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We propose an efficient method to numerically simulate the superradiant emission dynamics of large numbers of quantum emitters in ordered arrays in the presence of long-range dipole-dipole interactions mediated by the vacuum electromagnetic field. Using the spatial symmetries of the system, we rewrite the equations of motion in a collective spin basis and subsequently apply a higher-order cumulant expansion for the collective operators. By truncating the subradiant collective modes with a heavily suppressed decay rate and keeping only the effect from the radiating collective modes, we reduce the numerical complexity significantly. This allows to efficiently compute the dissipative dynamics of the observables of interest for linear and ring-shaped arrays of quantum emitters. In particular, we characterize the second-order intensity correlation function $g^{\left(2\right)}(\tau =0)$ , which is challenging to compute for extended systems with traditional cumulant expansion methods. 

The dynamical preparation of exotic many-body quantum states is a persistent goal of analog quantum simulation, often limited by experimental coherence times. Recently, it was shown that fast, non-adiabatic Hamiltonian parameter sweeps can create finite-size ``lakes'' of quantum order in certain settings, independent of what is present in the ground state phase diagram. Here, we show that going further out of equilibrium via external driving can substantially accelerate the preparation of these quantum lakes. Concretely, when lakes can be prepared, existing counterdiabatic driving techniques -- originally designed to target the ground state -- instead naturally target the lakes state. We demonstrate this both for an illustrative single qutrit and a model of a Z Rydberg quantum spin liquid. In the latter case, we construct experimental drive sequences that accelerate preparation by almost an order of magnitude at fixed laser power. We conclude by using a Landau-Ginzburg model to provide a semi-classical picture for how our method accelerates state preparation. 

We analyze the driven-dissipative dynamics of subwavelength periodic atomic arrays in free space, where atoms interact via light-induced dipole-dipole interactions. We find that depending on the system parameters, the underlying mean-field model allows four different types of dynamics at late times: a single monostable steady state solution, bistability (where two stable steady state solutions exist), limit cycles and chaotic dynamics. We provide conditions on the parameters required to realize the different solutions in the thermodynamic limit. In this limit, only the monostable or bistable regime can be accessed for the parameter values accessible via light-induced dipole-dipole interactions. For finite size periodic arrays, however, we find that the mean-field dynamics of the many-body system also exhibit limit cycles and chaotic behavior. Notably, the emergence of chaotic dynamics does not rely on the randomness of an external control parameter but arises solely due to the interplay of coherent drive and dissipation. Published by the American Physical Society2025