Quantum and classical dynamics of a diatomic molecule in laser fields with frequency in the region producing maximum dissociation

Abstract

By solving nonperturbatively the equations of Schr\odinger and of Hamilton, we have studied the time-dependent multiphoton dissociation of a diatomic molecule induced by a moderate low-frequency laser field. The photodissociation probabilities are calculated and analyzed as a function of the laser frequency, the intensity, and the pulse shape. A well-established quantum and classical result is that for laser intensities of the order of ${10}^{14}\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}$ the dissociation probability presents a maximum at the frequency ${\ensuremath{\omega}}_{\mathit{max}}\ensuremath{\sim}(0.80--0.90){\ensuremath{\omega}}_{01}$, where ${\ensuremath{\omega}}_{01}$ is the transition frequency from the ground to the first excited vibrational state (redshift phenomenon). In this work, we go further and explore the quantum and classical effects of radiation at the optimum frequency ${\ensuremath{\omega}}_{\mathit{max}}$ on the overall vibrational excitation and dissociation dynamics. First, it is shown that both quantum and classical results predict that ${\ensuremath{\omega}}_{\mathit{max}}$ continues to be the optimum frequency for photodissociation even at the order of $10\phantom{\rule{0.3em}{0ex}}\mathrm{TW}∕{\mathrm{cm}}^{2}$, i.e., low intensities. The quantum results show a multipeak structure versus laser frequency, which is attributed to resonant multiphoton transitions, while the classical results show a smooth curve with a broad maximum at ${\ensuremath{\omega}}_{\mathit{max}}$ which is explained by phase space arguments. Second, it is found that in both quantum and classical approaches ${\ensuremath{\omega}}_{\mathit{max}}$ marks a transition in the effects of turn-on time of the pulse shape on dissociation probability: for $\ensuremath{\omega}l{\ensuremath{\omega}}_{\mathit{max}}$ the gradual turn-on of the field leads to a noticeable reduction of the photodissociation probability, while for $\ensuremath{\omega}g{\ensuremath{\omega}}_{\mathit{max}}$ this effect is of minor importance. A classical interpretation of this finding is given, which is based on stickiness effects in phase space. Finally, the crucial role of ${\ensuremath{\omega}}_{\mathit{max}}$ is further demonstrated in the time dependence of bound-state occupation probabilities. The total survival probability decreases faster with time for $\ensuremath{\omega}l{\ensuremath{\omega}}_{\mathit{max}}$ rather than for $\ensuremath{\omega}g{\ensuremath{\omega}}_{\mathit{max}}$. Further, for $\ensuremath{\omega}g{\ensuremath{\omega}}_{\mathit{max}}$ the bound-state occupation probabilities exhibit multiphoton Rabi-type oscillations where more than two vibrational states are involved. These phenomena are predicted by both quantum and classical dynamics, although there are secondary differences which are revealed and discussed.