Enhancement of Vibrational Excitation and Dissociation of ${\mathbf{H}}_2^{\mathbf{+}}$ in Infrared Laser Pulses

We study vibrational excitations, dissociation, and ionization of ${\mathrm{H}}_2^{+}$ in few-cycle laser pulses over a broad wavelength regime. Our results of numerical simulations supported by model calculations show a many orders-of-magnitude enhancement of vibrational excitation and dissociation (over ionization) of the molecular ion at infrared wavelengths. The enhancement occurs without any chirping of the pulse, which was previously applied to take account of the anharmonicity of the molecular vibrations. The effect is related to strong-field two- and higher-order photon transitions between different vibrational states.

Figure 1

Numerical results for the dissociation (black solid line: numerical simulations, blue dashed line: two-level model) and ionization probability (red dash-dotted line) of hydrogen molecular ion interacting with an intense laser pulse as a function of wavelength. Laser parameters: $5\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ and 10 field cycles.

Figure 2

(a) Probability of ionization of the hydrogen molecular ion as a function of internuclear separation $R$ at $5\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ and $N=5$ for three different wavelengths (black solid line: $12\mu \mathrm{m}$, red dashed line: $10\mu \mathrm{m}$, blue dash-dotted line: $5\mu \mathrm{m}$). (b) Ionization probabilities integrated over $R=0–3.5\mathrm{a}.\mathrm{u}.$ (open symbols) and over $R=3.5–30\mathrm{a}.\mathrm{u}.$ (filled symbols) as a function of number of cycles for three different wavelengths (black circles: $12\mu \mathrm{m}$, red squares: $10\mu \mathrm{m}$, blue diamonds: $5\mu \mathrm{m}$) at $5\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$. The dashed line is the prediction for the tunnel ionization probability of an atom having the same ionization energy as the hydrogen molecular ion [24].

Figure 3

(a) Total excitation probability in all vibrational states at the end of the pulse as a function of the laser wavelength. (b) and (c) Excitation probability in individual vibrational levels (black solid line $\nu =1$, red dashed line $\nu =2$, blue dash-dotted line $\nu =3$, green dotted line $\nu =4$), normalized to the total excitation probability. Pulse parameters are the same as in Fig. 1.

Figure 4

Left column: Population in the ground state (black solid line) and all excited (dashed blue line) vibrational states and dissociation probability (red dash-dotted line) as a function of the number of cycles at $12\mu \mathrm{m}$ and $3\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ (upper panel), $5\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ (middle), and $7\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ (lower panel). Right column: Population in the lowest excited vibrational states, normalized to the total excitation probability, in a 3 cycle pulse at $12\mu \mathrm{m}$ and $3\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ (upper panel), $5\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ (middle), and $7\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ (lower panel).