Saturation of biphoton generation near atomic resonance

We have numerically investigated the biphoton generation rate as a function of several parameters in the spontaneous four-wave mixing in cold atoms.It has been found that the biphoton generation rate can easily reach saturation with the intensity of the coupling laser increasing.The saturation intensity is mainly dependent on the dephasing rate of the ground states,unrelated to the pumping laser.It implies that though the biphoton waveform can be manipulated by the coupling laser,the generation rate of the biphoton cannot increase markedly after the saturation.The saturation effect also suggests that there is an optimal coupling laser for obtaining the largest biphoton generation rate with a sufficiently long coherence time.