SU(4) based classification of four-level systems and their semiclassical solution

We present a systematic method to classify the four-level system using $SU(4)$ symmetry as the basis group. It is shown that this symmetry allows three dipole transitions which eventually leads to six possible configurations of the four-level system. Using a dressed atom approach, the semi-classical version of each configuration is exactly solved under rotating wave approximation and the symmetry of the Rabi oscillation among various models is studied and its implication is discussed.