Signatures of a Conical Intersection in Attosecond Transient Absorption Spectroscopy

We characterize attosecond transient absorption spectroscopy (ATAS) in molecules with coupled nuclear and electronic dynamics in the vicinity of a conical intersection between adiabatic potential energy surfaces. With respect to ATAS, the nonadiabatic vibronic coupling strength can be divided into weak, intermediate, and strong, and the characteristics of spectra belonging to each of these domains are discussed. The results can guide the analysis of ATAS experiments in molecules with conical intersections.

Figure 1

Adiabatic PESs (see text) corresponding to the adiabatic $|{\varphi }_2^{(a)}⟩$ (full line) and $|{\varphi }_3^{(a)}⟩$ (dashed line) states for $\kappa =0.0$ (left) and $\kappa =0.1$ (middle) [see Eq. (3)] as a function of $Q_1$ for ${\breve{Q}}_1=5.217$ and $Q_2={\breve{Q}}_2=0$, which makes the figure independent of the interstate coupling $\gamma$. The green (red) arrow indicates the position of the minimum of the PES corresponding to the adiabatic $|{\varphi }_1^{(a)}⟩$ ($|{\varphi }_4^{(a)}⟩$) state. (Right) Illustrates the diabatic electronic states $|{\varphi }_j^{(d)}⟩$ and their couplings [see Eqs. (2) and (3)].

Figure 2

(Bottom) XUV-only absorption spectrum as a function of $\gamma$ [See Eq. (3)]. (Top) The adiabatic potential energy curves as a function of $Q_2$ for ${\breve{Q}}_2=0$ and for $\gamma =0.00$, $\gamma =0.05$, and $\gamma =0.15$, respectively. We use $Q_1={\breve{Q}}_1=5.217$, which makes the figure independent of $\kappa$. Full and dashed lines show the adiabatic PESs of $|{\varphi }_2^{(a)}⟩$ and $|{\varphi }_3^{(a)}⟩$, respectively. The arrows are at $Q_2=0$ and indicate the position of the minimum of the PES for $|{\varphi }_1^{(a)}⟩$. The labels characterize the strength of the VC with respect to ATAS. The four dashed lines in the lower right of the bottom figure show selected adiabatic energies of the strongly VC-modified adiabatic potential.

Figure 3

ATAS spectrum for $\gamma =0.05$ (intermediate region in Fig. 2) for different delays between the XUV and the NIR pulse. A positive delay denotes that the XUV comes before the NIR. The lower part of the figure is concerned with the XUV-only case. The XUV is fired at time zero and the time-dependent populations of the diabatic state $|{\varphi }_2^{(d)}⟩$ (black line) and the adiabatic state $|{\varphi }_2^{(a)}⟩$ (red line) are shown on an axis from $5.0\times {10}^{-7}$ to $1.3\times {10}^{-6}$.

Figure 4

As Fig. 3 but for $\gamma =0.15$ (strong region in Fig. 2) and with a scale for the time-dependent populations in the lower part from $3.0\times {10}^{-7}$ to $1.4\times {10}^{-6}$.

Figure 5

Evolution of the density of the nuclear wave packet in the excited states at the instants indicated in (a)–(f) for $\gamma =0.15$ and the XUV-only case as in the lower panel of Fig. 4. The contours represent the adiabatic PES for the $|{\varphi }_2^{(a)}⟩$ state. The figure shows the oscillation period observed in Fig. 4.