Control of Nuclear Dynamics through Conical Intersections and Electronic Coherences

The effect of nuclear dynamics and conical intersections on electronic coherences is investigated employing a two-state, two-mode linear vibronic coupling model. Exact quantum dynamical calculations are performed using the multiconfiguration time-dependent Hartree method. It is found that the presence of a nonadiabatic coupling close to the Franck-Condon point can preserve electronic coherence to some extent. Additionally, the possibility of steering the nuclear wave packets by imprinting a relative phase between the electronic states during the photoionization process is discussed. It is found that the steering of nuclear wave packets is possible given that a coherent electronic wave packet embodying the phase difference passes through a conical intersection. A conical intersection close to the Franck-Condon point is thus a necessary prerequisite for control, providing a clear path towards attochemistry.

Figure 1

Time-dependent electronic purity [see Eq. (4)] of an initially equally weighted superposition of two electronic states in the presence of a C.I. for different values of the nonadiabatic coupling strength $\lambda$ and no relative phase [left, $\phi =0$, see Eq. (2)] and $\phi =\pi /2$ (center). On the right-hand side, cuts through the adiabatic potential energy surfaces at $y=0$ are shown. The ground state is included as well as the initial wave packet. From top to bottom, the C.I. is (i) at the Franck-Condon point, (ii) within, (iii) at the edge of, and (iv) outside the Franck-Condon region.

Figure 2

One-dimensional nuclear density along the coupling coordinate $y$ for different relative phases $\phi$ imprinted on the electronic states and nonadiabatic coupling $\lambda =0.01\mathrm{a}.\mathrm{u}.$ [(i)–(iii)], and stronger nonadiabatic coupling, $\lambda =0.2\mathrm{a}.\mathrm{u}.$ [(iv)], respectively. The C.I. is (i) at the Franck-Condon point, (ii) at the edge of, and (iii)–(iv) outside the Franck-Condon region.

Figure 3

Schematic of the nuclear wave packets on the two adiabatic surfaces (red and blue). The wave packets are created as a coherent superposition of ground-state wave packets on two diabatic surfaces (dashed lines) including an electronic phase difference (shading). Here, the wave packet extends across the C.I., and thus the projection on the upper adiabatic surface (red) embodies the phase difference. This leads to interference when the wave packet moves towards the C.I. The part projected on the lower adiabatic surface (blue) embodies the phase difference as well, but moves away from the C.I. and is not directly relevant for control.