Intense-Laser-Field Ionization of Molecular Hydrogen in the Tunneling Regime and Its Effect on the Vibrational Excitation of ${\mathrm{H}}_2^{+}$

${\mathrm{H}}_2$ molecules were ionized by Ti:sapphire (45 fs, 800 nm) and Nd-doped yttrium aluminum garnet lasers (6 ns, 1064 nm). The relative populations of the vibrational levels of the ${\mathrm{H}}_2^{+}$ ions were determined and found to be concentrated in the lowest vibrational levels. Tunneling ionization calculations with exact field-modified potential curves reproduce the experimental results. The reason for the departure from conventional Franck-Condon-like distributions is the rapid variation of the ionization rate with internuclear distance.

Figure 1

Field-induced modifications to the potential curves and the vibrational levels for parallel alignment. Not drawn to scale.

Figure 2

(a)–(d) Theoretically predicted vibrational excitation of ${\mathrm{H}}_2^{+}$ produced by tunneling ionization of ${\mathrm{H}}_2$ in intense laser fields. Calculations for molecules aligned parallel and perpendicular to the laser $E$ field are presented. The laser intensities are $3.5\times {10}^{13}\mathrm{W}{\mathrm{cm}}^{-2}$ (a), $5.4\times {10}^{13}\mathrm{W}{\mathrm{cm}}^{-2}$ (b), $7.8\times {10}^{13}\mathrm{W}{\mathrm{cm}}^{-2}$ (c), and $1.06\times {10}^{14}\mathrm{W}{\mathrm{cm}}^{-2}$ (d). (e) The vibrational excitation of ${\mathrm{H}}_2^{+}$ produced by electron impact ionization of ${\mathrm{H}}_2$ as measured by von Busch and Dunn [14].

Figure 3

A schematic top view of the experimental setup. The potential curve diagram illustrates the physics of the neutralization and subsequent predissociation processes.

Figure 4

(a) Kinetic energy release spectrum for the case in which ${\mathrm{H}}_2^{+}$ was produced by ionizing ${\mathrm{H}}_2$ with electrons of approximately 100 eV. The spectrum may be compared to the bar diagram of Fig. 2e. (b)–(e) Kinetic energy release spectra showing the vibrational excitation of ${\mathrm{H}}_2^{+}$ ions produced by tunneling ionization in intense laser fields. Spectra (b)–(d) were taken with a 45 fs, 800 nm Ti:sapphire laser. The laser intensities are $3\times {10}^{13}\mathrm{W}{\mathrm{cm}}^{-2}$ (b), $4.8\times {10}^{13}\mathrm{W}{\mathrm{cm}}^{-2}$ (c), and $1.5\times {10}^{14}\mathrm{W}{\mathrm{cm}}^{-2}$ (d). Spectrum (e) was taken with a Nd:YAG (6 ns, 1064 nm) at an intensity of $1\times {10}^{14}\mathrm{W}{\mathrm{cm}}^{-2}$.