What is a double quantum coherence?
When you put your sample in the magnet, all the spin half nuclei align either with or against the magnetic field. The population difference between these two orientations (known as the Boltzman distribution) is field dependent, and is determined by their energy difference. An NMR signal is observed when nuclei flip from one orientation to the other. This is a single quantum coherence. When two nuclei are coupled, they can flip together as though they were a single unit. If they flip in opposite directions, the flips “cancel each other out” (sort of) resulting in a zero quantum coherence. If they both flip the same way, you get a double quantum coherence. The frequency of a zero quantum coherence is between zero and a few kilohertz, so it is not directly observed. Similarly the frequency of a double quantum coherence is roughly twice the normal observe frequency, so that is not observed directly either. You can also have triple quantum coherences from groups of three coupled nuclei. The
