  In recent years, action-detected ultrafast spectroscopies have gained
popularity. These approaches offer some advantages over their
coherently-detected counterparts, enabling spatially-resolved and operando
measurements with high sensitivity. However, there are also fundamental
limitations connected to the different process of signal generation in
action-detected experiments. Specifically, state mixing by nonlinear
interactions during signal emission leads to a large static background which
can obscure the excited-state dynamics. This could severely limit the
applicability of action-detected spectroscopy to study energy transfer in
larger systems. Here we perform fluorescence-detected two-dimensional
electronic spectroscopy (F-2DES) of the light-harvesting II (LH2) complex from
purple bacteria. We demonstrate that the B800-B850 energy transfer process in
LH2 is barely discernable in F-2DES, representing a ~6.2% rise of the lower
cross-peak intensity. This is in stark contrast to measurements using
coherently-detected 2DES where the lower cross-peak reveals energy transfer
with 100% contrast. We explain the weak presence of excited-state dynamics
using a disordered excitonic model with realistic experimental conditions. We
further derive a general formula for the presence of excited-state signals in
multi-chromophoric aggregates, dependent on the aggregate geometry and size,
and the interplay of excitonic coupling and disorder. We find that, dependent
on the excitonic state structure, the excited state dynamics in F-2DES can be
visible even in large aggregates. Our work shows that the signatures of energy
transfer in F-2DES can be used to directly infer the excitonic structure in
multichromophoric systems.
