Beating the classical precision limit with spin-1 Dicke states of more than 10,000 atoms

TLDR

Interferometry precision is limited by the standard quantum limit (SQL), which scales as 1/√N for two‑mode setups and 1/[(M−1)√N] for M‑mode interferometers, and has been approached in systems such as LIGO and atomic clocks. This study demonstrates interferometric precision 2.42 dB beyond the three‑mode SQL using balanced spin‑1 Dicke states of thousands of entangled atoms. The Dicke states are deterministically produced via a controlled quantum phase transition, yielding near‑ideal quality input states. The results illustrate the feasibility of surpassing the SQL in multi‑mode interferometry with large entangled ensembles.

Abstract

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.