Probe gain via four-wave mixing based on spontaneously generated coherence

We have studied the probe gain via a double-Λ atomic system with a pair of closely lying lower levels in the presence of two probe and two coherent pump fields. The inversionless gain can be realized by using nondegenerate four-wave mixing under the condition of spontaneously generated coherence(SGC) owing to near-degenerate lower levels. Note that by using SGC, two probe fields can be amplified with more remarkable amplitudes, and the gain spectra of an extremely narrow linewidth can be obtained. Last but not least, our results show that the probe gain is quite sensitive to relative phases due to the SGC presence which allows one to modulate the gain spectra periodically by phase modulation, and can also be influenced by all laser field intensities and frequencies, and the angles between dipole elements.