As another limiting case, suppose the drive is far off-resonant, | ω ω d − − ω ω | ≫ ≫ 0 . We can figure out the dynamics in that case without solving the Schrödinger equation directly. Suppose the system starts in the ground state | g ⟩ ⟩ . Initially, the Hamiltonian will populate some component of | e ⟩ ⟩ . A small time later, however, it will populate roughly the same amount of | e ⟩ ⟩ but with completely different phase. Thus the effect of an off-resonant drive will tend to cancel itself out. This can also be expressed by saying that an off-resonant drive is rapidly rotating in the frame of the atom.