If both atoms are in the | 00 ⟩ ⟩ state, nothing happens so | 00 ⟩ ⟩ → → | 00 ⟩ ⟩ . If one of them is in the | 0 ⟩ ⟩ state, the other atom picks up a phase due to light shift: | 01 ⟩ ⟩ → → e i ϕ ϕ 1 | 01 ⟩ ⟩ and similarly | 10 ⟩ ⟩ → → e i ϕ ϕ 1 | 10 ⟩ ⟩ with: