Quantum-to-classical crossover in the spin glass dynamics of cavity QED simulators

By solving the quench dynamics of a frustrated many-body spin-boson problem, we investigate the role of spin size on the dynamical formation of spin glass order. In particular, we observe that quantum and classical spin glasses exhibit markedly different evolution. The former displays a quick relaxation of magnetization together with an exponential dependence of the spin glass order parameter on spin size, while the latter has long-lasting prethermal magnetization and a spin glass order parameter independent of spin size. The quantum-to-classical crossover is sharp and occurs for relatively small spins, highlighting the fragility of the quantum regime. Furthermore, we show that spin glass order is resonantly enhanced when the frequency of the bosonic mediators of the interactions approaches the value of the transverse field. Our predictions are relevant for all spin glass systems with $SU(2)$ degrees of freedom away from equilibrium, and can be examined in recently developed multi-mode cavity QED experiments.