Two-colour coherent control of nuclear and electron dynamics in photoionization of molecular hydrogen with FEL pulses
The extension of coherent $ω$-$2ω$ control schemes, recently implemented in free-electron lasers (FELs), to molecular systems offers new opportunities to control chemical dynamics on the electronic timescale, potentially allowing for the steering of reactions along previously inaccessible pathways. We have implemented such a scheme at the seeded FERMI FEL to retrieve the relative phases between one-photon (frequency $2ω$) and two-photon (frequency $ω$) ionization paths in the hydrogen molecule as a function of photoelectron energy and emission angle. The narrow bandwidth of the XUV pulses enables selective excitation of vibrational levels of neutral intermediate H$_2$ states in the two-photon ionization path. Here we focus on $ω$--$2ω$ ionization of H$_2(X\,^{1}Σ_g^{+},\,v=0)$ into the H$_2^{+}(X\,^{2}Σ_g^{+},\,v_f)$ ground state involving the H$_2(B\,^{1}Σ_u^{+},\,v'=6)$ intermediate state. The relative phases of the $ω$ and $2ω$ interfering photoionization amplitudes exhibit a strong dependence on photoelectron energy, i.e.\ on the final vibrational state $v_f$ in the H$_2^{+}$ cation. With the help of accurate theoretical calculations, the observed phase jumps are assigned to the coupled electronic and nuclear dynamics at play in the two-photon process, significantly influenced by H$_2(^{1}Σ_g^{+}$ and $^{1}Π_g)$ autoionizing states and the mapping of the H$_2(B\,^{1}Σ_u^{+},\,v'=6)$ intermediate-state nuclear wavefunction into the final vibrational states of H$_2^{+}(X\,^{2}Σ_g^{+})$. The present work establishes the fundamental concepts required to access coupled electron--nuclear dynamics in molecules using $ω$--$2ω$ coherent control schemes currently available at free-electron laser facilities.