<p>Programmable quantum platforms have emerged as powerful tools for studying quantum many-body phenomena, with applications ranging from condensed matter and high energy physics to quantum algorithms. In this talk, I will discuss recent developments involving programmable Rydberg atom arrays, which allow for precise and coherent control of hundreds of atoms in two dimensions, along with individual addressability and reconfigurable geometry. First, I will describe explorations of ordering dynamics in a quantum magnet following a quantum phase transition. Using individual atom control, we uncover the interplay of quantum criticality and non-equilibrium phenomena, and observe long-lived oscillations of the order parameter akin to an amplitude (“Higgs”) mode, with interesting implications near the quantum critical point. I will then describe the digital realization of the Kitaev honeycomb model, including observation of an exotic non-Abelian spin-liquid, as well as the use of topological order to design a programmable fermionic simulator. These measurements introduce new avenues for the study of quantum criticality and fermionic models, respectively. Finally, I will briefly discuss future opportunities in explorations of quantum many-body physics with atom arrays, with emphasis on new frontiers in the study of quantum criticality.</p>
