Efficient atomic clocks operated with several atomic ensembles

Atomic clocks are typically operated by locking a local oscillator (LO) to a single atomic ensemble. In this article we propose a scheme where the LO is locked to several atomic ensembles instead of one. This results in an exponential improvement compared to the conventional method and provides a stability of the clock scaling as $(αN)^{-m/2}$ with $N$ being the number of atoms in each of the $m$ ensembles and $α$ is a constant depending on the protocol being used to lock the LO

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