Imagaing Ultrafast Molecular Dynamics wirh Quantum Tomography

Imaging the electronic and vibrational dynamics of an excited molecule can provide valuable insight into fundamental molecular processes. Experimentally determining the time dependent density matrix, so-called quantum tomography, for the excited molecule can provide the electronic and vibrational probability density in the molecular frame. To use quantum tomography methods developed in the quantum information sciences (QIS) the definition of a measurement operator is required. Here we develop the general form of the measurement operator for time resolved measurements of molecular dynamics in the lab frame. We demonstrate the application of this measurement operator to perform quantum tomography on the electronically excited ammonia molecule, using the Maximal Entropy Approach, previously demonstrated in IBM Q. The resulting density matrix provides the time evolving charge density at any molecular orientation, as well as the time evolving molecular axis distribution. Correlations between these distribution provide direct evidence of rotational-electronic coupling, demonstrating the effect of rotation on charge migration. We discuss the potential extension of these methods to Jahn-Teller active modes of ammonia, which couple to electronic motion. We end by discussing the value of applying a QIS framework, starting with quantum tomography, to develop an understanding of the transition between the quantum and statistical regimes in moleuclar dyanmics.