Many-body entanglement is often created through system evolution, aided by non-linear interactions between the constituting particles. The very dynamics, however, can also lead to fluctuations and degradation of the entanglement if the interactions cannot be controlled. Here, we demonstrate neardeterministic generation of an entangled twin-Fock condensate of ∼ 11000 atoms by driving a 87 Rb Bose-Einstein condensate undergoing spin mixing through two consecutive quantum phase transitions (QPTs). We directly observe number squeezing of 10.7 ± 0.6 dB and normalized collective spin length of 0.99 ± 0.01. Together, these observations allow us to infer an entanglementenhanced phase sensitivity of ∼ 6 dB beyond the standard quantum limit and an entanglement breadth of ∼ 910 atoms. Our work highlights the power of generating large-scale useful entanglement by taking advantage of the differ-1
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), [Formula: see text], 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 Laser Interferometer Gravitational-Wave Observatory and today's best atomic clocks. For multimode interferometry, the SQL becomes [Formula: see text] using 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 [Formula: see text] 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.
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