## Single resonance driven by stochastic pulses

**Figure 8.** Single resonance driven by stochastic pulses. The FWHM of the total yield of RA electrons 〈*Q*_{2}〉 is plotted as a function of the field bandwidth. (a) The dependence of the FWHM on the bandwidth γ (see table 1), for the PDM (filled symbols) and the Gaussian-correlated noise (open symbols), for various pulse durations. (b) A close-up of (a) for the FWHM reported in [10], i.e., ≈1.38Γ_{2}. The vertical dashed arrows mark the corresponding values of γ for the various models and pulse durations. The thick dashed curves correspond to the best fits to the numerical data (symbols). (c) The dependence of the FWHM on the combined bandwidth Δω_{s}, for Gaussian-correlated noise and various pulse durations. The solid line is the FWHM corresponding to the Voigt profile (see equation (33)). (d) A close up of (c) for the FWHM reported in [10]. The vertical dashed arrow marks the corresponding value of Δω_{s}. The thick dashed curves correspond to the best fits to the numerical data, and they are very close to the solid curve of (c). Other parameters: Gaussian pulse profile, \Omega _s^{(0)}=10^{-2}\Gamma _2, 2000 random pulses.

**Abstract**

Motivated by recent experiments pertaining to the interaction of weak SASE-free-electron-laser (FEL) pulses with atoms and molecules, we investigate the conditions under which such interactions can be described in the framework of a simple phase-diffusion model with decorrelated atom–field dynamics. The nature of the fluctuations that are inevitably present in SASE-FEL pulses is shown to play a pivotal role in the success of the decorrelation. Our analysis is performed in connection with specific recent experimental results from FLASH in the soft x-ray regime.