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中国物理学会期刊

光晶格原子钟Rabi谱的Fisher信息及最佳测量

Fisher Information and Optimal Measurement of Rabi Spectrum in Optical Lattice Atomic Clocks

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  • Fisher信息是在参数估计中至关重要的因素。本文探究了不同退相干强度下光晶格原子钟Rabi谱的Fisher信息,发现其极大值点并非为谱线半高宽点。通过数值仿真模拟了钟激光闭环过程中的艾伦方差,证明了通过选择最大Fisher信息点进行闭环可以提高光钟稳定度。

    Optical lattice atomic clocks have achieved remarkable fractional frequency uncertainties, playing a vital role in precision metrology and fundamental physics. In the closed-loop operation of an optical clock, stabilizing the clock laser to the ultra-narrow atomic transition is essentially a parameter estimation problem. While measurements are conventionally performed at the full-width at half-maximum (FWHM) of the Rabi spectrum to maximize the discriminator slope, it remains unclear whether this point provides the maximum Fisher information under the influence of system decoherence. In this paper, we theoretically and numerically investigate the Fisher information of the Rabi spectrum under varying decoherence strengths. We introduce a coherence contrast parameter α (α ∈ (0, 1) to accurately quantify the decoherence effect in the system.
    By analyzing the physical competition between the spectral line slope (signal sensitivity) and the quantum projection noise (QPN), we reveal the underlying mechanism governing the optimal measurement point. Under ideal fully coherent conditions (α = 1), the maximum Fisher information is located exactly at the resonance center. However, when decoherence is present (α < 1), the non-zero QPN at resonance forces the maximum Fisher information point to shift towards the FWHM to seek a larger spectral slope. Furthermore, we demonstrate that a weaker decoherence effect (i.e., a larger α) yields a more significant relative information gain when choosing this exact optimal point over the conventional FWHM. Numerical simulations of the laser locking process confirm that tracking the optimal detuning point (e.g., ∆δ = 0.653g at α = 0.9) effectively reduces the Allan variance compared to the traditional FWHM measurement (∆δ ≈ 0.8g). Our study proposes a dynamic optimization strategy that improves the stability of optical lattice clocks without requiring additional hardware modifications.

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