Monte-Carlo simulations of superradiant lasing

Abstract

We simulate the superradiant dynamics of ensembles of atoms in the presence of collective and individual atomic decay processes. We apply the Monte-Carlo wave-function method and identify quantum jumps in a reduced Dicke state basis, which reflects the permutation symmetry of the system. 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 superradiant pulses from initially excited atoms agree quantitatively with recent experimental results of strontium atoms but rapid atom loss in these experiments does not permit steady-state superradiance. By introducing an incident flux of new atoms to maintain a large average atom number, our theoretical calculations predict lasing with a millihertz linewidth despite rapid atom number fluctuations. of a high dimensional Hilbert space, the conditional wave-functions are lower dimensional objects than density matrices. This renders the MCWF method an efficient numerical tool for complex system simulations. The symmetries mentioned above restrict the dynamics to sub-spaces and further speed up the wave-function calculations. In the following, we will review briefly the master equation in the Dicke state basis and then demonstrate its unraveling and effective simulation with the MCWF method. J M N J MM J , . The equations for r ¢ MM J P JM

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