Deterministic entanglement generation from driving through quantum phase transitions

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 near-deterministic generation of an entangled twin-Fock condensate of $\sim11000$ 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 $10.7\pm0.6$ dB and normalized collective spin length of $0.99\pm0.01$. Together, these observations allow us to infer an entanglement-enhanced phase sensitivity of $\sim6$ dB beyond the standard quantum limit and an entanglement breadth of $\sim910$ atoms. Our work highlights the power of generating large-scale useful entanglement by taking advantage of the different entanglement landscapes separated by QPTs.