Using Time-Resolved Experiments and Coherent Control to Determine the Phase of Transition Dipole Moments between Individual Energy Eigenstates

We develop an imaging method which uses bichromatic coherent control (BCC) in conjunction with time-resolved fluorescence to extract the complex amplitudes of individual transition dipole matrix elements (TDMs) as well as the amplitude of time-evolving wave packets. The method relies on determining the phase relation between the BCC fields, which look to deplete the population of different pairs of excited energy eigenstates, through the computation of a Fourier integral of the time-resolved fluorescence at the beat frequencies of these pairs of states. We illustrate our procedure by determining the amplitudes of the TDM’s linking the vibrational states of the A 1 ∑ u + and those of the X 1 ∑ u + electronic states of Na 2 . Furthermore, we demonstrate its broad applicability by extracting the expansion coefficients of a wave packet in the basis of vibrational energy eigenstates in the strong spin–orbit coupling potentials in RbCs. The approach, which is found to be quite robust against errors can be readily generalized to the imaging of wave packets of polyatomic molecules.