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

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