Suppressed Dissociation of ${\mathbf{H}}_2^{+}$ Vibrational States by Reduced Dipole Coupling

The suppression of ${\mathrm{H}}_2^{+}$ strong-field dissociation has intrigued experimentalists and theorists since the early days of laser-molecular science. We unravel a vibrational suppression effect due to weak dipole-matrix element coupling strengths of certain vibrational states, dependent on the laser frequency—a form of Cooper minima. This effect is demonstrated by our full-dimensional calculations on ${\mathrm{H}}_2^{+}$ dissociation and persists for a broad range of laser conditions including both weak and strong-field dissociation. Using a crossed-beams coincidence, three-dimensional momentum-imaging technique, the vibrational suppression effect is clearly observed for ${\mathrm{H}}_2^{+}$ and ${\mathrm{HD}}^{+}$ at 790 and 395 nm, in good agreement with our theory.

Figure 1

(a) ${\mathrm{H}}_2^{+}$ potentials and wave functions, see text. (b) Square of the amplitude of the ${\mathrm{H}}_2^{+}$ dipole-matrix elements ($|D_v(E){|}^2$) as a function of $v$ and KER. Curves shown for 790 and 395 nm are defined by $\mathrm{KER}=E_v+\hslash \omega +13.6\mathrm{eV}$. (c) ${\mathrm{H}}_2^{+}$ dissociation probability density using perturbation theory ($4\times {10}^{10}\mathrm{W}/{\mathrm{cm}}^2$) for 7 and 100 fs, 790 nm pulses, after Franck-Condon averaging.

Figure 2

Calculated kinetic energy release (KER) distributions of ${\mathrm{H}}_2^{+}$ using 45 fs, $4\times {10}^{12}\mathrm{W}/{\mathrm{cm}}^2$ pulses at (a) 790 nm and (b) 395 nm. Vibrational-comb ticks for one-photon dissociation are shown along the top of the panels. The corresponding dissociation probabilities $P_D$ are shown in (c) 790 nm and (d) 395 nm (solid points), as well as normalized perturbation results (dashed lines).

Figure 3

Experimental kinetic energy release (KER) distributions of ${\mathrm{H}}_2^{+}$ using 40 fs, $3\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ pulses at (a) 790 nm and (b) 395 nm. Vibrational-comb ticks for one-photon dissociation are shown along the top of the panels. Error bars denote the statistical uncertainty. The corresponding relative dissociation probabilities $P_D$ are shown in (c) 790 nm and (d) 395 nm. Error bars are a sampling estimate of the uncertainty from the fitting procedure.

Figure 4

Same as Figs. 3a, 3c for ${\mathrm{HD}}^{+}$ dissociation into $\mathrm{H}+{\mathrm{D}}^{+}$ (the ${\mathrm{H}}^{+}+\mathrm{D}$ channel is similar). The dashed line in (b) is a normalized perturbation calculation.