Optimal scaling of atomic-clock stability with atom number under laser noise
In plain words
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 statement
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.
What would settle it
A matching lower bound and explicit protocol for the Allan deviation exponent as a function of N for each noise type.
Status in the literature
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.