Excitation energy transfer in complex systems often proceeds through series of intermediate states. One of the goals of time-resolved spectroscopy is to identify the spectral signatures of all of them in the acquired experimental data and to characterize the energy transfer scheme between them. It is well known that in the case of transient absorption spectra such decomposition is ambiguous even if many simplifying considerations are taken. In contrast to transient absorption, absorptive 2D spectra intuitively resemble population transfer matrices. Therefore, it seems possible to decompose the 2D spectra unambiguously. Here we show that all necessary information is encoded in the combination of absorptive 2D and linear absorption spectra. We set up a simple model describing a broad class of absorptive 2D spectra and prove analytically that they can be inverted uniquely towards physical parameters fully determining the species-associated spectra of individual constituents together with all connecting intrinsic rate constants. Due to the matrix formulation of the model, it is suitable for fast computer calculation necessary to efficiently perform the inversion numerically by fitting the combination of experimental 2D and absorption spectra. Moreover, the model allows for decomposition of the 2D spectrum into its stimulated emission, ground-state bleach, and excited-state absorption components almost unambiguously. The numerical procedure is illustrated exemplarily.

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