Quantum simulation of the Dicke model in a two-dimensional ion crystal: chaos, quantum thermalization, and revivals

Quantum many-body systems driven far from equilibrium can exhibit chaos, entanglement, and non-classical correlations, yet directly observing these phenomena in large, closed quantum systems remains challenging. Here we realize the Dicke model -- a fundamental description of light-matter interactions -- in a two-dimensional crystal of approximately 100 trapped ions. The ions' internal state is optically coupled to the center of mass vibrational mode via an optical spin-dependent force, enabling unitary many-body dynamics beyond the mean-field and few-body limits. In the integrable regime, where the phonons can be adiabatically eliminated, we observe a dynamical phase transition between ferromagnetic to paramagnetic spin phases. In contrast, when the spins and phonons are strongly coupled, we observe clear signatures of non-integrable chaotic dynamics, including erratic phase-space trajectories and the exponential growth of excitations and entanglement quantified by the one-body Rényi entropy. By quenching from an unstable fixed point in the near-integrable regime, quantum noise can generate correlated spin-phonon excitations. Our numerical calculations, in clear agreement with experiment, reveal the generation of two-mode spin-phonon squeezing, 2.6 dB below the standard quantum limit (4.6 dB relative to the initial thermal state), followed by generalized vacuum Rabi collapses and revivals. Our results establish large ion crystals as scalable analog quantum simulators of non-equilibrium light-matter dynamics and provide a controlled platform for experimental studies of information scrambling and entanglement in closed many-body systems.