灵敏度的影响，如自旋压缩和多模相干动力学，可以利用原子间的相互作用建设性。环结构及其推广到圆柱或环面，以及可选的晶格结构将被开发为一个全面的量子动力学模拟器：用环晶格模式模拟原子中的电子跃迁可以模拟具有外部自由度的量子光学;量子纠缠可以在集体自旋态中产生并应用于量子隐形传态等效应;光学效应的物质波对应物以及涉及非典型非厄米哈密顿算子的宇称-时间（PT）对称物理，可以在闭环晶格的新背景下进行模拟;非-平凡拓扑辅以旋转允许模拟与量子霍尔效应和合成规范相关的动力学拓扑效应领域;环形晶格的有限无界配置允许模拟多体物理，包括相变和量子动力学，只需较少的近似。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Harnessing the exotic features of quantum mechanics to reach beyond the limits of classical physics has emerged as one of the most prominent themes of technological innovations set to define this century. Rather than displace, quantum rules are poised to substantially extend the capacity of existing technologies, with the most promising thrusts being in the realms of computation, sensing and simulation. This project focuses on the last two aspects as their benefits can have a broad impact: Sensitivity to acceleration and force fields can be dramatically enhanced by quantum effects, with direct applications in metrology and systems control. It has also been long recognized that quantum effects are most effectively simulated by quantum systems. The fragility of quantum states when interfaced with the human scale continues to drive a quest for better platforms. This project investigates an alternate platform comprising of ultracold atoms confined to a ring-shaped periodic lattice, a system that is robust, yet encompasses all quantum features relevant for applications. The essence of quantum mechanical advantage lies in the deep hierarchy of correlations within a system that transcends classical notions of locality. Furthermore, applications require a system to evolve in time, necessitating a thorough understanding of its quantum dynamics. This research will conduct a thorough analysis of these two fundamental aspects of the ring lattice system in the context of utility in multiple pathways for simulators of quantum processes and development of an array of quantum sensors that push the limits of sensitivity. Training of numerous undergraduate students in physics research will be a priority, building on success under prior grants to leverage the experience to channel students into STEM career paths, including many from under-represented demographics. Sensor development will prioritize a mechanism patented under a prior grant to do high precision sensing of rotation and magnetic fields. Instead of interferometry, the staple of precision sensing for over a century, the operating principle is based on a localization transition for coherent media in ring lattices. Its development and deployment will hinge on how dynamics and quantum correlations impact sensitivity and calibration. Quantum advantage will be sought in enhancing sensitivity with effects like spin-squeezing and multimode coherent dynamics, that can utilize inter-atomic interactions constructively. The ring structure and its generalization to cylinder or torus, with optional lattice structure will be developed as a comprehensive quantum dynamical simulator: Mimicking electronic transitions in atoms with those of the modes of a ring lattice can simulate quantum optics with external degrees of freedom; Quantum entanglement can be generated in collective spin states and applied to effects like quantum teleportation; Matter wave counterparts of optical effects as well as parity-time (PT) symmetric physics that involves atypical non-Hermitian Hamiltonians, can be simulated within the novel context of closed loop lattices; The non-trivial topology supplemented by rotation allows simulation of dynamical topological effects associated with the quantum Hall effect and synthetic gauge fields; The finite unbounded configuration of a ring lattice allows simulation of many-body physics, including phase transitions and quantum dynamics with fewer approximations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.