Photon counting statistics in single multi-level quantum system

We theoretically study the statistics of photon emission of a single multi-level quantum system by employing the generating functions approach developed recently. The generalized decay constants are included in a single multi-level quantum system with quasi-degenerated levels in this work although they are normally neglected in the absence of (quasi-)degeneracies in a multi-level quantum system within the rotating wave approximation. The quantum beats, the line shapes and the Mandel's Q parameters, etc. are studied.