Correlation and Dynamics of Ultracold Atoms in Optical Tweezer Arrays

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.