Imprint of electron returning dynamics on ion momentum spectra in strong-field nonsequential double ionization

Nonsequential double ionization (NSDI) of atoms driven by parallel -polarized two-color (PPTC) fields composed of two equal -intensity multiple -cycle laser pulses is investigated using a three-dimensional classical ensemble model. The ion momentum distribution shows pronounced asymmetry and strongly depends on the relative phase of the two pulses. The ion momentum distributions exhibit a double- or not yet observed triple -hump structure, depending on the relative phase of the two pulses. More interestingly, the three peaks of the ion momentum distribution correspond to the first -returning recollision, the odd -returning recollision (without the first returning recollision), and the even -returning recollision. This means that the number of electron returnings is mapped onto the ion momentum distribution. The information about the number of electron returnings can be directly retrieved from the observed ion momentum distribution in the PPTC field with equal intensities. Moreover, the proportions of the three types of trajectories in NSDI, the returning energy of the ionized electron, and the ionization mechanism can be well manipulated by changing the relative phase of the two pulses.