Symmetry-based efficient simulation of higher-order coherences in quantum many-body superradiance

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msup><a:mi>g</a:mi><a:mrow><a:mo>(</a:mo><a:mn>2</a:mn><a:mo>)</a:mo></a:mrow></a:msup><a:mrow><a:mo>(</a:mo><a:mi>τ</a:mi><a:mo>=</a:mo><a:mn>0</a:mn><a:mo>)</a:mo></a:mrow></a:mrow></a:math>, which is challenging to compute for extended systems with traditional cumulant expansion methods.