Phase-Space Methods for Mirrorless Superradiant Lasers

Exact numerical simulations of dissipative spin systems are often intractable due to the exponential growth of the Hilbert space with system size. Semiclassical approaches, such as the Truncated Wigner Approximation and its recent extensions to dissipative regimes, offer computationally-efficient alternatives by capturing leading-order quantum fluctuations. Here, we discuss refinements to existing approaches and propose a generalization to other phase space distributions. Additionally, we extend the method to calculate multi-time correlation functions, thereby extending the scope of semiclassical simulations of open spin systems to include coherence and spectral properties, as well as directional correlations of collectively radiating emitters. These developments are key to study exotic light sources driven by collective dissipative dynamics, such as mirrorless superradiant lasers.