Bohmian-trajectory analysis of high-order-harmonic generation: Ensemble averages, nonlocality, and quantitative aspects

Abstract

We perform a Bohmian-trajectory analysis of high-order-harmonic generation (HHG), focusing on the fact that typical HHG spectra are best reproduced by the Bohmian trajectory starting at the innermost part of the core [J. Wu, B. B. Augstein, and C. Figueira de Morisson Faria, Phys. Rev. A 88, 023415 (2013)]. Using ensemble averages around this central trajectory, we show that for the high-plateau and cutoff harmonics, small ensembles of Bohmian trajectories are sufficient for a quantitative agreement with the numerical solution of the time-dependent Schr\"odinger equation (TDSE), while larger ensembles are necessary in the low-plateau region. Furthermore, we relate the Bohmian trajectories to the short and long trajectories encountered in the strong-field approximation (SFA) and show that the time-frequency maps from the central Bohmian trajectory overestimate the contributions of the long SFA trajectory, in comparison to the outcome of the TDSE computations. We also discuss how the time-frequency profile of the central trajectory may be influenced nonlocally by degrading the wave-packet propagation far from the core.