If both atoms are in the excited state | 11 ⟩ ⟩ the effective system evolves in the subspace of { | 1 r ⟩ ⟩ , | r 1 ⟩ ⟩ , | 11 ⟩ ⟩ } . It is convenient to rewrite the Hamiltonian in terms of bright | b ⟩ ⟩ = 1 2 ( | r 1 ⟩ ⟩ + | 1 r ⟩ ⟩ ) and dark | d ⟩ ⟩ = 1 2 ( | r 1 ⟩ ⟩ − − | 1 r ⟩ ⟩ ) basis states, along with | 11 ⟩ ⟩ . In this basis, the Hamiltonian is given by