Consider states | 1 ⟩ ⟩ , | 2 ⟩ ⟩ and | 3 ⟩ ⟩ with the goal of transferring population initially in state | 1 ⟩ ⟩ to state | 3 ⟩ ⟩ without populating state | 2 ⟩ ⟩ . Allow the system to interact with two coherent radiation fields, the pump and Stokes fields. Let the pump field couple only states | 1 ⟩ ⟩ and | 2 ⟩ ⟩ and the Stokes field couple only states | 2 ⟩ ⟩ and | 3 ⟩ ⟩ , for instance due to far-detuning or selection rules. Denote the Rabi frequencies and detunings of the pump and Stokes couplings by Ω Ω P / S and Δ Δ P / S . Setting the energy of state | 2 ⟩ ⟩ to zero, the rotating wave Hamiltonian is given by