  The accuracy of an atomic clock depends in part on the bandwidth of the
relevant atomic transitions. Here we consider an ensemble of $N$ atoms whose
transition frequencies have been independently perturbed by environmental
effects or other factors. We consider the possibility of using the quantum Zeno
effect to lock the relative phase of the atoms, which would decrease their
effective bandwidth by a factor of $1/\sqrt{N}$. We analyze an example in which
the quantum Zeno effect can be used to lock the relative phase of a pair of
atoms, after which the elapsed time can be determined. Practical applications
may require $N>>1$ in order to achieve a good signal-to-noise ratio.
