Spin squeezing generated by the anisotropic central spin model

Spin squeezing, as a crucial quantum resource, plays a pivotal role in quantum metrology, enabling us to achieve high-precision parameter estimation schemes. Here, we investigate the spin squeezing and the quantum phase transition in an anisotropic central spin system. We find that this kind of central spin system can be mapped to the anisotropic Lipkin-Meshkov-Glick model in the limit where the ratio of transition frequencies between the central spin and the spin bath tends towards infinity. This property can induce a one-axis twisting interaction and provides another possibility for generating spin squeezing. We consider the generation of spin-squeezed states through the ground state and the dynamical evolution of the central spin model, respectively. The results show that the dynamical approach is more effective, and the spin-squeezing parameter improves as the anisotropy parameter decreases, while its value scales with system size as N^-2/3. Furthermore, we obtain the critical exponent of the quantum Fisher information around the critical point by numerical simulation, and find its value tends to 4/3 as the frequency ratio and the system size approach infinity. This paper offers a promising scheme for generating spin-squeezed state and paves the way for potential advancements in quantum sensing.