Importance of one- and two-photon transitions in the strong-field dissociation of ${\mathrm{NO}}^{2+}$

Employing a coincidence three-dimensional momentum imaging technique, we investigate the ultrafast, intense laser-induced dissociation of a metastable ${\mathrm{NO}}^{2+}$ ion beam into ${\mathrm{N}}^{+}+{\mathrm{O}}^{+}$. Based on the kinetic energy release and angular distributions, measured using both 774-nm and second-order-harmonic 387-nm pulses, we show that the main processes driving dissociation in pulses of about ${10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ peak intensity are one- and two-photon transitions from the $X{}^2\mathrm{\Sigma }^{+}$ ground state to the $A{}^2\mathrm{\Pi }$ first-excited state. First-order perturbation theory calculations also corroborate these findings.

Figure 1

(a) Lowest lying doublet potential energy curves of ${\mathrm{NO}}^{2+}$. Zero energy is defined as $v^{\prime }=0$ of the $X{}^2\mathrm{\Sigma }^{+}$ state. The $B$ ${}^2\mathrm{\Sigma }^{+}$ state dissociation limit is –0.55 eV, and that of the $X{}^2\mathrm{\Sigma }^{+}$ and $A{}^2\mathrm{\Pi }$ states is –3.87 eV. These limits are from the same structure calculations [77]. The inset shows the $X{}^2\mathrm{\Sigma }^{+}$–$A{}^2\mathrm{\Pi }$ transition dipole moment [77]. (b) Franck-Condon (FC) population at the interaction point for the $X{}^2\mathrm{\Sigma }^{+}$ state of ${\mathrm{NO}}^{2+}$ resulting from $\mathrm{NO}\to {\mathrm{NO}}^{2+}$ vertical ionization by fast electron impact in the ion source (see text). This distribution only includes vibrational levels that survive to the laser interaction.

Figure 2

The ionization and dissociation rates of ${\mathrm{NO}}^{2+}$ by a 27-fs, 774-nm pulse as a function of peak intensity $I_0$. (a) The yields of dissociation (${\mathrm{N}}^{+}+{\mathrm{O}}^{+}$) and ionization (${\mathrm{N}}^{2+}+{\mathrm{O}}^{+}$ and ${\mathrm{N}}^{+}+{\mathrm{O}}^{2+}$) normalized to the same focal volume as the highest intensity, assuming stable beam current, laser pulses, and beam crossing throughout these consecutive measurements. The main sources of errors are instabilities in these quantities. (b) The ionization-to-dissociation ratio. Note that ionization is of the order of 1% or less for intensities below $5\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 3

[(a), (b)] The yield of ${\mathrm{N}}^{+}+{\mathrm{O}}^{+}$ as a function of KER and $\cos \theta$ for 774-nm pulses with peak intensities $4\times {10}^{14}$ and $1\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, respectively. Recall that $\theta$ is the angle between the ${\mathrm{N}}^{+}$ momentum and the laser polarization. [(c), (d)] 1D KER projections of panels (a) and (b), respectively. In panel (c), the purple and red combs indicate expected KER values for one- and two-photon $X{}^2\mathrm{\Sigma }^{+}\to A{}^2\mathrm{\Pi }$ transitions, respectively. The numbers above the combs indicate the initial vibrational level $v^{\prime }$ of the $X{}^2\mathrm{\Sigma }^{+}$ state for these transitions.

Figure 4

Measured angular distributions of narrow KER ranges (indicated on each panel) for (a) 774 nm, $1\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, (b) 774 nm, $4\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, and (c) 387 nm, $1\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. The data in each panel are fitted with the indicated angular distribution (see text).

Figure 5

(a) The KER spectra computed using first-order perturbation theory. Here, “cont.” indicates transitions to the vibrational continuum of the $A{}^2\mathrm{\Pi }$ state. Note that there are two sharp peaks due to resonances at around 6.6-eV KER, one for $v^{\prime }=4\to v^{″}=8$ (blue, which also includes a weaker and broader feature at lower energy) and another for $v^{\prime }=5\to v^{″}=8$ (red). (b) Comparison of the computed and experimental KER spectra for 774-nm and peak intensity of $4\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. The navy blue dash-dotted curve shows the calculated dissociation probability convoluted with the experimental resolution (see text), summed over all transitions, and scaled to match the measured peak at around 6.5 eV.

Figure 6

The KER spectra for 774-nm (peak intensity $4\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$) and 387-nm (peak intensity $1\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$) central wavelength pulses. The dashed blue line corresponds to the 387-nm results scaled to match the amplitude of the higher KER peak in the 774-nm spectrum. The gray line represents the first-order perturbation theory result at 387 nm, convoluted with the KER resolution and scaled to the 774-nm data.