Beating the classical precision limit with spin-1 Dicke state of more than 10000 atoms.

Interferometry is a paradigm for most precision measurements. Using $N$ uncorrelated particles, the achievable precision for a two-mode (two-path) interferometer is bounded by the standard quantum limit (SQL), $1/\sqrt{N}$, due to the discrete (quanta) nature of individual measurements. Despite being a challenging benchmark, the two-mode SQL has been approached in a number of systems, including the LIGO and today's best atomic clocks. Employing multi-mode interferometry, the SQL becomes $1/[(M-1)\sqrt{N}]$ using M modes. Higher precision can also be achieved using entangled particles such that quantum noises from individual particles cancel out. In this work, we demonstrate an interferometric precision of $2.42^{+1.76}_{-1.29}\,$dB beyond the three-mode SQL, using balanced spin-1 (three-mode) Dicke states containing thousands of entangled atoms. The input quantum states are deterministically generated by controlled quantum phase transition and exhibit close to ideal quality. Our work shines light on the pursuit of quantum metrology beyond SQL.