Spin squeezing of one-axis twisting model in the presence of phase dephasing

We present a detailed analysis of spin squeezing of the one-axis twisting model with a many-body phase dephasing, which is induced by external field fluctuation in a two-mode Bose-Einstein condensates. Even in the presence of the dephasing, our analytical results show that the optimal initial state corresponds to a coherent spin state |θ0, φ0〉 with the polar angle θ0 = π/2. If the dephasing rate γ ≪ S−1/3, where S is total atomic spin, we find that the smallest value of squeezing parameter (i.e., the strongest squeezing) obeys the same scaling with the ideal one-axis twisting case, namely ξ ∝ S−2/3. While for a moderate dephasing, the achievable squeezing obeys the power rule S−2/5, which is slightly worse than the ideal case. When the dephasing rate γ > S1/2, we show that the squeezing is weak and neglectable.