Wave packet theory of dynamic absorption spectra in femtosecond pump–probe experiments

Abstract

The large spectral width of ultrashort optical pulses makes it possible to measure the complete time-resolved absorption spectrum of a sample with a single pulse, offering simultaneously high resolution in both the time and frequency domains. To quantitatively interpret these experiments, we start with the usual perturbative density matrix theory for the third-order susceptibility of a multilevel system. However, the theory is formulated in terms of four-time correlation functions which are interpreted as the time-dependent overlap of bra and ket vibrational wave packets propagating independently on the ground and excited electronic state potential surfaces. This approach captures the critical distinction between electronic population decay and pure dephasing processes, while retaining the intuitive physical picture offered by the time-dependent wave packet theories of molecular spectroscopy. A useful simplification is achieved by considering the absorption of the probe pulse as the first-order spectroscopy of the nonstationary state created by the pump pulse. In this case, the dynamic spectrum is obtained through the Fourier transform of the time-dependent overlap of the initial wave packet propagating on its potential surface and a second wave packet, created by the probe pulse, which evolves simultaneously on the final surface. Calculations for model systems using harmonic surfaces and δ-function pulses are presented to illustrate the application of this theory and to clarify the unique spectral behavior of the nonstationary states created in femtosecond pump–probe experiments. Finally, we demonstrate the practical application of the theory for anharmonic surfaces and finite pulses by analyzing the dynamic spectroscopy of the excited state torsional isomerization of the bacteriorhodopsin chromophore.