Near-Unitary Spin Squeezing in $^{171}$Yb in an optical cavity

In this work, we experimentally demonstrate the generation of a near-unitary SSS in an ensemble of $^{171}$Yb atoms created by a one-axis twisting interaction using cavity feedback squeezing [1]. The near-unitary spin squeezing is engineered between the magnetic sublevels of the ground state of $^{171}$Yb using light detuned from the system's resonances [2]. The observed spin noise suppression and metrological gain are limited by the state readout to 9.4(4)~dB and 6.5(4)~dB, respectively, while the generated states offer a spin noise suppression of 15.9(6)~dB and a metrological gain of 12.9(6)~dB over the SQL. When limiting the squeezing to 30\% of unitarity, we demonstrate an interferometer that improves the averaging time over the SQL by a factor of 3.7(2). This squeezing can be mapped in the future onto an optical transition to improve the performance of an $^{171}$Yb state-of-the-art clock. [1] M. H. Schleier-Smith et al. Phys. Rev. A 81, 021804(R) (2010). [2] Y.-L. Zhang et al. Phys. Rev. A 91, 033625 (2015).