Non-Hermitian Physics in Ultracold Atoms and Photonics

量子和光学技术正在成为两个主要的研究前沿，它们可能会给现代科学和工程的计算、通信、安全、测量和传感带来革命性的变化。这些技术的一个共同基础是基本量子方程的一部分，即哈密顿量，它控制着物理系统的内部相和动力学。描述真实物理可见的么正时间演化的量子哈密顿量被称为厄米特(以数学家查尔斯·厄米特的名字命名)。这项工作探索了由非厄米哈密顿量描述的系统的动力学。在探索经典光子系统中的非厄米物理方面，已经取得了重大的理论和实验进展。经典系统的进步自然建议将研究扩展到量子平台，如超冷原子，它们拥有经典光子学所缺乏的主要成分。这个项目研究了经典光子学和超冷原子中的非厄米物理，并探索了它们在器件上的应用。这一研究不仅为光子和超冷原子系统的非厄米控制奠定了基础，也将对光学和冷原子物理的基础研究产生重要影响。该项目为研究生和本科生提供了一个多样化的平台，让他们探索理论冷原子、光学和凝聚态物理。该项目的范围还包括针对K-12学生的具体外展活动，并包括来自代表性不足群体的学生，如女性和少数族裔学生，以扩大参与范围。该计划的总体目标是研究经典光子学中的非厄米驱动的拓扑物理和超冷原子中的非厄米量子物理。具体项目包括：i)通过厄米和非厄米控制构建和表征新的拓扑光子晶格(如分形和3D高阶拓扑绝缘体)；ii)研究由独特的连续双曲超材料产生的新型拓扑相(例如耦合边态促进的拓扑光子晶格)；iii)利用非厄米超冷原子的量子、相互作用或费米性质生成和控制非厄米超冷原子。我们将使用多种分析和数值工具(例如平均场理论、非厄米密度矩阵重整化群算法等)来研究一系列不同的物理问题和系统。拟议的项目不仅将导致探索非厄米物质的实验进展，还将为开发新的光子和量子技术提供平台。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Quantum and optical technologies are emerging as two major research frontiers that could potentially revolutionize computing, communication, security, measurement, and sensing for modern science and engineering. A common foundation for these technologies is that part of the underlying quantum equation, the Hamiltonian, that governs the internal phases and dynamics of the physical system. A quantum Hamiltonian that describes the unitary time-evolution of real physical observables is said to be Hermitian (named after the mathematician Charles Hermite). This work explores the dynamics of systems described by a non-Hermitian Hamiltonian. Significant theoretical and experimental progress has been made in exploring non-Hermitian physics in classical photonic systems. Advances in classical systems naturally suggest extending the studies to quantum platforms such as ultracold atoms, which possess major ingredients that are lacking in classical photonics. This project investigates the non-Hermitian physics in both classical photonics and ultracold atoms and explores their device applications. The proposed research will not only pave the way for non-Hermitian control of photonic and ultracold atomic systems for many important applications, but also influence fundamental research in optical and cold atom physics. The project provides a diverse platform for both graduate and undergraduate students to explore theoretical cold atomic, optical and condensed matter physics. The scope of this project also includes specific outreach activities for K-12 students and involving students from under-represented groups, such as women and minority students, for broadening participation.The overall objective of the proposal is to investigate the non-Hermitian driven topological physics in classical photonics and non-Hermitian quantum physics in ultracold atoms. Specific projects include: i) construction and characterization of new topological photonic lattices (e.g., fractal and 3D higher-order topological insulator) through Hermitian and non-Hermitian control; ii) study of novel topological phases (e.g. coupled edge states facilitated topological photonic lattice) arising from unique continuous hyperbolic metamaterials; iii) generation and control of non-Hermitian ultracold atomic matters utilizing their quantum, interacting, or fermionic properties. A diverse set of physical problems and systems will be investigated using versatile analytic and numerical tools (e.g., mean field theory, non-Hermitian density-matrix-renormalization-group algorithm, etc.). The proposed projects will not only lead to the experimental advances for exploring non-Hermitian matter, but also provide platforms for developing novel photonic and quantum technologies.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.