Numerical study of the spatial coherence of light in collective spontaneous emission

We present a numerical study of the spatial coherence of light that is radiated from a dilute ensemble of atoms. The spatial coherence is established as a result of the collective (cooperative) coupling of the atoms to the light and is qualitatively different from the coherence of a laser. Specifically, the coherence in collective spontaneous emission does not rely on population inversion and stimulated emission, is governed by antiphasing of the dipoles (subradiance), and the key figure of merit for the observed coherence is $\ensuremath{\approx}N/(L/\ensuremath{\lambda})$. Here, $N$ is the number of atoms in the ensemble, $L$ is the size of the sample, and $\ensuremath{\lambda}$ is the wavelength of the emitted light.