Hidden harmonic quantum states in proteins: Did Davydov get the sign wrong?

We revisit mid-IR pump-probe experiments at the FELIX picosecond Free Electron Laser which probed the vibrational dynamics of the α-helix rich protein in search of long-lived anharmonic trapped vibrational states (solitons). We analyze and try to understand something puzzling that we observed in the context of unusual 'hidden' quantum phenomena in proteins which probably are of no biological consequences, but bears re-examination. We observed in a narrow (0.5 cm^-1) spectral range of the amide-I band a very large response in terms of degenerate 4-wave mixing scattering. We propose that this narrow but strong scattering signal is not due to anharmonic trapping but rather is the imaginary (index of refraction) component of a super-linear response of the amide I band to high levels of vibrational excitation.