Classical and quantum-mechanical treatments of nonsequential double ionization with few-cycle laser pulses

We address nonsequential double ionization induced by strong, linearly polarized laser fields of only a few cycles, considering a physical mechanism in which the second electron is dislodged by the inelastic collision of the first electron with its parent ion. The problem is treated classically, using an ensemble model, and quantum mechanically, within the strong-field and uniform saddle-point approximations. In the latter case, the results are interpreted in terms of “quantum orbits,” which can be related to the trajectories of a classical electron in an electric field. We obtain highly asymmetric electron momentum distributions, which strongly depend on the absolute phase, i.e., on the phase difference between the pulse envelope and its carrier frequency. Around a particular value of this parameter, the distributions shift from the region of positive to that of negative momenta, or vice versa, in a radical fashion. This behavior is investigated in detail for several driving-field parameters, and provides a very efficient method for measuring the absolute phase. Both models yield very similar distributions, which share the same physical explanation. There exist, however, minor discrepancies due to the fact that, beyond the region for which electron-impact ionization is classically allowed, the yields from the quantum-mechanical computation decay exponentially, whereas their classical counterparts vanish.