Tracing the photodissociation probability of ${\mathrm{H}}_2{}^{+}$ in intense fields using chirped laser pulses

The temporal evolution of the dissociation probabilities for various vibrational levels of ${\mathrm{H}}_2{}^{+}$ is observed in terms of shifts in the kinetic energy release dissociation spectra, induced by linearly chirped intense laser pulses. In contrast to previous observations, in which no dependence on the chirp sign was observed, the energy spectrum reported here shows peak shifts, up for negative chirp and down for positive chirp. For some vibrational levels, dissociation takes place early on in the pulse; hence, care must be taken while interpreting the effect of pulse duration in photodissociation studies. This interpretation is supported by numerical solutions of the time-dependent Schrödinger equation.

Figure 1

A schematic of the experimental setup.

Figure 2

Charts showing $\cos \theta$ vs kinetic energy release (KER) spectra of ${\mathrm{H}}_2{}^{+}$ photodissociation by (a) negatively chirped pulse; (b) positively chirped pulse, both with peak intensity ($I_0=2\times {10}^{13}$ W/cm${}^2$); and (c) zero chirp pulse ($I_0=5\times {10}^{12}$ W/cm${}^2$ with about half the bandwidth). All pulse envelopes have the same duration of 120 fs. (d) Projection of the data shown in panel (c) onto the KER axis for $\left|\cos \theta \right|⩾0.9$. The solid line is the KER spectrum, calculated as described in the main text. The dotted vertical lines indicate the expected position of the vibrational-level peaks for 795-nm photons.

Figure 3

(a) Time-dependent laser intensity envelope and (b)–(e) calculated dissociation probability for a few vibrational states of ${\mathrm{H}}_2{}^{+}$ as a function of time, for negative (dashed) and positive (solid) chirp pulse with a peak intensity of $5\times {10}^{12}$ W/cm${}^2$. Note that the dissociation for vibrational levels $v⩾$ 8 becomes saturated about 50–100 fs before the pulse peaks. (f) Calculated KER spectra incorporating intensity averaging over the focal volume and the initial vibrational (but not rotational) distribution of the molecular target.

Figure 4

(a) Kinetic energy release (KER) spectra of ${\mathrm{H}}_2{}^{+}$ for negatively and (b) positively chirped pulses taken at different peak intensities: ($◯$) 2$\times {10}^{13}$, ($\square$) 7$\times {10}^{12}$, ($\times$) 2$\times {10}^{12}$, ($♦$) 1$\times {10}^{12}$, and ($+$) 1$\times {10}^{11}$ W/cm${}^2$. The spectra are generated by summing the signal over all angles. The solid arrows indicate the directional shift in the KER peak position connected with the vibrational level $v=9$. The inset in panel (a) shows the KER spectrum for the lowest peak intensity along with the calculated spectrum (solid line) using perturbation theory (see text).