This two-stage process is where the advantage lies: if the exciting pulse has a much shorter wavelength than the ionizing laser pulse, it can be switched on at many points in the ionizing pulse's cycle, and only at these points will electrons be in a position to tunnel. Then, by noting when in the ionizing laser's cycle the electrons tunnel, a picture of how the electrons leave the atom can gradually be reconstructed.
Strangely enough, it is quite similar to how we do our laser fine-delay scan in our accelerator photoinjector. The rf in the electron gun cavity is at 1.3 GHz, meaning that it has a period of about 770 ps. Our laser has a pulse duration of about 10-15 ps. So we can shoot the laser at various phase within a single rf cycle and this will correspond to the electric field strength that the photoelectrons will see when they are emitted. By varying the phase that the laser hits the photocathode, we can vary this field strength.
This is almost the same thing that was done in this paper from that description, where the exciting pulse, having a much shorter wavelength than the ionizing pulse, is equivalent to our pulsed laser. Fancy that!
Edit: more review here.
Zz.
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