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

Double-lambda microscopic model for entangled light generation by four-wave-mixing