Quantum tomography of molecules using ultrafast electron diffraction

Abstract: We propose a quantum tomography (QT) approach to retrieve the temporally evolving reduced density matrix in elecotronic state basis, where the populations and coherence between 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 ab initio quantum chemical CASSCF method. From 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 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.