Gain without population inversion in a yoked superfluorescence scheme

We consider a medium composed of three-level (cascade scheme of Fig. 1) atoms prepared with coherence between the upper and the ground state (Yoked superfluorescence system). We obtain analytical solutions for seed pulse evolution on the upper and lower transitions for arbitrary level populations and pulse shapes. We find that if the initial coherence is large enough and intermediate level is populated the system can have gain without population inversion. Coherence can also yield gain suppression in the inverted medium. We obtain conditions for the gain in terms of level populations and coherence.