Imprint of electron returning dynamics on ion momentum spectra in strong-field nonsequential double ionization

Nonsequential double ionization (NSDI) of atoms driven by parallel-polarized two-color (PPTC) fields composed of two equal-intensity multiple-cycle laser pulses is investigated using a three-dimensional classical ensemble model. The ion momentum distribution shows pronounced asymmetry and strongly depends on the relative phase of the two pulses. The ion momentum distributions exhibit a double- or not yet observed triple-hump structure, depending on the relative phase of the two pulses. More interestingly, the three peaks of the ion momentum distribution correspond to the first-returning recollision, the odd-returning recollision (without the first returning recollision), and the even-returning recollision. This means that the number of electron returnings is mapped onto the ion momentum distribution. The information about the number of electron returnings can be directly retrieved from the observed ion momentum distribution in the PPTC field with equal intensities. Moreover, the proportions of the three types of trajectories in NSDI, the returning energy of the ionized electron, and the ionization mechanism can be well manipulated by changing the relative phase of the two pulses.

Figure 1

The ion momentum distribution along the laser polarization direction vs the relative phase between two pulses. (a) All double-ionization events, (b) FRR double-ionization events, (c) ORR double-ionization events without those FRR events, and (d) ERR double-ionization events.

Figure 2

Correlated (a) and (c)electron momentum distributions and (b) and (d) ion momentum distributions along the laser polarization direction for relative phases of (a) and (b) $0.75\pi$ and (c) and (d) $1.25\pi$. Solid blue curve: all events; dash-dotted black curve: FRR events; dotted purple curve: ORR events without the FRR; and dashed red curve: ERR events. The maximum value in (b) and (d) has been normalized to 1.

Figure 3

The time distributions of (a) and (d) the single ionization, (b) and (e) recollision, and (c) and (f) double ionization for relative phases of $0.75\pi$ (top row) and $1.25\pi$ (bottom row). Black bars: FRR events; purple bars: ORR events without the FRR; and red bars: ERR events. The dashed and solid lines show the laser electric field and negative vector potential in arbitrary units.

Figure 4

The sum of the vector potentials at a single-ionization instant and a double-ionization instant vs the relative phase. (a) FRR events, (b) ORR events without the FRR, and (c) ERR events.

Figure 5

(a) The traveling time vs the relative phase. (b) The proportion of the trajectories with different returning numbers in NSDI vs the relative phase.

Figure 6

The proportion of the RDI mechanism vs the relative phase for (a) all NSDI events, (b) the FRR events, (c) the ORR events without the FRR, and (d) the ERR events.

Figure 7

The distributions of returning energy vs the relative phase for (a) all NSDI events, (b) the FRR events, (c) the ORR events without the FRR, and (d) the ERR events.