Angle-resolved Rabi flopping in strong-field dissociation of molecules

Rabi flopping is a paradigm of two-level quantum systems in the presence of an oscillatory driving field. Different from atoms, the Rabi flopping in a molecule depends on its bond length and orientation with respect to the light polarization direction. Here we explore the Rabi flopping in the strong-field dissociation of ${\mathrm{H}}_2{}^{+}$ in which the two lowest electronic states are photon coupled. ${\mathrm{H}}_2{}^{+}$ aligned along different angles experiences different laser intensities, building the Rabi flopping with angle-dependent frequencies. During the laser-${\mathrm{H}}_2{}^{+}$ interaction, the electron completes different fractions of Rabi flopping for ${\mathrm{H}}_2{}^{+}$ aligned in different directions, leading to the angular nodes and maxima in the dissociative proton momentum distribution. Our study reveals that one-photon dissociation undergoes the alternation of absorbing and emitting one photon, instead of the one-off photon absorption. This study also provides a universal explanation for the angular distribution of the dissociative fragments in strong laser fields.

Figure 1

Proton momentum distributions calculated by (a) and (b) the full TDSE model and (c) and (d) the two-level model for (a) and (c) laser wavelength 400 nm, intensity $5\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$, and duration of six optical cycles (8 fs) and (b) and (d) laser wavelength 800 nm, intensity $6\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$, and duration of four optical cycles (10.7 fs). The distributions are normalized by their own maxima in each panel.

Figure 2

Time-evolved angular distribution ${\chi }_u(\mathbf{R},t)$, calculated by (a) and (b) the two-level model, (c) and (d) the simpler two-level model by assuming transitions solely happen at $R_r$ without using the rotating-wave approximation, and (e) and (f) the rotating-wave approximation for (a), (c), and (e) laser wavelength 400 nm, intensity $5\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$, and duration 8 fs and (b), (d), and (f) laser wavelength 800 nm, intensity $6\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$, and duration 10.7 fs. The distributions are normalized by their own maxima in each panel.

Figure 3

(a) Proton momentum angular distribution as a function of the laser intensity. (b) Maxima (black solid curves) and minima (red dashed curves) formulated by $I{cos}^2\theta =\mathrm{const}$ detailed in the text. (c) Focal-volume intensity-averaged proton momentum angular distribution as a function of the laser peak intensity. (d) Proton momentum angular distribution driven by uniform laser intensities, extracted from the intensity-integrated data in (a). The laser wavelength is 400 nm and the pulse comprises six optical cycles. The distributions are normalized by their own maxima in (a), (c), and (d).