Two years ago Seth Olsen and I published a paper, pointing out that in the Green Fluorescent Protein there should be a dark excited state [i.e. a state which does not contribute significantly to the one-photon absorption cross section] which should have a large two photon absorption (TPA) cross section. This has a natural explanation in terms of a valence bond description of the three lowest lying singlet states of the chromophore.
We were very pleased that last year there was a long article in Nature methods, Two-photon absorption properties of fluorescent proteins, by Drobizhev et al.. It contains the data below. The peak on the left (around 650 nm) is due to TPA from the dark excited state.
latest paper on vibronic effects in two-photon absorption.