Subharmonic pumping of a Josephson-parametric amplifier and the pitchfork instability

We report the observation of substantial amplification due to multiwave (more than four) mixing in a Josephson-parametric amplifier. Amplification was achieved with subharmonic pumping at 2/3, 2/5, and 2/7 of the signal frequency near 19 GHz. The processes reponsible for the amplification were, correspondingly, five-, seven-, and nine-wave mixing. For the case of five-wave mixing we have observed amplification in excess of 35 dB and noise referred to input of a few degrees kelvin before the amplifier undergoes a pitchfork instability. The noise rise at the pitchfork bifurcation was also studied and compared with theory.