We analyze the generation of spin-squeezed states via coupling of three-level atoms to an optical cavity and continuous quantum measurement of the transmitted cavity field in order to monitor the evolution of the atomic ensemble. Using analytical treatment and microscopic simulations of the dynamics, we show that one can achieve significant spin squeezing, favorably scaling with the number of atoms N. However, contrary to some previous literature, we clarify that it is not possible to obtain Heisenberg scaling without the continuous feedback that is proposed in optimal approaches. In fact, in the adiabatic cavity removal approximation and large N limit, we find the scaling behavior N−2/3 for spin squeezing and N−1/3 for the corresponding protocol duration. These results can be obtained only by considering the curvature of the Bloch sphere, since linearizing the collective spin operators tangentially to its equator yields inaccurate predictions. With full simulations, we characterize how spin-squeezing generation depends on the system parameters and departs from the bad cavity regime, by gradually mixing with cavity-filling dynamics until metrological advantage is lost. Finally, we discuss the relevance of this spin-squeezing protocol to state-of-the-art optical clocks.

中文翻译：

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连续测量空腔耦合原子系综中自旋挤压产生的分析


我们通过将三能级原子耦合到光学腔并对传输腔场进行连续量子测量来分析自旋压缩态的生成，以监测原子系综的演化。通过动力学的分析处理和微观模拟，我们表明可以实现显着的自旋压缩，有利地随原子数 N 缩放。然而，与之前的一些文献相反，我们澄清，如果没有最佳方法中提出的连续反馈。事实上，在绝热腔去除近似和大 N 限制中，我们发现自旋压缩的缩放行为为 N−2/3，相应协议持续时间的缩放行为为 N−1/3。这些结果只能通过考虑布洛赫球的曲率来获得，因为将与其赤道相切的集体自旋算子线性化会产生不准确的预测。通过完整的模拟，我们通过逐渐与空腔填充动力学混合直到失去计量优势，来描述自旋挤压的产生如何取决于系统参数并偏离不良空腔状态。最后，我们讨论了这种自旋挤压协议与最先进的光学时钟的相关性。