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Accepted · first revision · record

Title: Optimal scaling of atomic-clock stability with atom number under laser noise
Plain: A clock steers a laser using N atoms, but the laser itself jitters, which limits how long atoms can be probed. The best possible improvement from entangling the atoms, given this jitter, is not known.
Precise: For a Ramsey-type optical clock with $N$ atoms and local-oscillator frequency noise with power spectrum $S(f)\sim h_\alpha f^{-\alpha} (\alpha=0, 1, 2)$, determine the optimal asymptotic scaling with $N$ of the long-term Allan deviation $\sigma_y(\tau)$, optimizing over entangled states, adaptive measurements and feedback, and whether any protocol reaches $1/N$ scaling up to logarithmic factors.
Settled by: A matching lower bound and explicit protocol for the Allan deviation exponent as a function of N for each noise type.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: partially-resolved
Status note: Protocols with near-Heisenberg scaling up to logarithmic factors are known for white phase noise; matching bounds for 1/f and random-walk laser noise are lacking.
Posed since: (empty)