Lasing without inversion in a closed four-level system

We show lasing without population inversion in a closed four-level atomic system which is no longer incoherently pumped on the transition at which lasing occurs. The four-level system can overcome some limits in the typical lambda-type and V-type three-level systems, furthermore it is possible to achieve lasing even in the absence of the inversion condition for the thermal radiation fields or of the inversion of spontaneous decay rate. We find that when the detuning of probe field is equal to that of coherent coupling field, there is a peak value along with the increase of the detuning. To explain it, we bring forward that there are adiabatic and nonadiabatic stimulated Raman processes when a three-level atomic system is interacted with two coherent fields, so there are two mechanisms influencing the change of probe field. We believe that it can explain more general lasing without inversion processes because of quantum interference induced by coherent fields.