Resonance fluorescence in a band-gap material: Direct numerical simulationof non-Markovian evolution - art. no. 043803

A numerical method of calculating the non-Markovian evolution of a driven a tom radiating into a structured continuum is developed. The formal solution for the atomic reduced density matrix is written as a Markovian algorithm by introducing a set of additional, virtual density matrices which follow, to the level of approximation of the algorithm, all the possible trajectori es of the photons in the electromagnetic held. The technique is perturbativ e in the sense that more virtual density matrices are required as the produ ct of the effective memory time and the effective coupling strength becomes larger. The number of density matrices required is given by 3(M) where M i s the number of time steps per memory time. The technique is applied to the problem of a driven two-level atom radiating close to a photonic band gap and the steady-state correlation function of the atom is calculated.