  Optical lattice clocks have the potential for extremely high frequency
stability owing to the simultaneous interrogation of many atoms, but this
precision may come at the cost of systematic inaccuracy due to atomic
interactions. Density-dependent frequency shifts can occur even in a clock that
uses fermionic atoms if they are subject to inhomogeneous optical excitation
[1, 2]. Here we present a seemingly paradoxical solution to this problem. By
dramatically increasing the strength of atomic interactions, we suppress
collisional shifts in lattice sites containing $N$ > 1 atoms; strong
interactions introduce an energy splitting into the system, and evolution into
a many-particle state in which collisions occur is inhibited. We demonstrate
the effectiveness of this approach with the JILA Sr lattice clock by reducing
both the collisional frequency shift and its uncertainty by more than a factor
of ten [3], to the level of $10^{-17}$. This result eliminates the compromise
between precision and accuracy in a many-particle system, since both will
continue to improve as the particle number increases.
