Correlation and Dynamics of Ultracold Atoms in Optical Tweezer Arrays

这个项目解决了最近关于光镊阵列中强相互作用原子的实验所带来的开放性问题。在这些实验中，每个镊子（由激光制成）容纳一个单独的原子，而镊子阵列通过编程将原子聚集到所需的空间构型中，并在精确控制下隧穿和相互作用。这个新平台有望从底层开始，一个原子一个原子地组装量子物质，以实现迄今为止仍然无法实现的相关量子相。镊子阵列还提供了一种可扩展的架构，以生成和探测对量子信息至关重要的纠缠态。提出的研究开发了新的数值算法来计算和理解镊子阵列中相互作用原子的相关性和动力学。部分受到机器学习和数字量子模拟的启发，所提出的算法将补充基于微扰理论的传统多体技术。这个项目的结果有助于理解正在进行的实验中观察到的冷原子的集体行为。首席研究员将继续改善当地对学生专业发展的支持，并指导高中生进行暑期研究。更具体地说，建议的工作分为三个部分。项目A使用两种创新技术解决二维镊子阵列中Rydberg原子的量子自旋模型：基于多自旋波函数的神经网络表示的变分分析和高分辨率功能重整化群。这两种方法都忠实地处理所有相互竞争的、较长距离的自旋相互作用，从而得到相图。项目B计算了小型镊子阵列上费米-哈伯德气体的实空间相关函数。费米子相互作用的问题被精确地映射到一组具有非局部相互作用的量子比特（自旋）上，然后解决这个问题以寻求配对的开始和它的轨道对称性。项目C发展了一维里德伯原子在重复测量和后选择下的纠缠跃迁的场理论。总体而言，该项目探索了量子多体物理的未知机制，并激发了原子物理、凝聚态物质、量子信息和机器学习之间的对话。该奖项反映了美国国家科学基金会的法定使命，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。

This project addresses open problems brought forth by recent experiments on strongly interacting atoms in optical tweezer arrays. In these experiments, each tweezer (made of laser light) holds an individual atom, while the tweezer array is programmed to herd the atoms into desired spatial configurations with the tunneling and interactions under precise control. This new platform promises to assemble quantum matter from the ground up, atom by atom, to realize correlated quantum phases which have remained inaccessible so far. Tweezer arrays also furnish a scalable architecture to generate and probe entangled states of central importance to quantum information. The proposed research develops novel numerical algorithms to compute and understand the correlations and dynamics of interacting atoms in tweezer arrays. Inspired in part by machine learning and digital quantum simulation, the proposed algorithms will be complementary to traditional many-body techniques based on perturbation theory. The outcomes of this project help understand the collective behaviors of cold atoms observed in ongoing experiments. The principal investigator will continue to improve the local support for student professional development and mentor high school students in summer research.More specifically, the proposed work is divided into three parts. Project A solves quantum spin models of Rydberg atoms in two-dimensional tweezer arrays using two innovative techniques: a variational ansatz based on the neural network representation of many-spin wave functions and high-resolution functional renormalization group. Both approaches faithfully treat all competing, longer-range spin interactions to yield the phase diagrams. Project B computes the real space correlation functions of Fermi-Hubbard gas on small tweezer arrays. The problem of interacting fermions is mapped exactly to a set of qubits (spins) with non-local interactions, which is then solved to seek the onset of pairing and its orbital symmetry. Project C develops field theory for the entanglement transition in one-dimensional arrays of Rydberg atoms under repeated measurements and post-selection. Overall, the project explores unknown regimes of quantum many-body physics, and stimulates the dialogue between atomic physics, condensed matter, quantum information, and machine learning.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.