Time-dependent analytical $R$-matrix approach for strong-field dynamics. I. One-electron systems

We develop a flexible analytical approach to describe strong-field dynamics in atoms and molecules. The approach is based on the ideas of the $R$-matrix method. Here, we illustrate and validate our approach by applying it to systems with one active electron bound by the Coulomb potential and benchmark our results against the standard theory of Perelomov, Popov, and Terent'ev [Sov. Phys. JETP 23, 924 (1966)]. We discuss corrections to the ionization amplitude associated with the interplay of the Coulomb potential and the laser field on the sub-laser cycle time scale and the shape of the tunneling wave packets associated with different instants of ionization.

Figure 1

(a) Partitioning of the configuration space. (b) Schematic representation of the boundary condition for the exact Green's function (left) and the approximate eikonal-Volkov Green's function used in this paper (right). Note that the eikonal-Vokov approximation includes unwanted incoming solutions, indicated by the red arrows. However, in strong-field ionization problems, such pathways have to traverse the classically forbidden region to reach the origin. Therefore, they are strongly suppressed and introduce only exponentially small errors.

Figure 2

The integration contour for integral Eq. (81) and its relation to the boundary of the outer region.

Figure 3

Nonadiabatic Coulomb correction $e^{2W_{C2}}$, plotted against time after ionization $\omega t$, and scaled electron momentum, ${\overline{p}}_{\left|\right|}=p_{\left|\right|}/p_0$, $p_0=F/\omega$. We consider only those electrons which leave in the negative $z$ direction with negative momentum. This corresponds to ionization times ${\phi }_i\in (-\pi /2,0)$. Note that we must have $\omega t>{\phi }_i$. We assume an 800-nm laser field with intensity $1.3\times {10}^{14}$ W/cm${}^2$ and an ionization potential $I_p=0.57$.