  In trapped-atom clocks, the primary source of decoherence is often the phase
noise of the oscillator. For this case, we derive theoretical performance gains
by combining several atomic ensembles. For example, M ensembles of N atoms can
be combined with a variety of probe periods, to reduce the frequency variance
to M 2^-M times that of standard Ramsey clocks. A similar exponential
improvement is possible if the atomic phases of some of the ensembles evolve at
reduced frequencies. These ensembles may be constructed from atoms or molecules
with lower-frequency transitions, or generated by dynamical decoupling. The
ensembles with reduced frequency or probe period are responsible only for
counting the integer number of 2 pi phase wraps, and do not affect the clock's
systematic errors. Quantum phase measurement with Gaussian initial states
allows for smaller ensemble sizes than Ramsey spectroscopy.
