Figure 1: (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.