  Techniques for coherent multidimensional optical spectroscopy have been
developed and utilised to understand many different processes, including energy
transfer in photosynthesis and many-body effects in semiconductor
nanostructures. Double-quantum 2D spectroscopy is one variation that has been
particularly useful for understanding many-body effects. In condensed matter
systems, however, there are often many competing signal pathways, which can
make it difficult to isolate different contributions and retrieve quantitative
information. Here, a means of separating overlapping pathways while maintaining
the fidelity of the relevant peak/s is demonstrated. This selective approach is
used to isolate the double-quantum signal from a mixed two exciton state in a
semiconductor quantum well. The removal of overlapping peaks allows analysis of
the relevant peak-shape and thus details of interactions with the environment
and other carriers to be revealed. An alternative pulse ordering identifies a
double-quantum state associated only with GaAs defects, the signature of which
has previously been confused with other interaction induced effects. The
experimental approach described here provides access to otherwise hidden
details of excitonic interactions and demonstrates that the manner in which the
double-quantum coherence is generated can be important and provide an
additional control to help understand the many-body physics in complex systems.
