Analytical solutions to the finite-pulse Bloch model for multidimensional coherent spectroscopy

We present perturbative analytical solutions to the optical Bloch equations at third order, with finite duration Gaussian pulse envelopes. We find that a given double-sided Feynman diagram in this approximation can be conveniently described in the frequency domain as a product of the expression in the impulsive limit and a finite-pulse factor. Finite-pulse effects are Feynman-diagram-dependent, however, and include nontrivial phase corrections that can occur even in the case of transform-limited pulses. The results constitute a practical framework for modeling phenomena in multidimensional coherent spectroscopy that cannot easily be captured in the impulsive limit, including the roles of bandwidth, resonance, and pulse chirp.