Stimulated Raman adiabatic passage (STIRAP)

For a resonant three-level chain with couplings ${\Omega }_1,{\Omega }_2$, the zero-energy dark state of a driven Hamiltonian is $|D⟩=({\Omega }_2|1⟩-{\Omega }_1|3⟩)/\sqrt{{\Omega }_1^2+{\Omega }_2^2}$. Turning on the target-to-intermediate coupling first and sweeping ${\Omega }_1/{\Omega }_2$ from zero to infinity rotates this state from $|1⟩$ to $-|3⟩$. The other eigenvalues are $\pm \sqrt{{\Omega }_1^2+{\Omega }_2^2}$, so $\hslash |\dot{\theta }|\ll \sqrt{{\Omega }_1^2+{\Omega }_2^2}$ controls nonadiabatic leakage. Ideally the intermediate state remains unoccupied, suppressing spontaneous-emission loss. The gap must not close while the dark state is rotating.