Monte-Carlo Simulations of Superradiant Lasing

We present simulations of the superradiant dynamics of ensembles of atoms in the presence of collective and individual atomic decay processes. We unravel the density matrix with Monte-Carlo wave-functions and identify the quantum jumps in a reduced Dicke state basis, which reflects the permutation symmetry of the identical atoms. While the number of density matrix elements in the Dicke representation increases polynomially with atom number, the quantum jump dynamics populates only a single Dicke state at the time and thus efficient simulations can be carried out for tens of thousands of atoms. The calculated superradiance pulses from initially excited atoms agree quantitatively with recent experimental results with strontium atoms but rapid atom loss in these experiments does not permit steady-state superradiance. By introducing an incident flux of new atoms, the system can maintain a large average atom number, and our theoretical calculations predict lasing with millihertz linewidth despite rapid atom number fluctuations.