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Atomic projection noise limits the ultimate precision of all atomic sensors,including clocks, inertial sensors, magnetometers, etc. The independent quantumcollapse of $N$ atoms into a definite state (for example spin up or down) leadsto an uncertainty $\Delta \theta_{SQL}=1/\sqrt{N}$ in the estimate of thequantum phase accumulated during a Ramsey sequence or its many generalizations.This phase uncertainty is referred to as the standard quantum limit. Creatingquantum entanglement between the $N$ atoms can allow the atoms to partiallycancel each other's quantum noise, leading to reduced noise in the phaseestimate below the standard quantum limit. Recent experiments have demonstratedup to $10$~dB of phase noise reduction relative to the SQL by making collectivespin measurements. This is achieved by trapping laser-cooled Rb atoms in anoptical cavity and precisely measuring the shift of the cavity resonancefrequency by an amount that depends on the number of atoms in spin up.Detecting the probe light with high total efficiency reduces excess classicaland quantum back-action of the probe. Here we discuss recent progress and atechnique for reducing the relative frequency noise between the probe light andthe optical cavity, a key requirement for further advances.

Generating Entanglement between Atomic Spins with Low-Noise Probing of an Optical Cavity