Cavity quantum electrodynamics describes the fundamental interactions between light and matter, and how they can be controlled by shaping the local environment. For example, optical microcavities allow high-efficiency detection and manipulation of single atoms. In this regime, fluctuations of atom number are on the order of the mean number, which can lead to signal fluctuations in excess of the noise on the incident probe field. Here we demonstrate, however, that nonlinearities and multi-atom statistics can together serve to suppress the effects of atomic fluctuations when making local density measurements on clouds of cold atoms. We measure atom densities below 1 per cavity mode volume near the photon shot-noise limit. This is in direct contrast to previous experiments where fluctuations in atom number contribute significantly to the noise. Atom detection is shown to be fast and efficient, reaching fidelities in excess of 97% after 10 μs and 99.9% after 30 μs
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