Semiclassical two-step model for strong-field ionization

Abstract

We present a semiclassical two-step model for strong-field ionization that accounts for path interferences of tunnel-ionized electrons in the ionic potential beyond perturbation theory. Within the framework of a classical trajectory Monte Carlo representation of the phase-space dynamics, the model employs the semiclassical approximation to the phase of the full quantum propagator in the exit channel. By comparison with the exact numerical solution of the time-dependent Schrödinger equation for strong-field ionization of hydrogen, we show that for suitable choices of the momentum distribution after the first tunneling step, the model yields good quantitative agreement with the full quantum simulation. The two-dimensional photoelectron momentum distributions, the energy spectra, and the angular distributions are found to be in good agreement with the corresponding quantum results. Specifically, the model quantitatively reproduces the fanlike interference patterns in the low-energy part of the two-dimensional momentum distributions, as well as the modulations in the photoelectron angular distributions.

Coulomb-corrected quantum interference in above-threshold ionization: Working towards multitrajectory electron holography

“…The same spider-like pattern is seen in [55,57], in which the quantum-trajectory Monte Carlo (QTMC) model is applied to mid-IR fields, and experimentally in [32,56], and it is attributed to these forward scattered trajectories. The on-axis contribution of orbit 3 to the overall PADs improves the agreement with the time-dependent Schrödinger equation (TDSE) [26,32,36] and with experiments [13,14,35,56], and can be seen in Coulomb-corrected computations in which orbit 3 has been included implicitly [52,55]. It is also worth noting that classical soft forward-scattered trajectories associated with the low-energy structure (LES) [6] are the same type of trajectories as orbit 3.…”

“…While our method is similar to other approaches such as the trajectory-based Coulomb-corrected strong-field approximation (TCSFA) [36,37] and the QMTC model [52,55,57], there are some key differences. The TCSFA and the QMTC method solve the forward problem.…”

How to understand the tunneling in attosecond experiment?

“…We also note that the internal clock or the intrinsic time point of view is similar to what occurs in special relativity, where a moving particle has its own time in its inertial frame, which differs from the time from the viewpoint of other inertial frames, as discussed in [14]. Finally we mention that some authors [42,43] use the notation ts = t R + i t T , where ts refers to the solution of the saddle point equation, t R or the real part of ts denoted as the ionization time (after tunneling) and the imaginary part t T as the T-time. The partition of ts this way, in a real part for ionization and an imaginary part for the tunneling, lets some questions be opened.…”

“…11) and Büttiker [17] (chap. 9), although many authors claim, and it is widely accepted, that it is an imaginary quantity [42,43], [44] (and [17] chap. 7).…”

The plateau in above-threshold ionization: the keystone of rescattering physics

“…Reprinted figure with permission from [28], copyright (2008) by the American Physical Society. different attempts have been made to include the Coulomb field into the phases of the quantum orbits or, starting from a completely classical description, to augment the classical orbits by suitable phases [66,67,[107][108][109][110][111][112][113][114][115][116]. The exact relation of these approaches to the ISFA is not known.…”