  We describe a collective state atomic clock with Ramsey fringes narrowed by a
factor of $\sqrt{N}$ compared to a conventional clock, N being the number of
non-interacting atoms, without violating the uncertainty relation. This
narrowing is explained as being due to interferences among the collective
states, representing an effective $\sqrt{N}$ fold increase in the clock
frequency, without entanglement. The detection process, which measures a
collective state, can be used to increase the quantum efficiency of detection
significantly, yielding a net improvement in stability by as much as a factor
of 10.
