  The generation and amplification of photons by parametric down-conversion in
quadratic nonlinear media is used as a source of entangled photons, squeezed
light, and short optical pulses at difficult to access wavelengths. Optical
nonlinearities are inherently weak, and therefore the pump energy required to
produce sufficient gain for efficient down-conversion has been limited to
energies in excess of nanojoules. Here we use dispersion-engineered nonlinear
nanowaveguides driven by femtosecond pulses to demonstrate efficient
down-conversion at the picojoule level; we observe parametric gains in excess
of 70 decibels with pump pulse energies as little as 4 picojoules. When driven
with pulse energies in excess of 10 picojoules these waveguides amplify vacuum
fluctuations to $>$10\% of the pump power, and the generated bandwidth broadens
to span an octave. These results represent a new class of parametric devices
that combine sub-wavelength spatial confinement with femtosecond pulses to
achieve efficient operation with remarkably low energy.
