A four-level double-ladder cold atoms system with spontaneously generated coherence trapped in a moving optical lattice is explored to achieve optical nonreciprocity. When spontaneously generated coherence（SGC） is present, the remarkable contrast optical nonreciprocity of light transmission and reflection can be generated at each induced photonic bandgap in the optical lattice with a velocity of a few m/s. However, when the SGC effect is absent, the optical nonreciprocity becomes weak or even vanishing due to the strong absorption. It is found that the optical nonreciprocity is related to the asymmetric Doppler effect in transmission and reflection, meanwhile the degree and position of optical nonreciprocity can be tuned by the SGC effect and the Rabi frequency of the trigger field.
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.
