This study explores quantum coarsening and collective dynamics in a programmable quantum simulator based on Rydberg atom arrays, focusing on the dynamics across a (2+1)D Ising quantum phase transition. The researchers observe the gradual growth of correlations through the coarsening of antiferromagnetically ordered domains after crossing the quantum critical point. They demonstrate that coarsening is driven by the curvature of domain boundaries and accelerate near the critical point. The study also identifies long-lived oscillations of the order parameter, corresponding to an amplitude (Higgs) mode. These observations provide insights into emergent collective dynamics in strongly correlated quantum systems and nonequilibrium quantum processes. The study uses a programmable quantum simulator to investigate the collective out-of-equilibrium dynamics associated with the growth of order following an Ising quantum phase transition. Key features of beyond-mean-field quantum coarsening processes are observed, including the curvature-driven dynamics of domain walls and their acceleration when approaching the critical point. The study also explores self-similarity and universality in the ordering process and observes long-lived coherent oscillations of the correlation length and the order parameter on both sides of the QPT, identified as an amplitude (Higgs) mode. These findings are consistent with theoretical predictions and extend studies in a regime difficult to simulate classically. The experiments are conducted using a two-dimensional programmable atom array, with measurements performed on a 16×16 square lattice of 87Rb atoms trapped in optical tweezers. The atoms are initialized in the electronic ground state and coupled to the Rydberg state through two-photon excitation. The study reveals the dynamics of the correlation length and the order parameter, showing that the correlation length grows over time and exhibits long-lived oscillations. The results highlight the role of quantum fluctuations in the coarsening dynamics and the emergence of the Higgs mode. The study also demonstrates the importance of quantum fluctuations in the vicinity of the quantum critical point and provides insights into the universal properties of quantum phase transitions.This study explores quantum coarsening and collective dynamics in a programmable quantum simulator based on Rydberg atom arrays, focusing on the dynamics across a (2+1)D Ising quantum phase transition. The researchers observe the gradual growth of correlations through the coarsening of antiferromagnetically ordered domains after crossing the quantum critical point. They demonstrate that coarsening is driven by the curvature of domain boundaries and accelerate near the critical point. The study also identifies long-lived oscillations of the order parameter, corresponding to an amplitude (Higgs) mode. These observations provide insights into emergent collective dynamics in strongly correlated quantum systems and nonequilibrium quantum processes. The study uses a programmable quantum simulator to investigate the collective out-of-equilibrium dynamics associated with the growth of order following an Ising quantum phase transition. Key features of beyond-mean-field quantum coarsening processes are observed, including the curvature-driven dynamics of domain walls and their acceleration when approaching the critical point. The study also explores self-similarity and universality in the ordering process and observes long-lived coherent oscillations of the correlation length and the order parameter on both sides of the QPT, identified as an amplitude (Higgs) mode. These findings are consistent with theoretical predictions and extend studies in a regime difficult to simulate classically. The experiments are conducted using a two-dimensional programmable atom array, with measurements performed on a 16×16 square lattice of 87Rb atoms trapped in optical tweezers. The atoms are initialized in the electronic ground state and coupled to the Rydberg state through two-photon excitation. The study reveals the dynamics of the correlation length and the order parameter, showing that the correlation length grows over time and exhibits long-lived oscillations. The results highlight the role of quantum fluctuations in the coarsening dynamics and the emergence of the Higgs mode. The study also demonstrates the importance of quantum fluctuations in the vicinity of the quantum critical point and provides insights into the universal properties of quantum phase transitions.