Autoresonant excitation and control of molecular degrees of freedom in three dimensions

A classical, three-dimensional analysis of excitation and control of vibrational-rotational degrees of freedom of a polar diatomic molecule by chirped laser field is presented. The control strategy is based on autoresonance (adiabatic nonlinear synchronization) phenomenon, in which the molecule automatically adjusts its state for staying in a persistent resonance with the laser field despite variation of the laser frequency. Thresholds on driving field amplitudes for entering the autoresonant excitation regime by passage through different resonances are calculated. In autoresonance, the molecule can be excited to large energies and approach the dissociation limit by substantially weaker laser fields than with constant-frequency drives.

Figure 1

Geometry of the classical 3D motion of the reduced mass $\mu$. The $z$ axis represents the direction of polarization of the laser field, $\mathbf{L}$ is the total angular momentum, $i$, $\varphi$, and $\psi$ are the conventional Euler angles ($OA$ is the line of nodes), while $r$, $\phi$, and $\theta$ are spherical coordinates of the mass. The unperturbed motion of the mass is in the plane perpendicular to $\mathbf{L}$

Figure 2

Autoresonant evolution. (a) Normalized energy $\overline{E}$, (b) angular momentum ${\overline{I}}_2$, and (c) inclination $i$ versus normalized time $\tau$. The dashed and solid lines correspond to driving amplitudes just below and above the threshold for synchronization, respectively.

Figure 3

The phase locking and radial evolution. (a) Phase mismatch $\Phi$ versus normalized time $\tau$ above (solid line) and below (dashed line) the threshold. (b) Normalized radius $\overline{r}$ versus time [above threshold (black), below threshold (gray)].

Figure 4

The normalized threshold amplitude ${\overline{a}}_{+}^{\mathit{th}}$ as a function of initial rotational action ${\overline{I}}_2\left(0\right)$ for different values of initial normalized radius ${\overline{r}}_0$ in the case of $\omega \left(t\right)\simeq {\Omega }_2-{\Omega }_3$ resonance. Gray triangles, black squares, black circles, and black triangles show the simulation results, while solid lines represent theoretical predictions. Also shown is the ${\overline{a}}_{-}^{\mathit{th}}$ threshold in the case of $\omega \left(t\right)\simeq {\Omega }_2+{\Omega }_3$ resonance at $r_0=3.6$ in simulations (gray diamonds) and theory (solid line).

Figure 5

The normalized energy $\overline{E}$, angular momentum ${\overline{I}}_2$, ${\overline{J}}_{+}$ [(c), upper trace] and ${\overline{J}}_{-}$ [(c), lower trace] versus normalized time $\tau$ in the case of $\omega \left(t\right)\simeq {\Omega }_2+{\Omega }_3$ autoresonance.

Figure 6

The normalized energy $\overline{E}$, angular momentum ${\overline{I}}_2$, ${\overline{J}}_{+}$ [(c), upper trace] and ${\overline{J}}_{-}$ [(c), lower trace] versus normalized time $\tau$ in the case of $\omega \left(t\right)\simeq {\Omega }_2-{\Omega }_3$ autoresonance.