By combining TA and TG measurements, we have described the complex third-order, 2D susceptibility of the 1S resonance of PbSe quantum dots. 
We have demonstrated a parameter extraction procedure that is reproducible for different quantum dot samples, and that some of the parameters, such as the pure dephasing time, are batch dependent. 
Inhomogeneity, exciton-induced broadening, exciton-exciton coulombic coupling shifts, and intraband absorption are all required to reconcile both datasets. 
TA features about 1S exciton band are not exclusively assigned as 1S transitions, which can have important consequences for interpreting the evolution of the 1S bleach.

While the TA spectra show prominent 1S-resonant features, the intraband absorption and its associated refractive index signature are most visible in the TG dataset, so that disentangling the 1S resonant response and the broadband response is a more well-defined problem when both datasets are used together. 
This approach is thus useful for characterization of non-linear signals in spectrally congested systems.
