Time-resolved sequential double ionization of ${\mathrm{D}}_2$ molecules in an intense few-cycle laser pulse

The kinetic energy spectra of ${\mathrm{D}}^{+}$ ions resulting from the sequential double ionization of ${\mathrm{D}}_2$ molecules in an intense few-cycle laser field are calculated. The ${\mathrm{D}}_2$ molecule is first ionized at its equilibrium distance, followed by further ionization of $\mathrm{D}_2{}^{+}$ at larger internuclear separations. The time evolution of the nuclear wave packet is calculated including loss from ionization by the time-dependent laser field. The calculated ${\mathrm{D}}^{+}$ energy spectra are compared with the recent experiment, and the time duration between the two ionization events is deduced to subfemtosecond accuracy.

Figure 1

Static ionization rates of $\mathrm{D}_2{}^{+}$ as a function of internuclear separation at two field strengths. The thick lines are from the complex-scaling calculations and the thin lines are from the MO-ADK model. The electric field is parallel to the molecular axis.

Figure 2

The time profile of the field strength of a laser pulse of peak intensity $2.8\times {10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$ and pulse length $8.6\mathrm{fs}$, with center wavelength at $800\mathrm{nm}$. The single ionization probability of ${\mathrm{D}}_2$ in this laser field as a function of time is also displayed.

Figure 3

${\mathrm{D}}^{+}$ pair energy spectra due to the sequential double ionization obtained from the present calculation at three intensities. The experimental data are from Ref. 1 with a peak intensity of 2.8 $I_0$ where $I_0={10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$. The pulse duration is $8.6\mathrm{fs}$.

Figure 4

(Color online) Second ionization probability of $\mathrm{D}_2{}^{+}$ as a function of internuclear separation and the time following the first ionization. The laser pulse is linearly polarized, with peak intensity $2.8\times {10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$ and pulse length $8.6\mathrm{fs}$.

Figure 5

(Color online) Second ionization probability distribution of $\mathrm{D}_2{}^{+}$ vs time and $R$ following the first ionization of ${\mathrm{D}}_2$. The lasers are linearly polarized, with peak intensities of $2.8\times {10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$ and pulse durations of 5 and $12\mathrm{fs}$, respectively.

Figure 6

First ionization probability of ${\mathrm{D}}_2$ by circularly polarized laser pulses. The peak intensities are 1.2 and 2.8 $I_0$, respectively, where $I_0={10}^{15}\mathrm{W}{\mathrm{cm}}^2$. The pulse length is $10.5\mathrm{fs}$.

Figure 7

${\mathrm{D}}^{+}$ energy spectra due to the sequential double ionization of ${\mathrm{D}}_2$ by a circularly polarized laser pulse. The experimental data are from Ref. 1. The peak intensity of the circulary polarized laser are 1.2 and 2.8 $I_0$ where $I_0={10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$. The pulse length is $10.5\mathrm{fs}$.

Figure 8

(Color online) Second ionization probability distribution of $\mathrm{D}_2{}^{+}$ vs time and $R$ following the first ionization of ${\mathrm{D}}_2$. The lasers are circularly polarized, with peak intensities of $2.8\times {10}^{15}$ and $1.2\times {10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$, respectively, and the pulse length is $10.5\mathrm{fs}$.