Spin squeezing in a generalized one-axis twisting model

TL;DR

This paper explores how initial state angles and detuning affect spin squeezing in a generalized one-axis twisting model, deriving analytic formulas and revealing scaling behaviors of squeezing and optimal timing.

Contribution

It provides analytic expressions for minimal variance and squeezing time in a generalized model, extending previous ideal one-axis twisting results.

Findings

Minimal variance scales as N^{2/3} for small deviations from the ideal state.

Maximal squeezing time scales as N^{-5/6}.

Analytic results agree with numerical simulations.

Abstract

We investigate the dependence of spin squeezing on the polar angle of the initial coherent spin state $|\theta_0, \phi_0>$ 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 is recovered as long as $\theta_0=\pi/2$. For a small departure of $\theta_0$ from $\pi/2$, however, the achievable variance $(V_{-})_{\min}\sim N^{2/3}$, 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, which agree with numerical simulations.