Crossover resonance (${\nu }_{\mathrm{co}}=({\nu }_a+{\nu }_b)/2$)

Two allowed optical transitions sharing a lower quantum state can produce an extra saturation spectroscopy feature even where there is no additional energy level difference. Approximate their wavenumbers by the same $k$, and let their angular frequencies be ${\omega }_a,{\omega }_b$. A pump resonant with one transition and an opposed probe resonant with the other satisfysoExchanging the two transitions selects the opposite velocity. Both beams can then modify the same shared population, producing a crossover near the midpoint. This requires the relevant velocities to be occupied and the transitions to be connected by the population dynamics; not every pair must produce a visible feature. Strength and sign depend on optical pumping and the multilevel structure. Assigning every narrow feature to a separate atomic transition would therefore give false energy levels.