Modelling Non-Gaussian Light Emission from large ensembles of driven two level atoms in truncated Wigner approximation

Motivated by the recent observation of non-Gaussian light emitted from an extended cloud of coherently driven two level atoms emitting into free space [G. Ferioli et al., arXiv:2311.13503 (2023)], we theoretically investigate the underlying mechanism by proposing an effective model of position-disordered atoms coupled to a lossy waveguide. Using a dissipative extension of the Discrete Truncated Wigner Approximation [C. Mink, M. Fleischhauer, SciPost Phys. 15, 233 (2023)], we study the competition of atomic synchronisation due to collective decay and disorder and reconstruct the Wigner function of the light propagating along the optical fiber, illustrating the departure of the measured correlation function g⁽²⁾(t, τ=0) < 2 from thermal light. We conclude by simulating a realistic configuration of a cigar-shaped cloud of driven atoms in free space and reproduce the non-classical emission of light.