Analysis of electron trajectories with two-color strong-field ionization

Two-color ionization of atoms with a strong 800-nm fundamental component and a weak 400-nm component with perpendicular polarization gives detailed insight into the ionization dynamics. When the delay between the two colors is varied on a subcycle scale, the slow-electron signal shows an oscillatory structure due to intracycle interference between different ionization times. Using a trajectory-based interference model, we extract the relative strength of the two contributing pathways. Ionization times can be read directly from the delay scan, and the times for the long trajectories agree well with the quantum-orbit model. The fast electrons arise predominantly from long rescattering trajectories.

Figure 1

(a) Photoelectron momentum distribution at the two-color delay $\varphi =0.96\pi$, which gives the largest fast-electron yield; the black line shows the positive $p_x$ axis and the circles indicate the integration limits used to obtain the results in panel (b). (b) Delay scan of the photoelectron signal integrated over three different energy ranges. The signal is given relative to the signal from an 800-nm single-color field.

Figure 2

(a) Photoelectron spectrum from the 800-nm single-color field at $p_y=0$. (b) Contrast for every momentum of the delay scan. (c) Delay scan at $p_y=0$. The two horizontal dotted orange (gray) lines show the classical limits of slow $\left(p_x=A_0=\sqrt{2U_{\mathrm{p}}}\right)$ and fast electrons $(p_x=\sqrt{2\left(10U_{\mathrm{p}}\right)}$ [40]). Within the slow electrons two dashed lines (red and blue) give the results for the classical model. The two solid lines give the corresponding solutions of the QO model. The descending branch of the models (red [gray] lines) corresponds to electrons born while the electric field decreases, i.e., electrons able to recollide. At high momenta a classical model for the fast electrons is shown, with the colors indicating the short (dot-dashed green [gray] line) and long trajectories (yellow [light gray] solid line) according to HHG conventions. The inset in panel (b) illustrates the respective ionization times using the same colors.

Figure 3

Comparison of the spectrum from the 800-nm single-color field and observables from the two-color calculation. (a) Single-color spectrum before (black dashed line) and after averaging over the ATI peaks (red [gray] solid line). (b) Positions of the maxima in Fig. 2 (red [gray] solid line), compared to the maximum of $\left|b\right|$ (black dashed line) and a modified QO model (blue [gray] dashed line). (c) Interference term extracted from the averaged TDSE spectrum in panel (a) with the maxima highlighted by gray dotted vertical lines.

Figure 4

(a) Comparison of reconstructed and predicted ionization times. (b) Delay scan from Fig. 2 for the slow electrons, with the original (blue [gray] dashed line) and smoothed (red [gray] solid line) maxima ${\varphi }_{\mathrm{i}}\left(p_x\right)$.