Tracking origins of below-threshold harmonics with a trajectory-resolved fully quantum approach

Suppressed short-trajectory near-threshold harmonics as a sign of tunnel exit

“…Similar treatments are also used for the y axis. Since the rescattering electrons associated with short and long electron trajectories have different maximal displacements predicted by the classical HHG three-step model, we can separate the contributions of desired trajectories from others by putting the mask function at the absorbing boundary at different spatial positions [34,39,40]. Alternatively, for the present cases, with setting x b =0.9x q and keeping y b =L y /8 unchanged, we obtain the short-trajectory TDSE results where the contributions of long trajectory and multiple returns to HHG are removed.…”

“…Recent studies [30][31][32][33][34][35][36] have shown that multiphoton processes such as bound-bound transitions and continuumcontinuum transitions, which are neglected in the description of the LM, can play an important role in the emission of near and below-threshold harmonics. In addition, the coulombmodified quantum orbits including long trajectories and multiple returns and relating to tunneling can also influence importantly on the generation of harmonics near or below the threshold.…”

Below- and near-threshold harmonic generation from multiple orbitals

“…In this case, R − L is generally much larger than the maximal displacement of the electron in the driving field. Moreover, in our study, such a computational trick can also be used to help explore the mechanism of below-and near-threshold harmonic generation, as one can separate the contributions of trajectories evolving closely around the core from others by setting the absorbing area at proper spatial positions [47,48], as discussed in detail in section 4.2. Finally, the harmonic spectrum is obtained by the Fourier transform of the time-dependent dipole acceleration…”

Virtual detector theory for strong-field atomic ionization

“…The computational load quickly becomes infeasible as the number of electrons increases. In fact, many strong-field time-dependent Schrödinger equation (TDSE) calculations are still based on the single-active-electron approximation using an effective potential describing the remaining ion core [12][13][14][15]. Ab initio calculations on the helium atom interacting with strong (extreme ultraviolet to near infrared) laser fields have been performed by a few groups using supercomputers [16][17][18][19][20].…”