Precise rotation angle measurement $8.44$ dB beyond the standard quantum limit

We demonstrate an interferometric measurement precision beyond the standard quantum limit (SQL) using a spin-1 Dicke state containing more than 10000 entangled atoms. The high quality Dicke state is deterministically generated through controlled quantum phase transition in a Bose-Einstein condensate of ground state $F=1$ $^{87}$Rb atoms. Compared to the twin-Fock state (spin-$1/2$ Dicke state) we reported earlier[1], the spin-1 Dicke state allows for a higher precision using SU(2) three-mode interferometry, which couples the three Zeeman states $|F=1,m_F=0,\pm1\rangle$ symmetrically using a resonant radio-frequency field. We achieve a rotation angle measurement sensitivity $8.44$dB below the two-mode SQL of $1/\sqrt N$ and $2.42$dB below the three-mode SQL of $1/(2\sqrt N)$. \\ \\ {[1] Luo, X. Y., Zou, Y. Q., Wu, L. N., Liu, Q., Han, M. F., Tey, M. K., You, L. Science, {\bf 355}, 620 (2017).}