Collective Radiative Interactions of Many-Particle Systems in the Discrete Truncated Wigner Approximation

In a recent work [Mink et. al., Phys. Rev. Research, 4, 043136 (2022)] we have extended the Discrete Truncated Wigner Approximation, which provides a semiclassical and numerically efficient approximation to the dynamics of an interacting ensemble of two-level systems in the Wigner phase space, to dephasing and spontaneous emission.

Here we discuss the application of this approach to collective radiative interactions between atoms such as Dicke superradiance, collective emission processes in Cavity QED and atomic arrays. We show that the correspondence rules of collective spin operators attain a simple approximate form for highly cooperative atom-field interactions. This allows us to derive approximate and numerically inexpensive stochastic differential equations for rather general Hamiltonians and linear Lindblad generators.

For the example of the totally symmetric Dicke-decay, which is exactly solvable, we find near perfect agreement, but show that the approach fails for subradiant phases.

Finally, we investigate the dynamics of a coherently driven 2D gas in a harmonic trap coupled to the free space and study the influence of the trap aspect ratio on its superradiant properties.