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.
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