Collective Radiative Interactions and the Discrete Truncated Wigner Approximation to Dissipative Spin Systems*

Interfaces of light and matter serve as a platform for exciting many-body physics and photonic quantum technologies. Due to the recent experimental realization of atomic arrays at sub-wavelength spacings, collective interaction effects such as superradiance have regained substantial interest. I discuss a semiclassical approach to this problem that allows to describe the coherent and dissipative many-body dynamics of interacting spins while taking into account lowest-order quantum effects. For this purpose we extend the discrete truncated Wigner approximation, originally developed for unitarily coupled spins [1], to include dissipative [2] and collective [3] spin processes resulting in a set of semiclassical, numerically inexpensive stochastic differential equations. I benchmark our method with exact results for the case of Dicke decay, which shows excellent agreement. Then superradiance in a spatially extended three-dimensional, coherently driven gas is analyzed and the dynamics of atomic arrays coupled to the quantized radiation field 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,

            Many-body quantum spin dynamics with monte carlo trajectories on a discrete   phase space

            Phys. Rev. X 5, 011022 (2015).

 

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

            Hybrid discrete-continuous truncated Wigner approximation for driven, dissipative spin systems

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

 

[3]       Christopher D. Mink and Michael Fleischhauer

            Collective Radiative Interactions in the Discrete Truncated Wigner Approximation

            SciPost Physics 15, 233 (2023)