Phase-dependent propagation in a two-level system with intermediate states

We study the phase-dependent propagation of a strong, resonant pump and two weak symmetrically detuned fields in a two-level system with population decay through a cascade of intermediate levels. As this system forms a closed loop, the propagation is phase-dependent. For an initial total phase Φ=0, there is constructive interference between the two weak fields, leading to parametric amplification on propagation. When Φ=π, destructive interference occurs, leading to absorption of the weak fields on propagation. When the weak fields are initially equal in intensity, and Φ=0,π, Φ remains constant on propagation. For other initial phases, Φ changes on propagation. Dramatic phase changes from π to 0 can occur when the weak fields are initially unequal in intensity and Φ=π.