Fano resonance in the XUV generated by helium with few-cycle intense laser pulses and its classical analogy

We numerically integrate the Schr"odinger equation for a model helium atom irradiated by an intense few-cycle laser pulse and find the emitted XUV spectra. They demonstrate resonant Fano peaks at the frequencies of the transitions from the doubly excited autoionizing states (AISs) to the ground state. Studying XUV intensity and phase, we show that the resonant peak should be described with an essentially complex asymmetry parameter. The Stark shift of the AIS and the decay of the AIS due to photoionization by the laser field result in the asymmetry parameter describing a spiral path in the complex plane when the laser pulse duration increases. This behavior, in particular, corresponds to the decrease of the resonant contribution with the increase of the laser pulse duration, in agreement with published experimental data. Moreover, we find a remarkable similarity of this behavior of the asymmetry parameter in the complex plane to that of the classical double pendulum. We conclude that transient perturbation of the natural frequency and friction in the upper pendulum can be treated as a classical analogy of the transient frequency shift and extra depopulation of the excited state in the quantum system demonstrating the Fano resonance.