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 vertical bar theta(0), phi(0)> in a generalized one-axis twisting model, where the detuning delta is taken into account. We show explicitly that regardless of delta and phi(0), previous results of the ideal one-axis twisting are recovered as long as theta(0) = pi/2. For a small departure of theta(0) from pi/2, however, the achievable variance (V-)(min) similar to 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.