Contributions of different quantum pathways to nonsequential double ionization by monochromatic and bichromatic laser fields

When nonsequential double ionization is treated using the strong-field approximation and the saddle-point (SP) method, the transition amplitude can be expressed as a coherent sum of the partial amplitudes corresponding to different SP solutions. For the case of the recollision excitation with subsequent ionization (RESI) mechanism of the nonsequential double ionization, we examine the partial contributions of the SP solutions which correspond to the electron responsible for the excitation. For a monochromatic linearly polarized laser field, we find that, in addition to the pair of the SP solutions with the shortest travel time, other SP solutions may also make a significant contribution to the photoelectron yield. Moreover, the SP solutions appear in pairs and exhibit notable modifications in comparison to those observed in high-order above-threshold ionization. Furthermore, for a bichromatic linearly polarized driving field, we investigate the intensity range obtained using the simpleman's model for which the RESI mechanism is dominant. We find that this range must be modified if the photoelectron yield corresponding to the SP solution for which the photoelectron has the highest energy upon return to the parent ion is small. This is particularly the case for the excitation channels involving loosely bound excited states.