The physics of this Hamiltonian can be divided into several subspaces depending on the initial state. The | 00 ⟩ ⟩ state is decoupled and does not evolve. Suppose only the i-th the atom is in | 1 ⟩ ⟩ state ( | 10 ⟩ ⟩ , | 01 ⟩ ⟩ ), then the Hamiltonian is given by H i . This Hamiltonian is the standard two-level Rabi hamiltonian. It characterizes the "light shift" in a two level system and has eigenvalues E L S ( 1 ) = 1 2 ( Δ Δ ± ± Ω Ω 2 + Δ Δ 2 ) .