Electron-rotation coupling in diatomics under strong-field excitation

The photoexcitation and photodissociation of diatomic molecules by intense pulse lasers has been the subject of extensive investigations over the past decades. However, the usually employed theoretical framework neglects the coupling between the molecular rotational angular momentum ($\mathbf{R}$) and the angular momentum of the electrons projected onto the molecular axis $\mathrm{\Omega }=\mathrm{\Lambda }+\mathrm{\Sigma }$, which results in the known $\mathrm{\Lambda }$-doubling phenomenon in high-resolution electronic spectra of diatomic molecules. While neglecting this coupling is an excellent approximation in the weak-field or perturbative regime owing to the large mass difference between the rotating atoms and the electrons, the approximation breaks down for intense laser pulses because of the repeated Rabi cycling of the electronic transitions, which can have a significant effect on the rotational degrees of freedom of the molecule. By correcting the transition dipole matrix elements and introducing angular basis sets based on Wigner D functions, the conventional theoretical treatment is generalized to a universal description valid for both the weak- and strong-field regimes. The theoretical treatment developed here is applied to the $|{}^1\mathrm{\Sigma }\rangle$ to $|{}^1\mathrm{\Pi }\rangle$ transitions in diatomic systems. Our results reveal that, for field intensities resulting in about one Rabi cycling for extreme ultraviolet or x-ray transitions, the theoretical predictions by the conventional theoretical frame need to be corrected when considering observables such as the molecular alignment and the angular distribution of the photofragments.

Figure 1

Schematics of Hund's case-(a) coupling. The same convention as in Zare [47] is used to name the various quantities.

Figure 2

(a) Potential-energy curves for the electronic transitions from the ground state $|{}^1\mathrm{\Sigma }\rangle$ to a bound excited state $|{}^1\mathrm{\Pi }\rangle$. (b) The dynamics of the upper electronic state population simulated by the conventional (“$\mathrm{\Sigma }-\mathrm{\Pi }$”) and full (“${}^1\mathrm{\Sigma }-{}^1\mathrm{\Pi }$”) theoretical treatments with respect to the Rabi frequency ${\mathrm{\Omega }}_{\mathrm{Rabi}}$ are shown by blue and red-dotted curves, respectively. The ratio of the population difference $[({\mathrm{P}}_{{}^1\mathrm{\Sigma }-{}^1\mathrm{\Pi }}-{\mathrm{P}}_{\mathrm{\Sigma }-\mathrm{\Pi }})/{\mathrm{P}}_{{}^1\mathrm{\Sigma }-{}^1\mathrm{\Pi }}]$ between the two treatments is shown in black. (c), (d) Dynamics of time-dependent population and alignment of the upper electronic state for selected cases with ${\mathrm{\Omega }}_{\mathrm{Rabi}}=0.01$, 0.18, and 0.52 eV, respectively.

Figure 3

(a) Potential-energy curves for the electronic transitions from the ground state $|{}^1\mathrm{\Sigma }\rangle$ to a dissociative excited state $|{}^1\mathrm{\Pi }\rangle$ and snapshots of the dissociative nuclear wave packets for ${\mathrm{\Omega }}_{\mathrm{Rabi}}=0.52$ eV at ${\mathrm{t}}_1=10$ and ${\mathrm{t}}_2=25$ fs. (b) The total fragment yield simulated in the conventional (“$\mathrm{\Sigma }-\mathrm{\Pi }$,” blue curve) and improved (“${}^1\mathrm{\Sigma }-{}^1\mathrm{\Pi }$,” red-dotted curve) theoretical treatments with respect to the Rabi frequency ${\mathrm{\Omega }}_{\mathrm{Rabi}}$. The black curve shows the difference between the two models (results of the improved one minus the conventional one). (c), (d) The KER spectra and angular distribution of photofragments of the excited dissociative state for selected cases with ${\mathrm{\Omega }}_{\mathrm{Rabi}}=0.01$, 0.18, and 0.52 eV, respectively.