Spin squeezing in a generalized one-axis twisting model

We investigate the dependence of spin squeezing on the polar angle of the initial coherent spin state |θ₀, phi₀rang in a generalized one-axis twisting model, where the detuning δ is taken into account. We show explicitly that regardless of δ and phi₀, previous results of the ideal one-axis twisting are recovered as long as θ₀=π/2. For a small departure of θ₀ from π/2, however, the achievable variance (V _-)_min ~N^2/3, which is larger than the ideal case N^1/3. We also find that the maximal squeezing time t_min scales as N^-5/6. Analytic expressions of (V_-)_min and t_min are presented and they agree with numerical simulations.