## 2 Laser Control of Ring Currents in a Molecule Having a Single Aromatic Ring
### Beyond the Frozen-Nuclei Approximation: Nonadiabatically Coupled Vibronic Dynamics
#### 2.3.4 Laser Control of Wave Packet Interference
The effects of WP interference are therefore reversed from those for \(\mathbf{e}^{(-)}\): For DCP, the interference is destructive on the lower PES but constructive on the higher one around \(t\sim 5\)-10 fs. The amount of the WP created by the nonadiabatic transition from \(|X\rangle\) to \(|Y\rangle\), which interferes with \(\psi_{Y}(\mathbf{Q},t)\), is smaller than that for the transition from \(|Y\rangle\) to \(|X\rangle\), which interferes with \(\psi_{X}(\mathbf{Q},t)\); this is the reason why the resultant upward population transfer is small in Figure 4a. The WPs on the two PESs then reach the avoided crossing and the reverse population transfer occurs around \(t\sim 10\)-14 fs. The interference enhances low vibrational states in \(\psi_{X}(\mathbf{Q},t)\). In the cases of circular polarizations, \(\psi_{X}(\mathbf{Q},t)\) and \(\psi_{Y}(\mathbf{Q},t)\) are initially neither in phase nor out of phase because \(\theta=\pm(\eta_{Y}-\eta_{X})\) for \(\mathbf{e}_{\pm 1}\); for DCP, \(\theta=\pm 0.35\pi\). Hence, no fully constructive or destructive interference takes place on either PES at \(t\sim 5\)-10 fs, resulting in the vibrational amplitudes in Figure 6b, which are intermediate between those for \(\mathbf{e}^{(+)}\) and \(\mathbf{e}^{(-)}\) in Figure 6a. As the relative quantum phase of  
Figure 8: Propagation of the adiabatic WPs on the two-dimensional potential energy surfaces (PESs) of \(|X\rangle\) and \(|Y\rangle\) for **(a)**\(\mathbf{e}^{(+)}\), **(b)**\(\mathbf{e}^{(-)}\), **(c)**\(\mathbf{e}_{+1}\), and **(d)**\(\mathbf{e}_{-1}\). The origin of the PESs is the optimized geometry of \(|G\rangle\) and the avoided crossing is designated by a circle. The bold contours represent the probability densities \(|\psi_{X}(\mathbf{Q},t)|^{2}\) and \(|\psi_{Y}(\mathbf{Q},t)|^{2}\). The arrows indicate the motion of the center of the WPs. Modified from [56] with permission of the American Chemical Society. DCP evolves in the negative direction, for \(\mathbf{e}_{-1}\) (\(\theta=-\)\(0.35\pi\)), it takes more time than for \(\mathbf{e}^{(-)}\) (\(\theta=\pi\)) but less time than for \(\mathbf{e}^{(+)}\) (\(\theta=0\)) to experience constructive and destructive interferences on the lower and higher PESs, respectively. As a consequence, the downward population transfer for \(\mathbf{e}_{-1}\) appears at \(t\sim\) 8-13 fs in Figure 4d. For \(\mathbf{e}_{+1}\) (\(\theta=0.35\pi\)), the WPs pass through the avoided crossing before the requirement of interference for population transfer is met; the nonadiabatic transition is therefore not completed until they come closer again to the avoided crossing at \(t\sim\) 30 fs as in Figure 4c. The present results indicate that the initial relative phase \(\theta\) governs not only ring currents but also the subsequent molecular vibration through nonadiabatic couplings. Furthermore, it is possible to control the time-dependent phase due to irradiation, i.e., \(\theta(t)\) by adjusting the other laser parameters such as the peak field strength \(E^{0}\) and pulse duration \(t_{f}\). This suggests that a superposition of the quasi-degenerate states with an arbitrary relative phase can be created by applying a laser pulse of arbitrary polarization. The interference between nuclear WPs in nonadiabatic transition can be controlled as desired by attosecond/several-femtosecond laser pulses, leading to sophisticated control of molecular vibrations.