We study the peculiarities of the coherent population trapping (CPT) dark resonance in atomic vapor confined in a finite-size cell. Taking into account the scattering of atoms on anti-relaxation coating of the walls, we analyze the line shape of the CPT resonance in $^{133}{\rm{Cs}}$ depending on various parameters, such as the width of laser radiation spectrum, the type of pumping, and the magnitude of static magnetic field for both lin || lin and ${\rm{lin}} \bot {\rm{lin}}$ polarization schemes. We show that for different parameters, the dependence of the line shape on the size of a cell is different, i.e., different factors affect the CPT resonance nonadditively. Thus, in the case when CPT resonance is excited by a narrowband laser, the shape of the resonance weakly depends on the size of a cell due to the laser-induced narrowing effect. We also show that the distortion of the line shape of the CPT resonance caused by nonresonant hyperfine sublevels of atomic excited states is modified with the size of a cell. Our calculation reveals the important role of accounting for the hyperfine and Zeeman structure of atomic levels. We have shown that the contrast of the CPT resonance differs about 5 times from the prediction of the simple three-level Λ model. The obtained results can be used for the optimization of the quantum frequency standards based on the CPT effect. In the final part of the paper, on the basis of the shot noise approximation we estimate the short-term stability of such standards.

中文翻译：

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有限尺寸电池中光学稀薄的¹³³ Cs原子蒸气中的相干人口陷阱

我们研究限制在有限大小的单元格中的原子蒸气中的相干人口陷阱（CPT）黑暗共振的特殊性。考虑到原子在壁的抗松弛涂层上的散射，我们根据各种参数（例如激光的宽度）分析了$ ^ {133} {\ rm {Cs}} $中CPT共振的线形lin ||的辐射光谱，泵浦类型和静磁场的大小 lin和$ {\ rm {lin}} \ bot {\ rm {lin}} $极化方案。我们表明，对于不同的参数，线形对细胞尺寸的依赖性是不同的，即，不同的因素会非累加地影响CPT共振。因此，在由窄带激光器激发CPT共振的情况下，由于激光引起的变窄效应，共振的形状弱地取决于单元的尺寸。我们还表明，由原子激发态的非共振超细亚能级引起的CPT共振线形的畸变会随着晶胞的大小而改变。我们的计算揭示了解释原子级的超精细和塞曼结构的重要作用。我们已经证明，CPT共振的对比度与简单的三级Λ模型的预测相差约5倍。获得的结果可用于基于CPT效应的量子频率标准的优化。在本文的最后部分，基于散粒噪声近似值，我们估计了此类标准的短期稳定性。