Theory of quantum beats in time-resolved multiphoton ionization of molecules

An expression for the probability of time-resolved three-photon ionization via coherently excited resonant states of a molecular system is derived in the perturbative density matrix formalism with the aid of the Liouville space Feynman diagram. It is shown how the time evolution of the molecular coherence in the first resonant state can be detected as a function of the delay time between the pumping and probing lasers through the probing two-photon ionization process. The three-photon ionization process consists of the simultaneous and sequential processes which are classified by the Liouville space Feynman diagrams. The possibility of appearance of quantum beats in the pump-probe three-photon ionization is discussed by performing model calculations of the probability of ionization. The role of the direct and redistributed processes is discussed. The redistributed process is induced by intramolecular processes in the resonant state. The theoretical treatment is applied to the (1 + 2) three-photon ionization of pyrazine observed by Knee et al. It is demonstrated that the fast decay component ( 110 ps) of the pyrazine spectra originates from the intramolecular dephasing of the vibronic coherence created by the pumping pulse laser, and this component appears only when the redistributed process (the ionization process through triplet levels) is absent.