Action-detection has expanded the scope and applicability
of 2D
electronic spectroscopy, while posing new challenges for the unambiguous
interpretation of spectral features. In this context, identifying
the origin of cross-peaks at early waiting times is not trivial, and
incoherent mixing is often invoked as an unwanted contribution masking
the nonlinear signal. In this work, we elaborate on the relation between
the nonlinear response and the incoherent mixing contribution by analyzing
the action signal in terms of one- and two-particle observables. Considering
a weakly interacting molecular dimer, we show how cross-peaks at early
waiting times, reflecting exciton–exciton annihilation dynamics,
can be equivalently interpreted as arising from incoherent mixing.
This equivalence, on the one hand, highlights the information content
of spectral features related to incoherent mixing and, on the other
hand, provides an efficient numerical scheme to simulate the action
response of weakly interacting systems.