RESUMO
We propose a quantum tomography (QT) approach to retrieve the temporally evolving reduced density matrix in electronic state basis, where the populations and coherence between the ground state and excited state are reconstructed from the ultrafast electron diffraction signal. In order to showcase the capability of the proposed QT approach, we simulate the nuclear wavepacket dynamics and ultrafast electron diffraction of photoexcited pyrrole molecules using the ab initio quantum chemical CASSCF method. From the simulated time-resolved diffraction data, we retrieve the evolving density matrix in a crude diabatic representation basis and reveal the symmetry of the excited pyrrole wavepacket. Our QT approach opens the route to make a quantum version of "molecular movie" that covers the electronic degree of freedom and equips ultrafast electron diffraction with the power to reveal the coherence between electronic states, relaxation, and dynamics of population transfer.