Perturbative theory of statistically averaged atomic dynamics in fluctuating laser fields

We have developed a perturbative method to model the resonant ionization of atomic systems in fluctuating laser fields. The perturbative method is based on an expansion in terms of the multitime cumulants, a suitable combination of moments (field's coherence functions), used to represent the field's statistical properties. The second-order truncated expansion is expressed in terms of the radiation's power spectrum and the intensity autocorrelation function. We investigate the range of validity of the model in terms of the field's coherence temporal length and peak intensity and have compared the results with conventional Monte-Carlo calculations. We apply the theory in the case of a near-resonant ionization of the Helium 2s2p autoionizing state with a SASE FEL pulse with square-exponentially dependent 1st-order coherence function. The ionization lineshape profile acquires a Voight profile; the degree of the Gaussian or Lorentzian character of which to depend crucially on the field's coherence time.