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Is it possible to infer the time evolving quantum state of amultichromophoric system from a sequence of two-dimensional electronic spectra(2D-ES) as a function of waiting time? Here we provide a positive answer for atractable model system: a coupled dimer. After exhaustively enumerating theLiouville pathways associated to each peak in the 2D-ES, we argue that byjudiciously combining the information from a series of experiments varying thepolarization and frequency components of the pulses, detailed information atthe amplitude level about the input and output quantum states at the waitingtime can be obtained. This possibility yields a quantum process tomography(QPT) of the single-exciton manifold, which completely characterizes the openquantum system dynamics through the reconstruction of the process matrix. Thisis the first of a series of two articles. In this manuscript, we specialize ourresults to the case of a homodimer, where we prove that signals stemming fromcoherence to population transfer and viceversa vanish upon isotropic averaging,and therefore, only a partial QPT is possible in this case. However, this factsimplifies the spectra, and it follows that only two polarization controlledexperiments (and no pulse-shaping requirements) suffice to yield the elementsof the process matrix which survive under isotropic averaging. The anglebetween the two site transition dipole moments is self-consistently obtainedfrom the 2D-ES. Model calculations are presented, as well as an error analysisin terms of the angle between the dipoles and peak overlap. In the secondarticle accompanying this study, we numerically exemplify the theory forheterodimers and carry out a detailed error analysis for such case. Thisinvestigation provides an important benchmark for more complex proposals ofquantum process tomography (QPT) via multidimensional spectroscopicexperiments.

Quantum process tomography of molecular dimers from two-dimensional electronic spectroscopy I: General theory and application to homodimers