S-Matrix theory of laser-induced nonsequential double ionization: from electron-electron dynamics to absolute-phase diagnosis

Full text: We provide a summarizing account of a series of investigations, in which laser-induced nonsequential double ionization (NSDI) is described as the inelastic collision of an electron with its parent ion, and treated quantummechanically, within the strong-field approximation. In particular, we employ a specific uniform saddle-point approximation whose only validity requirement is that the saddles occur in pairs. As a first step, we address the question of how the type of the interaction by which the second electron is dislodged, as well as final-state electron-electron repulsion, influences the NDSI differential electron momentum distributions. We found that a contact-type interaction and uncorrelated final electron states yields the best agreement with the experimental results, namely circular-shaped distributions peaked at p1II = p2II = ±2√Up, where pnII (n = 1,2) denotes the electron momentum components parallel to the laser-field polarization and Up the ponderomotive energy. Final-state repulsion leads to a broadening in such distributions, with respect to p1II = p2II, whereas a Coulomb-type interaction favors unequal momenta. The influence of the interaction and of final-state electron-electron repulsion is most extreme if at least one of the transverse momentum components is kept small, while, for large transverse momenta, different types of interaction or two-electron final states lead to minor discrepancies. In all cases, we obtain very similar results as compared to a classical ensemble computation, in which electrons are released with a quasi-static tunneling rate, apart from minor differences near the boundary of the momentum region for which the collision process in question is classically allowed. Such results suggest that the residual ion has a strong influence on the dynamics of both electrons in NSDI, screening the long-range interaction and the final-state Coulomb repulsion. This interpretation is strengthened by more recent studies, in which a systematic analysis of the influence of the initial bound states of both electrons, and of the spatial extension of the electronic wave function, on the NSDI momentum distributions, has been performed. Such studies have shown that the best agreement with experiments should occur for highly localized bound states and an effective short-range interaction. In the above-stated studies, the external laser field has been approximated by a monochromatic wave. This is a reasonable assumption if the laser pulses in question are relatively long. For few-cycle pulses, however, one expects a very different behavior and, in particular, that the so-called absolute phase, i.e., the phase difference between the pulse envelope and its carrier oscillation, influences the momentum distributions in question. Within this context, we have shown that the differential momentum distributions are highly asymmetric and either concentrated in the first or the third quadrant of the (p1II, p2II) plane. Around a critical value of the absolute phase, the distributions shift from one region to the other. Such a behavior can be explained in terms of the trajectories of an electron recombining inelastically with its parent ion, and the critical phase can be traced to a change in the dominant set of trajectories. This effect is present both in a classical and a quantum-mechanical framework, with the difference that, in the quantum-mechanical case, the distributions start to shift at a slightly smaller phase. This is due to the fact that, if NSDI is classically forbidden, the quantum mechanical distributions are exponentially decaying, whereas their classical counterparts vanish. This behavior is more extreme than those observed for other high-intensity phenomena, such as above-threshold ionization or high-harmonic generation, so that NSDI is an efficient tool for absolute-phase measurements. Refs. 3 (author)