We observe 30% two-photon optical amplification of a probe laser-held
propagating through a laser-pumped potassium vapor. This amplification
is spectrally isolated and substantially larger than that of previous
ly reported continuous-wave two-photon amplifiers. The combination of
large amplification and spectral isolation of the two-photon gain feat
ure will greatly facilitate precise studies of the photon statistics o
f this highly nonlinear quantum amplifier and the development and char
acterization of a two-photon laser based on this gain medium. We also
observe spectrally-distinct three-photon amplification (similar to 5%)
in the same system under different experimental conditions. We presen
t a simple model of the interaction that gives qualitative agreement w
ith our observations and explains the dependence of the two-photon gai
n on the various system parameters. This model predicts that the size
of the two-photon gain is quite sensitive to an interference between t
wo different quantum pathways.