Theory of quantum jumps in three-state atoms

We apply a general formalism for the separation of rapid and slow time scales in linear evolution equations to three-state atoms with a strong and a weak radiative transition. This leads to an expression for the intensity correlation function that constitutes a good approximation on both time scales. This result can also be translated into an expression for the waiting-time distribution for the next photon emission after a previous one. The slow evolution is expressed in two rate constants, which determine the statistical distribution for dark and bright periods in the fluorescent emission. The result is applied to various configurations of the radiative couplings between the three states.