An algebraic approach to the interaction of a three-level atom interactingwith quantized radiation field

The system of a three-level atom in the Xi configuration coupled to two qua ntized field modes with arbitrary detuning and density-dependent multiphoto n interaction is studied by dynamical algebraic method. With the help of an su(3) algebraic structure, we diagonalize the Hamiltonian by making use of unitary transformations and obtain the eigenvalues, eigenstates and time e volution operator for the system. Based on this su(3) structure, we also sh ow that the system of a three-level atom in the Xi configuration can be exa ctly transformed to an effective two-level Hamiltonian by an unitary transf ormation. Finally, we show that there exist an su(N) algebraic structure in the system of a N-level atom interacting with N-1 field modes.