  The origin of the coherences in two-dimensional spectroscopy of
photosynthetic complexes remains disputed. Recently it has been shown that in
the ultrashort-pulse limit, oscillations in a frequency-integrated pump-probe
signal correspond exclusively to electronic coherences, and thus such
experiments can be used to form a test for electronic vs. vibrational
oscillations in such systems. Here we demonstrate a method for practically
implementing such a test, whereby pump-probe signals are taken at several
different pulse durations and used to extrapolate to the ultrashort-pulse
limit. We present analytic and numerical results determining requirements for
pulse durations and the optimal choice of pulse central frequency, which can be
determined from an absorption spectrum. Our results suggest that for numerous
systems the required experiment could be implemented by many ultrafast
spectroscopy laboratories using pulses of tens of femtoseconds in duration.
Such experiments could resolve the standing debate over the nature of
coherences in photosynthetic complexes.
