The first condition reveals that the critical two-photon resonance condition yields a dark state which is a superposition of only the initial and target state. By defining the mixing angle tan ⁡ ⁡ θ θ = Ω Ω P / Ω Ω S and utilizing the normalization condition | c 1 | 2 + | c 3 | 2 = 1 , the second condition can be used to express this dark state as