The effect of the incident relative phase on the four-wave mixing field and the electromagnetically induced transparency

In a Lambda-type system employing a two-photon pump field, a four-wave mixing field can be generated simultaneously and hence a closed-loop system forms. We study theoretically on the effect of the relative phase between the two incident fields on the generated four-wave mixing field and the electromagnetically induced transparency. It is found that the phase of the generated four-wave mixing field is a sum of the incident relative phase and a fixed phase which is irrelative to the incident relative phase. Hence the total phase of the closed-loop system is independent of the incident relative phase. As a result, the incident relative phase has no effect on electromagnetically induced transparency, which is different from the case of a Lambda-type loop system closed by a third incident field.