Mean-field Floquet theory for a three-level cold-atom laser

We present a theoretical description for a lasing scheme for atoms with three internal levels in a V configuration and interacting with an optical cavity. The use of a V-level system allows for an efficient closed lasing cycle to be sustained on a dipole-forbidden transition without the need for incoherent repumping. This is made possible by utilizing an additional dipole-allowed transition. We determine the lasing threshold and emission frequency by performing a stability analysis of the nonlasing solution.