  Motivated by recent experiments, we study four-wave-mixing in an atomic
double-{\Lambda} system driven by a far-detuned pump. Using the
Heisenberg-Langevin formalism, and based on the microscopic properties of the
medium, we calculate the classical and quantum properties of seed and conju-
gate beams beyond the linear amplifier approximation. A continuous variable
approach gives us access to relative-intensity noise spectra that can be
directly compared to experiments. Restricting ourselves to the cold-atom
regime, we predict the generation of quantum-correlated beams with a
relative-intensity noise spectrum well below the standard quantum limit (down
to -6 dB). Moreover entanglement between seed and conjugate beams measured by
an inseparability down to 0.25 is expected. This work opens the way to the
generation of entangled beams by four-wave mixing in a cold atomic sample.
