Laser-dressed scattering of an attosecond electron wave packet

We theoretically investigate the scattering of an attosecond electron wave packet launched by an attosecond pulse under the influence of an infrared laser field. As the electron scatters inside a spatially extended system, the dressing laser field controls its motion. We show that this interaction, which lasts just a few hundreds of attoseconds, clearly manifests itself in the spectral interference pattern between different quantum pathways taken by the outgoing electron. We find that the Coulomb-Volkov approximation, a standard expression used to describe laser-dressed photoionization, cannot properly describe this interference pattern. We introduce a quasiclassical model, based on electron trajectories, which quantitatively explains the laser-dressed photoelectron spectra, notably the laser-induced changes in the spectral interference pattern.

Figure 1

The ionic potential (solid line) dips at $q=0$ and $q=-24\hspace{0.5em}\text{a.u.}$ The initial state (dotted line) is localized at $q=0$. The reflected and direct trajectories are labeled with $R$ and $D$.

Figure 2

Laser-dressed photoelectron spectra numerically evaluated (a) from the temporal Schrödinger equation and (b) from the CVA. The CVA does predict a fringe pattern, but fails to account for its change under the laser field.

Figure 3

The amplitude (solid line) and phase (dashed line) of the wave parcel shows two separate contributions $|w_R^{(0)}(t_f)\rangle$ and $|w_D^{(0)}(t_f)\rangle$. The wave parcel is evaluated in the absence of the control field, as indicated by the superscript $(0)$. We removed the central momentum from the wave parcel to better visualize the phases of the direct and reflected components. Once projected into real space, the wave parcels $w_D^{(0)}(t_f,q)$ and $w_R^{(0)}(t_f,q)$ are located at the apparent starting points of the electron trajectories.

Figure 4

In panel (a), the reflection probability is plotted against the control field intensity, while panel (b) shows the momentum spectra of the reflected wave parcel, along with the classically expected final momentum of the reflected trajectory (dashed line).

Figure 5

The classically adjusted laser-dressed photoelectron spectra (b), based on the transformation (14) reproduce the correct fringe patterns predicted by the TDSE (a). It is the difference in the backpropagated action $\Delta S$, between the reflected and the direct trajectories, that sets the position of the fringes. The classically adjusted spectra shown in panel b are to be compared to those evaluated from the CVA [Fig. 2b].