The Discrete Truncated Wigner Approximation to Dissipative, Interacting Spin Systems

A semiclassical approach is introduced which allows to describe the coherent and dissipative many-body dynamics of many interacting spins while taking into account lowest-order quantum effects. For this purpose the discrete truncated Wigner approximation, originally developed for unitarily coupled spins [1] is extended to include dissipative [2] and collective [3] spin processes resulting in a set of semiclassical, numerically inexpensive stochastic differential equations. The method is then applied to collective phenomena of light-matter interaction such as superradiance. It is first benchmarked with exact results for the case of Dicke decay showing excellent agreement. Then superradiance in a spatially extended three-dimensional, coherently driven gas and atoms coupled to a waveguide are analyzed including intensity correlations and squeezing and the dynamics of atomic arrays coupled to the quantized radiation field is investigated. For small arrays we compare to exact simulations, again showing very good agreement at early times and at moderate to strong driving.



[1] J. Schachenmayer, A. Pikovski, and A. M. Rey,

Phys. Rev. X 5, 011022 (2015)

[2] Christopher D. Mink, David Petrosyan, and Michael Fleischhauer

Phys. Rev. Res. 4, 043136 (2022)

[3] Christopher D. Mink and Michael Fleischhauer

SciPost Physics 15, 233 (2023)