Quantum Fisher information and spin squeezing in one-axis twisting model

We consider the quantum Fisher information and spin squeezing in one-axis twisting model with a coherent spin state $\mathrm{\mid }{\theta }_0,{\varphi }_0⟩$. We analytically discuss the dependence of the two parameters: spin squeezing parameter ${\xi }_K^2$ and the average parameter estimation precision ${\chi }^2$ on the polar angle ${\theta }_0$ and the azimuth angle ${\varphi }_0$. Moreover, we discuss the effects of the collisional dephasing on the dynamics of the two parameters. In this case, the analytical solution of ${\xi }_K^2$ is also obtained.