Laser phase and amplitude fluctuations in the fluorescent Dicke model

We derive a master equation for the ensemble averaged atomic density operator for a system of N identical superimposed two-level atoms (the Dicke model) driven by an intense, fluctuating laser field of finite phase/amplitude bandwidth by using the theory of multiplicative stochastic processes. It is shown that in spite of the appearance of time-dependent terms, this master equation still describes a Markov process. The quantum regression theorem can, therefore, be used to calculate the fluorescent spectrum which is found to consist of a single Lorentzian located at the central driving laser frequency and a sum of symmetrically displaced Lorentzians. There are broadening and narrowing effects. The intensity correlations are also evaluated. The results are also extended to the case when the atomic system is in n-photon resonance with the phase fluctuating laser field.