Using coherent control to extract the phases of electronic transition-dipole matrices: the LiRb case

Abstract

We show that “bichromatic coherent control” (BCC) enables the determination of the amplitudes (= magnitudes + phases) of individual transition-dipole matrix elements (TDMs) and the amplitude of time-evolving wave packets from time-resolved fluorescence data. In the present use of BCC, one induces quantum interferences using two external laser fields to coherently deplete the population of different pairs of excited energy eigenstates. The BCC-induced depletion is supplemented by the computation of the Fourier integral of the time-resolved fluorescence at the beat frequencies of the two states involved. The combination of BCC and Fourier transform enables the determination of both the expansion coefficients of the wave packet in a basis of vibrational energy eigenstates and the amplitudes of the [Formula: see text] electronic TDMs linking the excited and ground rovibrational states. We illustrate our method by determining the amplitudes of the TDMs linking the vibrational states of the [Formula: see text] spin orbit coupled potentials to both the singlet [Formula: see text] and the triplet [Formula: see text] electronic ground states in LiRb. The approach, which is found to be quite robust against errors in the BCC procedure and experimental data, can be readily generalized to the imaging of wave packets of polyatomic molecules.