(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 D. (b) Triplet and singlet energy eigenstates for two interacting spins. In this picture, dephasing is a precession between the triplet state |t〉 and the singlet |s〉. The precession is inhibited when the spins interact strongly, ωex≫D, shifting the energy of the singlet state. (c) The interactions exert a torque ωex on the spins about their mean spin. When ωex≫D, the precession of the spins about the vector sum of the two torques ωex and D, so they no longer precess about the equator, giving extraordinarily long coherence times for a clock.