Fig. 1: Origin and magnitude of delays in population transfer.
From: Attosecond spectroscopy of molecular charge transfer uncovers a 1.5-fs delay in population transfer
A A three-state crossing in the diabatic basis; the diagonal entries of \(\hat{V}(x)\) are plotted alongside the initial wavefunction ψ0 (black). B The adiabatic PECs E(x) (colored) reveal the avoided crossing between the bottom states. The associated non-adiabatic coupling (NAC) Γ01 is also plotted (black). C The time-dependent populations resulting from a TDSE propagation of ψ0 according to \(\hat{H}(x)\) are shown. Solid (dashed) lines show the diabatic (adiabatic) populations. P0 (light-blue) and P2 (purple) are fit with AGND CDFs (red dotted). To emphasize the 1.3 fs delay in population transfer (red double-arrow), an amplitude-inverted and rescaled replica of the P0 AGND fit is plotted (gray). The diabatic population transfer probability (taken to be the maximum \(\left\vert 2\right\rangle\) population over the 29.0 fs-long simulation) is indicated with a single red arrow. D A parameter scan revealing the dependence of the delay and population transfer probability on the energy spacing c and the Schrieffer–Wolf two-state coupling γSW/2 = γ2/c (see Eq. 2). Four distinct regions are identified and illustrated with inset schematic diagrams. A black cross marks the parameters of the simulation shown in (A–C).
