Resonance fluorescence in $\Lambda$, $V$ and $\Xi$ -- type three-level configurations

We theoretically study the resonance fluorescence spectra of the lambda ($\Lambda$), vee ($V$) and cascade ($\Xi$) type three-level configurations. It is shown that each system with two detuning frequencies can be modelled using the $SU(3)$ symmetry group to derive a generalized optical Bloch equation. For each configuration, this equation is solved to calculate the two-time correlation function by invoking the quantum regression theorem. The incoherent part of the power spectra gives the characteristic multi-peak fluorescence profiles which are different for different configurations. We also discuss how the dressed-state structure of such system can explain the origin of quintuplet profile of the fluorescent spectrum.