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arXiv 1502.00470quant-ph
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双腔中的双轴自旋压缩

Two-axis spin squeezing in two cavities

Caifeng Li, Jingtao Fan, Lixuan Yu, Gang Chen, Tian-Cai Zhang, Suotang Jia

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摘要：

超高精细光学腔中的超冷原子是产生自旋压缩的有力平台，因为腔模的光子可以诱导非线性自旋-自旋相互作用，从而产生单轴扭转哈密顿量$H_{\text{OAT}}=qJ_{x}^{2}$，其对应的最大压缩因子标度为$N^{-2/3}$，其中$N$是原子序数.相反，对于另一个双轴扭转哈密顿量$H_{\text{TAT}}=q(J_{x}^{2}-J_{y}^{2})$，最大压缩因子为$N^{-1}$，接近海森堡极限。本文从最近的腔辅助拉曼跃迁实验中得到启发，提出了一种方案，利用超冷六能级原子系综与两个量子化腔场和两对拉曼激光相互作用，实现了一个可调谐的双轴自旋哈密顿量$%H=q(J_{x}^{2}+χJ_{y}^{2})+ω_{0}J_{z}$ .在适当的参数下，恢复了上述单轴和双轴扭转哈密顿量，并且最大压缩因子的$N^{-1}$的标度可以自然发生。另一方面，在双轴扭转哈密顿量中，自旋压缩通常随着原子有效共振频率$ω_{0}$的增加而减小。令人惊讶的是，我们发现，结合无量纲参数$χ(>-1)$，原子的有效共振频率$ω_{0}$可以大大增强自旋压缩.这些结果有利于在实验中实现所需的自旋压缩。

英文摘要：

Ultracold atoms in an ultrahigh-finesse optical cavity are a powerful platform to produce spin squeezing since photon of cavity mode can induce nonlinear spin-spin interaction and thus generate a one-axis twisting Hamiltonian $H_{\text{OAT}}=qJ_{x}^{2}$, whose corresponding maximal squeezing factor scales as $N^{-2/3}$, where $N$ is the atomic number. On the contrary, for the other two-axis twisting Hamiltonian $H_{\text{TAT}}=q(J_{x}^{2}-J_{y}^{2})$, the maximal squeezing factor scales as $N^{-1}$, approaching the Heisenberg limit. In this paper, inspired by recent experiments of cavity-assisted Raman transitions, we propose a scheme, in which an ensemble of ultracold six-level atoms interacts with two quantized cavity fields and two pairs of Raman lasers, to realize a tunable two-axis spin Hamiltonian $%H=q(J_{x}^{2}+χJ_{y}^{2})+ω_{0}J_{z}$. For proper parameters, the above one- and two- axis twisting Hamiltonians are recovered, and the scaling of $N^{-1}$ of the maximal squeezing factor can occur naturally. On the other hand, in the two-axis twisting Hamiltonian, spin squeezing is usually reduced when increasing the effective atomic resonant frequency $ω_{0}$. Surprisingly, we find that by combined with the dimensionless parameter $χ(>-1)$, the effective atomic resonant frequency $ω_{0}$ can enhance spin squeezing largely. These results are benefit for achieving the required spin squeezing in experiments.

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