Continuous-wave virtual-state lasing without ground state population inversion*

We present a theoretical description of a lasing scheme of cooled and trapped ytterbium atoms in an optical cavity. Here, continuous-wave lasing is achieved on the semi-forbidden intercombination line ${}^1 S_0 \longleftrightarrow {}^3 P_1$, therefore producing coherent light directly from a narrow-linewidth transition.  Lasing is realized by pumping the atoms to the ${}^3 P_1$ state that subsequently can emit a cavity photon by decaying to a virtual state. This process is enhanced by a two-photon transition induced by a second driving field that quasi-resonantly couples the virtual state to the broad-linewidth ${}^1 P_1$ state. We study this system using mean-field equations for the coupled atom-cavity dynamics. With this we determine the lasing threshold and the emission frequencies. The non-linear nature of this device is highlighted by its ability to form bistable lasing and non-lasing states and to show a hysteresis when slowly ramping the pump power above threshold and back. We discuss how our analysis can be extended to calculate the linewidth of the laser and how we could incorporate motional effects to describe lasing, trapping, and cooling.