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We perform coherent nonlinear spectroscopy of excitons in single-layers ofMoSe$_2$ and WSe$_2$ encapsulated between thin films of hexagonal boronnitride. Employing four-wave mixing microscopy we identify virtually disorderfree areas, generating exciton optical response at the homogeneous limit.Focussing on such areas, we measure exciton homogeneous broadening as afunction of environmental factors, namely temperature and exciton density.Exploiting FWM imaging, we find that at such locations, nonlinear absorption ofthe exciton excited states and their coherent couplings can be observed. Usingthe WSe$_2$ heterostructure, we infer coherence and density dynamics of theexciton 2S state. Owing to its increased radiative lifetime, at lowtemperatures, the dephasing of the 2S state is longer than of the 1Stransition. While scanning various heterostructures across tens of micrometers,we conclude that the disorder, principally induced by strain variations, remainto be present creating spatially varying inhomogeneous broadening.

Coherent dynamics and mapping of excitons in single-layer MoSe$_2$ and WSe$_2$ at the homogeneous limit