Granularity Noise Limit in Atomic-Ensemble-Based Metrology

TL;DR

This paper reveals that atomic-ensemble sensing is fundamentally limited by atomic granularity noise, which can dominate over optical measurement noise, and introduces a unified framework to understand this crossover affecting sensor optimization.

Contribution

It introduces a discrete-atom statistical framework and a noise-scaling law that captures the transition from optical noise to granularity noise in atomic sensors.

Findings

A unified noise-scaling law governed by the resource ratio $ $.

Counter-intuitive result: increasing probe power can worsen sensitivity.

Identification of a critical resource threshold $ _{crit}$ limiting quantum metrology advantages.

Abstract

Conventional noise analysis in atomic-ensemble sensing assumes a continuous-medium approximation, thereby treating the atomic system as a deterministic dielectric. Here, we demonstrate that this assumption breaks down due to the discrete, particulate nature of the ensemble, giving rise to an intrinsic "atomic granularity noise" (AGN) that fundamentally competes with the optical measurement noise (OMN, typically photon shot noise). By introducing a discrete-atom statistical framework, we derive a unified noise-scaling law governed by a single dimensionless resource ratio, $\mathcal{R} = \bar{N}_{\mathrm{ph}}/\bar{N}_{\mathrm{at}}$ at (the photon-to-atom flux ratio). This law predicts a continuous crossover from an OMN-limited regime to an AGN-limited regime. Crucially, our results reveal a counter-intuitive constraint for sensor optimization: increasing optical probe power -- standard practice to mitigate OMN -- can paradoxically degrade sensitivity by driving the system into the AGN-dominated regime. Furthermore, we identify a critical resource threshold, $\mathcal{R}_{\mathrm{crit}}$, beyond which quantum-enhanced metrology using non-classical light fails to improve sensitivity, as it becomes limited by the AGN.