(a) Bloch sphere representation of two atomic coherences that are described by fictitious red and blue spins. The spins dephase by precessing in the horizontal plane with opposite dephasing torques . (b) Triplet and singlet energy eigenstates for two interacting spins. In this picture, dephasing is a precession between the triplet state and the singlet . The precession is inhibited when the spins interact strongly, , shifting the energy of the singlet state. (c) The interactions exert a torque on the spins about their mean spin. When , the precession of the spins about the vector sum of the two torques and , so they no longer precess about the equator, giving extraordinarily long coherence times for a clock.