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 $|θ_{0},ϕ_{0}\rangle$. We analytically discuss the dependence of the two parameters: spin squeezing parameter $ξ^2_{K}$ and the average parameter estimation precision $χ^2$ on the polar angle $θ_{0}$ and the azimuth angle $ϕ_0$. Moreover, we discuss the effects of the collisional dephasing on the dynamics of the two parameters. In this case, the analytical solution of $ξ^2_K$ is also obtained.

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