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

An N-atom Collective State Atomic Clock with Root-N Fold Increase in Effective Frequency and Root-N Fold Reduction in Fringe Width