We investigate quantum interference effects in high-order harmonic generation in N 2 and N 2 + beyond the single-active-orbital approximation, with particular emphasis on the role of σ and π orbitals in the overall spectra. In the former case, we consider a simplified multielectron wave function which incorporates the 3σ g and 1π u orbitals, and, in the latter, we assume that the optically active electron is in a coherent superposition of the 3σ g and 1π * g one-electron states. If the orbitals are energetically close, such as the 3σ g and the 1π u orbitals of N 2 , we show that the quantum interference patterns observed in the high-order harmonic spectra are predominantly determined by the 3σ g orbital. If, on the other hand, there is a significant difference in their binding energies, such as for the 3σ g and the 1π * g orbitals of N 2 + , the most loosely bound orbital will determine the shape of the spectra.Due, however, to the different cutoffs encountered, the more deeply bound orbital will leave an imprint on the high-energy harmonics. This holds both for the situation in which the dynamics of the electron is restricted to the plane p x p z and for the full three-dimensional case, if the azimuthal angle is integrated over and the degeneracy of the π orbitals is taken into account.
We investigate high-order harmonic generation from a Bohmian-mechanical perspective, and find that the innermost part of the core, represented by a single Bohmian trajectory, leads to the main contributions to the high-harmonic spectra. Using time-frequency analysis, we associate this central Bohmian trajectory to an ensemble of unbound classical trajectories leaving and returning to the core, in agreement with the three step model. In the Bohmian scenario, this physical picture builds up non-locally near the core via the quantum mechanical phase of the wavefunction. This implies that the flow of the wavefunction far from the core alters the central Bohmian trajectory. We also show how this phase degrades in time for the peripheral Bohmian trajectories as they leave the core region.
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 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 Schrödinger 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 timefrequency 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.
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