Attosecond transient-absorption spectroscopy on aligned molecules

We discuss the characteristics of the dependence of attosecond transient-absorption spectra on the angle between the molecular alignment axis and the polarization of the pump and probe fields. We show how the dipole couplings and therefore the spectra can efficiently be controlled by exploiting the sensitivity of the transition dipoles on this relative orientation. The possibility to tune the dipole coupling by molecular alignment allows a detailed analysis of the complex structures of molecular attosecond transient-absorption spectra.

Figure 1

Potential energy curves of the present model. The ground state curve and bright state curves (dark state curves) are plotted using full (dashed) lines. The shaded areas show the shapes of the norm squared vibrational ground-state wave function of two selected curves. The short-dashed line shows the shape of the vibrational ground-state wave function of the electronic ground state in an excited state curve. The curves are labeled by their electronic wave function ${\psi }_i$ and irreducible representation.

Figure 2

The three color maps show $S(\omega ,\tau ,{\alpha }_0=0,{\beta }_0,{\theta }_L=0)$ of Eq. (1) as a function of the photon energy $\omega$ and the time delay $\tau$ for ${\alpha }_0=0$ and (a) ${\beta }_0=0$, (b) ${\beta }_0=\pi /4$, and (c) ${\beta }_0=\pi /2$. In the narrow boxes on the left of each color map horizontal lines show the vibrational ground-state energies of the excited states ${\psi }_2\left(A_g\right),{\psi }_3\left(B_{3u}\right),{\psi }_4\left(B_{2g}\right),{\psi }_5\left(B_{1u}\right)$ (Fig. 1) with respect to the ground-state energy. Full (dashed) black lines correspond to bright (dark) states. Bright states can be turned into double-dark states (see text) at particular alignment angles and double-dark states are denoted by full gray lines. In the side panels gray arrows show which states are coupled by the NIR field. Field parameters: $T_{\text{XUV}}=430\mathrm{as},T_{\text{NIR}}=10.5\mathrm{fs}$ [see Eq. (10)], ${\lambda }_{\text{XUV}}=78\mathrm{nm},{\lambda }_{\text{NIR}}=760\mathrm{nm},I_{\text{XUV}}=5\times {10}^7{\mathrm{W}/\mathrm{cm}}^2$, (b) $I_{\text{NIR}}=5\times {10}^{12}{\mathrm{W}/\mathrm{cm}}^2$ or [(a), (c)] $I_{\text{NIR}}=2.5\times {10}^{12}{\mathrm{W}/\mathrm{cm}}^2$ and (a) ${\theta }_L=0$.

Figure 3

The three color maps show $S(\omega ,\tau ,{\alpha }_0=0,{\beta }_0=\pi /4,{\theta }_L)$ of Eq. (1) as a function of the photon energy $\omega$ and the time delay $\tau$ for (a) ${\theta }_L=0$, (b) ${\theta }_L=\pi /4$, and (c) ${\theta }_L=-\pi /4$. In the narrow boxes on the left of each color map horizontal lines show the vibrational ground-state energies of the excited states ${\psi }_2\left(A_g\right),{\psi }_3\left(B_{3u}\right),{\psi }_4\left(B_{2g}\right),{\psi }_5\left(B_{1u}\right)$ (Fig. 1) with respect to the ground-state energy. Full (dashed) black lines correspond to bright (dark) states. In the side panels gray arrows show which states are coupled by the NIR field. Field parameters: $T_{\text{XUV}}=430\mathrm{as},T_{\text{NIR}}=10.5\mathrm{fs}$ [see Eq. (10)], ${\lambda }_{\text{XUV}}=78\mathrm{nm},{\lambda }_{\text{NIR}}=760\mathrm{nm},I_{\text{XUV}}=5\times {10}^7{\mathrm{W}/\mathrm{cm}}^2$, and (a) $I_{\text{NIR}}=5\times {10}^{12}{\mathrm{W}/\mathrm{cm}}^2$ or [(b), (c)] $I_{\text{NIR}}=2.5\times {10}^{12}{\mathrm{W}/\mathrm{cm}}^2$.