Multiple recollisions in strong-field nonsequential double ionization

With the three-dimensional classical ensemble model, we revisited the recollision dynamics in strong-field nonsequential double ionization (NSDI) by linearly polarized laser pulses. Back analysis of the NSDI trajectories shows that a significant part of the double ionization events undergo a multiple-recollision process. Similar to the previously revealed single recollision induced NSDI, the multiple recollisions induced NSDI also occurs through doubly excited states at low laser intensities. Further, we find that the contribution of multiple recollisions in NSDI decreases with the increasing laser intensity and wavelength.

Figure 1

(a) Correlated longitudinal electron momentum distribution for NSDI of Ar by a 780 nm laser pulse with the intensity of $0.8\times {10}^{14}$ W/${\mathrm{cm}}^2$. (b) Laser electric field phase at the final ionization of one electron vs the other. (c) Correlated longitudinal electron momentum distribution for the NSDI events where there is only one recollision. (d) The same as (c) but for the events experiencing two recollisions.

Figure 2

Left column: Time evolution of the energies of the two electrons for four illustrative NSDI trajectories. There is only one recollision in (a) and (c), and two recollisions in (e) and (g). Right column: The time evolution of the distance between each electron and the ion for the corresponding trajectories shown in the left column. The solid gray lines show the electric field of the laser pulse. The solid arrows indicate the recollisions. In (c), the dashed black and magenta arrows indicates the instant of single ionization and double ionization (see text for details), respectively. The double-headed arrow denotes the traveling time.

Figure 3

(a) Traveling time for the NSDI trajectories where there is only one recollision. (b) Time delay between the double ionization and the last recollision for the single-recollision (red squares) and double-recollision (blue triangles) NSDI events. (c) Time difference between the first recollision and tunneling ionization (circles) and the second recollision and tunneling ionization (squares) for the double-recollision NSDI events. (d) Time difference between the second and the first recollisions for the double-recollision NSDI events.

Figure 4

Energy transfer during the recollisions. (a) The red squares denote the recollision energy for single-recollision NSDI events. The blue triangles indicate the sum of the energy transfer during the two recollisions for the double-recollision NSDI events. (b) Energy transfer during the first (circles) and the second (squares) recollisions for the double-recollision NDSI events.

Figure 5

Correlated longitudinal electron momentum distributions for the (a) single-recollision and (b) double-recollision NSDI events. Here only the events corresponding to the first peak of the time delay distributions in Fig. 3 are included.

Figure 6

(a) Proportion of the double-recollision events in the total NSDI yield as a function of laser intensity at the wavelength of 780 nm. (b) Proportion of the double-recollision events in the total NSDI yield as a function of wavelength at the intensity of $0.8\times {10}^{14}$ W/${\mathrm{cm}}^2$.