  Coherent, purely-dispersive three-wave mixing systems in optics and
superconducting microwave circuits can be operated as parametric amplifiers,
generating from a pump wave at one frequency amplified signal and idler waves
at lower frequencies. Here we demonstrate the reciprocal process using a
Josephson amplifier in which coherently imposed signal and idler beams
up-convert to the pump frequency. For signal and idler beams strong enough to
significantly deplete the pump, we show that this reciprocal process ("coherent
cancellation") leads to large, phase-sensitive modulation and even enhancement
of the amplifier gain, in good agreement with theoretical predictions.
