Dynamic algebraic approach to the system of a three-level atom in the Λ configuration
Jing‐Bo Xu, Xu‐Bo Zou · Physical Review A · 1999
The system of a three-level atom coupled to two quantized field modes with arbitrary detuning and density-dependent multiphoton interaction is studied by a dynamical algebraic method. We find an alternative su(3) dynamical algebraic structure within the system. Based on this su(3) structure, we diagonalize the Hamiltonian by making use of unitary transformations and obtain the eigenvalues, eigenstates, and time evolution operator for the system. The effective two-level Hamiltonian is also derived by unitary transformation. Finally the system governed by the Milburn equation is discussed and the exact solution of the Milburn equation presented.