Without a drive, the phase of | e ⟩ ⟩ would oscillate relative to | g ⟩ ⟩ . In the Bloch sphere representation of a two-state system, this corresponds to rotation around the z-axis. Conceptually, we can remove this component of the dynamics by entering a rotating frame of reference defined by the unitary transformation U = e i ω ω t | e ⟩ ⟩ ⟨ ⟨ e | . Under this transformation, the Hamiltonian becomes