For a resonant three-level chain with couplings , the zero-energy dark state of a driven Hamiltonian is . Turning on the target-to-intermediate coupling first and sweeping from zero to infinity rotates this state from to . The other eigenvalues are , so controls nonadiabatic leakage. Ideally the intermediate state remains unoccupied, suppressing spontaneous-emission loss. The gap must not close while the dark state is rotating.