  We show that optical tachyonic dispersion corresponding to superluminal
(faster than-light) group velocities characterizes parametrically amplifying
media. The turn-on of parametric amplification in finite media, followed by
illumination by spectrally narrow probe wavepackets, can give rise to transient
tachyonic wavepackets. In the stable (sub-threshold) operating regime of an
optical phase conjugator it is possible to transmit probe pulses with a
superluminally advanced peak, whereas conjugate reflection is always
subluminal. In the unstable (above-threshold) regime, superluminal response
occurs both in reflection and in transmission, at times preceding the onset of
exponential growth due to the instability. Remarkably, the quantum information
transmitted by probe or conjugate pulses, albeit causal, is confined to times
corresponding to superluminal velocities. These phenomena are explicitly
analyzed for four-wave mixing, stimulated Raman scattering and parametric
downconversion.
