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