We demonstrate the use of multiresonant coherent multidimensional spectroscopy (CMDS) for obtaining 2D spectra of the diagonal and cross-peaks of the 1S and 1P excitons and biexcitons in PbSe quantum dots and their coherent and incoherent dynamics. We show that multiresonant CMDS line narrows the inhomogeneous broadening and resolves the excitonic peaks from the background that often obscures peaks. We develop theoretical methods that extract details of the homogeneous and inhomogeneous broadening, the Coulombic coupling within the biexciton, and the relative exciton and biexciton transition moments. The population dynamics are measured by scanning the excitation pulse time delays over all time orderings. Phase modulations of individual coherences are observed because of heterodyning between scattered light and the four-wave mixing signal. The experiments demonstrate that CMDS can be used to obtain quantum state resolved dynamics of the electronic states in complex nanostructures and other important materials.
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