Bohmian trajectory analysis of high-order harmonic generation: ensemble averages, non-locality and quantitative aspects

TL;DR

This paper uses Bohmian-trajectory analysis to understand high-order harmonic generation, showing that small ensembles of trajectories can accurately reproduce spectra and revealing nonlocal effects and differences from SFA predictions.

Contribution

It demonstrates that small Bohmian ensembles suffice for high-plateau harmonics and relates Bohmian trajectories to SFA trajectories, highlighting nonlocal influences.

Findings

Small ensembles accurately reproduce high-plateau HHG spectra.

Bohmian trajectories relate to short and long SFA trajectories.

Nonlocal effects influence the time-frequency profile of trajectories.

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 [Phys. Rev. A \textbf{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.