Extended Virtual Detector Theory for Strong-Field Atomic Ionization

Abstract

For time-dependent strong-field atomic ionization a new theoretical approach is described that combines the numerical time-dependent Schrödinger equation (TDSE) and the numerical time-dependent Newtonian equation (TDNE). This approach keeps both the accuracy of quantum calculations and the speed of classical calculations. It does not use approximate tunneling formulas. It is applied to a recent experimental result, and we show its successful comparison to extensive TDSE calculations made under exactly the same conditions.

Ionization Time and Exit Momentum in Strong-Field Tunnel Ionization

“…This model, however, cannot be used as a benchmark for experiments, because a possible match or mismatch of experimental data and the theoretical prediction by the two-step model may be explained by various pairs of nonzero delay τ A [22] and nonzero initial momentum p(t 0 + τ A ), which may a have nonzero component parallel to the electric field direction [23,24].Neither the delay τ A nor the initial momentum p(t 0 + τ A ) are directly accessible by experiments, and it is also challenging to calculate them analytically. Therefore, we employ ab initio quantum calculations and a virtual detector [25,26] at the tunnel exit. The virtual detector technique allows us to determine directly the electron's time of arrival at the tunnel exit as well as its exit momentum.We analyze theoretically an initially bound electron ionized by an electric field pulse.…”

Numerical Detector Theory for the Longitudinal Momentum Distribution of the Electron in Strong Field Ionization

“…By contrast, exploration of the confusion/conflict about important features of the exit momenta is very direct when using the SENE (Schrödinger equation -Newton equation) method, which has been introduced and extended in [21,22]. It provides, we believe, the first results that are not under the control of a tunneling assumption.…”

“…The circle of numerical detectors [21,22] with radius R d is shown, as well as outgoing classical particle trajectories that were initiated with the momentum values determined by the detectors. The trajectories continue to be fully affected by both laser action and ionic Coulomb attraction as the particles propagate outward to actual detection.…”

“…One does not need to rely on the unprovable presumption that an electron is ionized through tunneling despite being exposed to unknown dynamical effects, and finally appears outside the barrier with a specific momentum and a zero tunneling time. Instead, all information is obtained by integrating the TDSE and is extracted by numerical detectors (ND) described previously [21,22]. By splitting the computing space into an inner part and an outer part, the SENE method shares some common features with other advanced numerical methods (e.g., ARM by Barth, et al [23], t-SURFF by Scrinzi [24]).…”

Time-dependent renormalized-natural-orbital theory applied to laser-drivenH2+

“…Furthermore, in the case of DI, we calculate electronic kinetic-energy spectra using the extended virtual detector method [49]. Starting from the virtual detectors, classical trajectories are calculated in order to obtain the final momentum of the electron at the end of the laser pulse.…”