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

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