Theoretical Investigation of Superradiant Lasing in 2- or 3- Level Atoms in an Optical Lattice

Active optical atomic clocks operating on narrow linewidth clock transitions based on a superradiant lasing are predicted to achieve precision orders of magnitude higher than any currently existing optical atomic clocks. We introduce a general theory of superradiant lasing and implement it for the examples of Ca and Sr atoms. Our simulations coincide well with the experimental results and explain some features of it. The presented model is valid for any two- and three-level system in an optical lattice.