Ultrafast transient absorption revisited: Phase-flips, spectral fingers, and other dynamical features

Abstract

We rebuild the theory of ultrafast transient-absorption/transmission spectroscopy starting from the optical response of an individual molecule to incident femtosecond pump and probe pulses. The resulting description makes use of pulse propagators and free molecular evolution operators to arrive at compact expressions for the several contributions to a transient-absorption signal. In this alternative description, which is physically equivalent to the conventional response-function formalism, these signal contributions are conveniently expressed as quantum mechanical overlaps between nuclear wave packets that have undergone different sequences of pulse-driven optical transitions and time-evolution on different electronic potential-energy surfaces. Using this setup in application to a simple, multimode model of the light-harvesting chromophores of PC577, we develop wave-packet pictures of certain generic features of ultrafast transient-absorption signals related to the probed-frequency dependence of vibrational quantum beats. These include a Stokes-shifting node at the time-evolving peak emission frequency, antiphasing between vibrational oscillations on opposite sides (i.e., to the red or blue) of this node, and spectral fingering due to vibrational overtones and combinations. Our calculations make a vibrationally abrupt approximation for the incident pump and probe pulses, but properly account for temporal pulse overlap and signal turn-on, rather than neglecting pulse overlap or assuming delta-function excitations, as are sometimes done.