Theory of non-Condon femtosecond quantum beats in electronic transitions of dye molecules

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Recently experiments have been conducted in which the femtosecond oscillations of light absorption by dye molecules were observed. These oscillations were induced when the molecules were excited by femtosecond light pulses. It was shown that the oscillation frequencies correspond well to those of molecular vibrations. For this reason the oscillations observed were explained as the result of quantum beats of vibrational molecular states.1'2 As is already known the quantum beats can occur when several, at least two closely spaced quantum levels are excited simultaneously. Such excitation should be performed by a pulse which is shorter than the period of oscillations corresponding to the energetic distance between two levels. Then interference of the stationary wave functions occurs. If the probabilities of optical transitions from the levels considered to some third level are different the the interference of stationary states leads to the modulation of absorption or emission intensity. The vibrational quantum beats can exist when the coherent superposition of several stationary vibrational states is created. This actually means the oscillation in phase of a number of molecules, which can be observed in the absorption or emission of light. In this paper we should like to draw attention to the essential significance of whether the observation of vibrational quantum beats is carried out with spectral selectivity or without it.