Quantum Simulation and Dynamics with Synthetic Quantum Matter

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Significant advancements in controlling and manipulating individual quantum degrees of freedom have paved the way for the development of programmable strongly-interacting quantum many-body systems. Quantum simulation emerges as one of the most promising applications of these systems, offering insights into complex natural phenomena that would otherwise be difficult to explore. Motivated by these advancements, this dissertation delves into several analog quantum simulation proposals spanning different fields, including high-energy and condensed matter physics, employing various synthetic quantum systems. A primary objective is the investigation of the dynamical phenomena that can be effectively studied using these simulation approaches. The first part of the dissertation focuses on quantum simulation utilizing superconducting circuits. We demonstrate that this platform can natively realize several intriguing models including the massive Schwinger model (quantum electrodynamics (QED) in 1+1 dimensions) and various strongly interacting quantum impurity models. By studying high-energy scattering of quark and meson states within the Schwinger model, we reveal a wealth of rich phenomenology encompassing inelastic particle production, hadron disintegration, as well as dynamical string formation and breaking. Furthermore, we demonstrate how the presence of a single impurity (artificial atom) can profoundly modify the properties of light-matter interactions in a waveguide, leading to anomalous transport of a single photon, strong photon decay, and the emergence of atom-photon bound states. The second part of the dissertation focuses on quantum simulation with atomic, molecular, and optical (AMO) systems. Leveraging the tunable and long-range interactions available in platforms such as cavity-QED and trapped ions, we explore exotic regimes of quantum information dynamics. On the one hand, we demonstrate that the combination of simple and uniform all-to-all interactions together with chaotic short-range interactions can induce fast scrambling, a central feature associated with quantum black holes. On the other hand, we investigate how short-range yet non-local Rydberg interactions can strongly suppress atom tunneling in an optical lattice, resulting in frozen dynamics and Hilbert-space fragmentation. Finally, we propose a method of sympathetic cooling of neutral atoms using state insensitive Rydberg interactions, potentially enabling longer quantum simulations and computations with this platform.