Attosecond imaging of photoinduced dynamics in molecules using time-resolved photoelectron momentum microscopy

We explore the capabilities offered by attosecond extreme ultraviolet and x-ray pulses that can now be generated by free-electron lasers and high-order harmonic generation sources for probing photon-induced electron dynamics in molecules. We theoretically analyze how spatial and temporal dependence of charge migration in a pentacene molecule can be followed by means of time-resolved photoelectron microscopy on the attosecond timescale. Performing the analysis, we accurately take into account that an attosecond probe pulse leads to considerable spectral broadening. We demonstrate that the excited-state dynamics of a neutral pentacene molecule in real space map onto unique features of photoelectron momentum maps.

Figure 1

Energy-level diagram of the first four vertical spin-singlet excited states of pentacene (left), with bright states $S_1$ and $S_2$ in blue and dark states $S_3$ and $S_4$ in red. A wave packet in a coherent superposition of the first two excited states has an oscillation period of $5.73\text{fs}$. The corresponding orbital excitations contribute to the wave function of the states (right), while the arrow means an excitation from the left (HOMO $-$ $i$) to the right (LUMO $+$ $j$) orbital. For the visualization of the orbitals, we used the software luscus [82]

Figure 2

The time evolution of the electron-hole density after the excitation of the pentacene molecule to the first two excited states with the pump pulse at $t_0=0\text{fs}$. The blue isosurface shows the hole density (negative value), and the yellow one shows the electron density (positive value). For the visualization we used the software vesta [86].

Figure 3

Angle-integrated photoelectron spectra for photoelectrons either detached from the ground state $S_0$ or in the coherent superposition of the excited states $S_1$ and $S_2$. The vertical black dashed line shows the contribution at the photoelectron energy ${\epsilon }_e=99\text{eV}$. The probe-pulse duration is $0.5\text{fs}$ and has a central photon energy of $100\text{eV}$.

Figure 4

Time-dependent photoelectron momentum maps for photoelectrons emitted from the excited pentacene at different probe-pulse arrival times $t_p$. The probe-pulse duration is $0.5\text{fs}$, and the central photon energy is $100\text{eV}$. The momentum maps are shown at a photoelectron energy of ${\epsilon }_e=99\text{eV}$.

Figure 5

Time-dependent photoelectron momentum maps for photoelectrons emitted from the excited pentacene for different photoelectron energies ${\epsilon }_e$. Each set of momentum maps has a different probe-pulse arrival time $t_p$. The probe-pulse duration is $0.5\text{fs}$, and the central photon energy is $100\text{eV}$.

Figure 6

Time-dependent photoelectron momentum maps (PMMs) for photoelectrons emitted from the excited pentacene. In each column the PMMs are shown for different probe-pulse arrival times: (a), (e), and (i) $t_p=0T$, (b), (f), and (j) $t_p=T/4$, (c), (g), and (k) $t_p=T/2$, and (d), (h), and (l) $t_p=3T/4$. In the different rows the PMMs are shown for different probe-pulse durations: (a)–(d) ${\tau }_p=0.5\text{fs}$, (e)–(h) ${\tau }_p=T/4$, and (i)–(l) ${\tau }_p=T/2$. The probe pulse has a central photon energy of $100\text{eV}$. The momentum maps are obtained by averaging the signal over the range of ${\epsilon }_e=98.5\text{eV}$ to ${\epsilon }_e=99.5\text{eV}$ to simulate the energy resolution of 1 eV.