Symmetry based efficient simulation of dissipative quantum many-body dynamics in subwavelength quantum emitter arrays

We propose an efficient method to numerically simulate the dissipative 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 a linear, ring-shaped and planar arrays of quantum emitters. In particular, we characterize the excited population, the total photon emission rate and the second order intensity correlation function $g^{(2)}(\tau =0)$, which are challenging to compute for large systems with traditional cumulant expansion methods based on the individual spins.