AI 中文总结
该研究针对双碱金属共磁计暗物质搜寻，将核子耦合比提取视为统计估计问题，确定最优无校准可观测量，明确不同频率下相位差与振幅比的精度表现及适用场景。
AI 中文摘要
双碱金属单胞$^{87}$Rb-$^{39}$K-$^{3}$He共磁计可通过两个光旋转通道读取类轴子暗物质信号，将场的中子与质子自旋耦合比$\boldsymbol{\textit{R}}=\boldsymbol{\textit{ξ}}_\boldsymbol{\textit{n}}/\boldsymbol{\textit{ξ}}_\boldsymbol{\textit{p}}$编码在相对响应中。跨物种相位差$\boldsymbol{\textit{Δφ}}$已被提出作为对$\boldsymbol{\textit{R}}$敏感的无校准读出量。将$\boldsymbol{\textit{R}}$的提取视为统计估计问题，我们证明最优可观测量是复通道间比值，其可拆分为$\boldsymbol{\textit{Δφ}}$和振幅比，其中仅$\boldsymbol{\textit{Δφ}}$对相对增益不敏感，因此是无校准的。对于所选共磁计参数，在~100 Hz以上，仅相位差就捕获了大部分耦合比信息；在更低频率下，$\boldsymbol{\textit{Δφ}}$并非近似充分统计量，此时振幅比可使$\boldsymbol{\textit{R}}$的精度提升至少2倍（在~40 Hz以下）。然而，恢复该信息需要足够准确地知晓相对增益，因此即使$\boldsymbol{\textit{Δφ}}$并非最优可观测量，它仍是稳健的可观测量。
英文摘要
A dual-alkali single-cell $^{87}$Rb-$^{39}$K-$^{3}$He comagnetometer can read an axionlike dark matter signal through two optical-rotation channels, encoding the ratio $\mathcal{R}=ξ_n/ξ_p$ of the field's neutron and proton spin couplings in their relative response. The inter-species phase difference $Δφ$ has been proposed as a calibration-free readout that is sensitive to $\mathcal{R}$. Treating the extraction of $\mathcal{R}$ as a statistical estimation problem, we show that the optimal observable is the complex inter-channel ratio, which splits into $Δφ$ and an amplitude ratio, of which only $Δφ$ is insensitive to the relative gain and hence calibration-free. For our choice of comagnetometer parameters, above $\sim\!100$ Hz the phase difference alone captures most of the coupling-ratio information. At lower frequencies $Δφ$ is not near-sufficient: there the amplitude ratio would improve the precision on $\mathcal{R}$ by a factor of $\gtrsim2$ below $\sim\!40$ Hz. Recovering that information, however, requires the relative gain to be known sufficiently accurately, so $Δφ$ stays the robust observable even where it is not the optimal one.
Comments13 pages, 3 figures
