Laser-induced dissociative ionization of ${\mathrm{H}}_2$ from the near-infrared to the mid-infrared regime

We apply the Monte Carlo wave packet (MCWP) approach to investigate the kinetic energy release (KER) spectra of the protons following double ionization in ${\mathrm{H}}_2$ when interacting with laser pulses with central wavelengths ranging from the near-infrared (IR) (800 nm) to the mid-IR (6400 nm) regions and with durations of 3–21 laser cycles. We uncover the physical origins of the peaks in the nuclear KER spectra and ascribe them to mechanisms such as ionization following a resonant dipole transition, charge-resonance-enhanced ionization, and ionization in the dissociative limit of large internuclear distances. For relatively large pulse durations, i.e., for 15 or more laser cycles at 3200 nm and 10 or more at 6400 nm, it is possible for the nuclear wave packet in ${\mathrm{H}}_2{}^{+}$ to reach very large separations. Ionization of this part of the wave packet results in peaks in the KER spectra with very low energies. These peaks give direct information about the dissociative energy in the $2p{\sigma }_u$ potential energy curve of ${\mathrm{H}}_2{}^{+}$ at the one- and three-photon resonances between the $2p{\sigma }_u$ and $1s{\sigma }_g$ curves in ${\mathrm{H}}_2{}^{+}$. With the MCWP approach, we perform a trajectory analysis of the contributions to the KER peaks and identify the dominant ionization pathways. Finally, we consider a pump-probe scheme by applying two delayed pulses to track the nuclear dynamics in a time-resolved setting. Low-energy peaks appear for large delays and these are used to obtain the $2p{\sigma }_u$ dissociative energy values at the one-photon resonance between the $2p{\sigma }_u$ and $1s{\sigma }_g$ curves in ${\mathrm{H}}_2{}^{+}$ for different wavelengths.

Figure 1

Sketch of four field-free Born-Oppenheimer electronic potential energy curves [39]. These curves are the ${\left(1s{\sigma }_g\right)}^2$ ground-state curve in ${\mathrm{H}}_2$ labeled by $h$, the $1s{\sigma }_g$ and $2p{\sigma }_u$ curves in ${\mathrm{H}}_2{}^{+}$ labeled by $g$ and $u$, respectively, and the $1/R$ Coulombic curve labeled by $c$. A particular realization of a quantum trajectory with the MCWP approach is also shown: At some instant $T_1$, the first ionization occurs and the neutral wave packet is promoted to the singly ionized system where coherent evolution takes place. At some later instant $T_2^j$ ($j=a,b$), the second ionization occurs and then the nuclei undergo Coulomb repulsion. The final energy of the protons depends on the instants $T_1, T_2^j$.

Figure 2

(a)–(d) Renormalized nuclear KER spectra after double ionization of ${\mathrm{H}}_2$ interacting with laser pulses with different wavelengths ranging from 800 to 6400 nm and with different FWHM pulse durations ranging from 3 to 21 laser cycles. All the pulses have a peak intensity of $6\times {10}^{13}\text{W}/{\text{cm}}^2$. (e) Total yields of protons in units of ionization probability per molecule as a function of the number of laser cycles for several wavelengths.

Figure 3

Contributions from different trajectories to the low-energy peak around (a) 1.2 eV in Fig. 2 when interacting with a pulse with 21 laser cycles at 6400 nm, and (b) 1.5 eV in Fig. 2 when interacting with a pulse with 15 laser cycles at 6400 nm. The red dots mark the trajectories that give the largest contributions. The laser pulses are indicted by the grey lines and the parameters are as in Fig. 2.

Figure 4

Sketch of four processes of enhanced ionization at the two CREI positions of $R=7$ and $R=11$ (denoted by the outermost right arrows in the figures) after one- and three-photon resonance transitions. (a) and (b) CREI at $R=7$ and $R=11$ after the three-photon resonance. (c) and (d) CREI at $R=7$ and $R=11$ after the one-photon resonance.

Figure 5

(a) Nuclear KER distributions as a function of time delay between pump and probe pulses. The peak intensity of the pump (probe) pulse is $4\times {10}^{14}\text{W}/{\text{cm}}^2$ ($6\times {10}^{13}\text{W}/{\text{cm}}^2$). The two pulses have the same wavelength (750 nm) and the same duration (3 laser cycles). The data are plotted to the power of 0.2 in order to gain a larger visibility of the structures and after that the signal in the insert was multiplied by a factor of 3. (b) Cuts from (a) before multiplying by a factor 3 at time delays of 60 and 70 fs.

Figure 6

(a) Nuclear KER distributions as a function of time delay between pump and probe pulses. The peak intensity of the pump (probe) pulse is $4\times {10}^{14}\text{W}/{\text{cm}}^2$ ($6\times {10}^{13}\text{W}/{\text{cm}}^2$). Both the wavelengths are 1600 nm and the duration of both pulses is 3 laser cycles. The data are plotted to the power of 0.2 in order to gain a larger visibility of the structures. (b) Cuts from (a) at time delays of 80, 122, and 140 fs.

Figure 7

Contributions from different trajectories to the four peaks (8.5, 9.8, 13, and 1.4 eV) in the KER spectra in Fig. 6 when the delay is 122 fs. The distributions in the small $T_2\sim$ 1000 range result in three high-energy peaks around 8.5, 9.8, and 13 eV while the distributions in the large $T_2\sim$ 6000 range give the low-energy peak around 1.4 eV. The two pulses are also shown by the grey line in the top of the figure. To show the distributions clearly in a single figure, signals for $T_2\sim 6000$ have been multiplied by a factor of 5000.

Figure 8

Nuclear KER distributions as a function of time delay between the pump and probe pulses. The peak intensity of the pump (probe) pulse is $4\times {10}^{14}\text{W}/{\text{cm}}^2$ ($6\times {10}^{13}\text{W}/{\text{cm}}^2$). The pump (probe) wavelength is 800 nm (6400 nm). The duration of both pulses is 3 laser cycles. The data are plotted to the power of 0.2 in order to gain a larger visibility of the structures.

Figure 9

Total KER spectra integrated over all delays and shown as a function of KER energy. The red dashed line is for Fig. 5 and and the black solid line for Fig. 8, respectively.