氢原子钟双选态束光学系统仿真分析

梁悦; 谢勇辉; 陈鹏飞; 帅涛; 裴雨贤; 徐昊天; 赵阳; 夏天; 潘晓燕; 张朋军; 林传富

doi:10.7498/aps.72.20221363

摘要: 氢原子钟利用氢原子基态超精细能级跃迁信号进行精确计时, 具有中短期频率稳定度优异、频率漂移率低的特点. 氢原子钟需要通过磁选态将高能态原子选出, 目前广泛应用的磁选态方案中, 既有原子钟跃迁所需要的$ |F = 1, m_{\rm F} = 0\rangle $态, 还有钟跃迁所不需要的$ |F = 1, m_{\rm F} = 1 \rangle $态氢原子, 这使得氢原子钟的中长期频率稳定性难以进一步提高. 为了进一步提高氢原子钟原子跃迁谱线质量和整机性能, 通过计算和仿真, 构建了基于Majorana跃迁的氢原子钟双选态束光学系统, 优化了一级选态区、态反转区、二级选态区等关键部件的参数, 进一步排除了$ |F = 1, m_{\rm F} = 1 \rangle $态原子. 选态后的$ |F = 1, m_{\rm F} = 0\rangle $态原子纯度达到99%, 利用率为58%, 工程应用较为理想. 有效地提升了进入原子储存泡内$ |F = 1, m_{\rm F} = 0\rangle $态氢原子的占比, 同时原子的利用率处于可控范围. 通过实验对该方案的有效性进行了验证, 通过开启双选态系统, 可以观察到氢原子钟信号的增强; 通过调整双选态系统的线圈电流, 可以观察到信号随线圈电流的变化, 这验证了双选态系统的有效性.

关键词:

Abstract: Hydrogen maser uses the transition frequency of hydrogen atom at hyperfine energy level of ground state to realize precise timing. It has excellent frequency stability, especially in medium- and short-term, and low frequency drift. It has been used as high-precision frequency standard in engineering fields such as time keeping, navigation, and very long baseline interferometry. Clock transition of hydrogen maser is the transition between states of $|F = 1, m_{\rm F} = 0\rangle $ and $|F = 0, m_{\rm F} = 0\rangle $. State selection is realized by state selection magnet, through which high energy atoms are converged and low energy atoms are dispersed. In conventional magnet state-selecting system, both atoms of $|F = 1, m_{\rm F} = 0\rangle $ states, which are required for the maser transition, and useless atoms of $|F = 1, m_{\rm F} = 1\rangle $ states are focused into storage bulb, which places restrictions on the medium- and long-term frequency stability performance of hydrogen maser. In order to further improve the quality of atomic transition spectral lines and the performance of hydrogen maser, double state-selection beam optical system which is based on the Majorana transition mode is constructed through calculations and simulations. In this work, we use Majorana method to invert atomic states. The magnetic field required for Majorana transition is established by using two coils with reverse current. The two coils are separated by 71 mm, and the coil axes are aligned with the direction of atomic beam. The other two pairs of transverse Helmholtz coils are separated by 22 mm in the center of the state reversal to adjust the zero point of magnetic field, which should coincide with the atomic beam to ensure a complete reversal of atomic polarity. The state reversal region is surrounded by four magnetic shields to reduce the influence of stray magnetic fields. Relationship between selected-state magnetic field gradient and distance of magnetic poles is analyzed by simulation, and trajectories of the atoms with high and low energy under different selected-state magnetic fields are calculated. The utilization and purity of high energy state atoms entering into bulb atoms are obtained. The purity of the selected $|F = 1, m_{\rm F} = 0\rangle $ state atoms reaches 99% and the utilization rate is 58%. This is ideal for engineering applications. It effectively enhances the proportion of $|F = 1, m_{\rm F} = 0\rangle $ state atoms entering into the atomic storage bulb and ensures the utilization of atoms. We verify the state-selection beam optical system experimentally. By turning on double state-selection system the maser signal can be enhanced. By adjusting the coil current of the double state-selection system, the maser signal varies with coil current, which verifies the effectiveness of double state-selection system.

Key words:

图 1 选态原理

Figure 1. Principle of state selection.

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图 2 双选态示意图

Figure 2. Schematic diagram of the double state selection system.

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图 3 氢原子能级布局数随P值的变化

Figure 3. Variation of hydrogen atomic energy level layout number with P value.

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图 4 Majorana线圈与横向Helmholtz线圈位置示意图

Figure 4. Position diagram of Majorana coils and transverse Helmholtz coils.

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图 5 四极选态磁铁示意图

Figure 5. Quadrupole state selective magnet.

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图 6 (a) 仿真磁场示意图; (b) 不同磁极间距对应的磁场大小

Figure 6. (a) The simulated magnetic field; (b) the right figure shows the magnetic field of different magnetic poles.

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图 7 $|F = 0, m_{\rm F} = 0\rangle $和$|F = 1, m_{\rm F} = -1\rangle $态原子在一级选态区运动轨迹

Figure 7. Trajectories of $|F = 0, m_{\rm F} = 0\rangle $ and $|F = 1, m_{\rm F} = $$ -1\rangle $ state atoms in the first selected region.

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图 8 $|F = 1, m_{\rm F} = 1\rangle $态和$|F = 1, m_{\rm F} = 0\rangle $态原子在一级选态区内运动轨迹

Figure 8. Trajectories of $|F = 1, m_{\rm F} = 1\rangle $ and $|F = 1, m_{\rm F} = $$ 0\rangle $ state atoms in the first selected region.

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图 9 $|F = 1, m_{\rm F} = 1\rangle $态和$|F = 1, m_{\rm F} = 0\rangle $态原子在二级选态区入口处偏转距离

Figure 9. $|F = 1, m_{\rm F} = 1\rangle $ and $|F = 1, m_{\rm F} = 0\rangle $ state atoms deflection distance at the entrance of the secondary selected region.

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图 10 束光学系统三维模型

Figure 10. The model of beam optical system.

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图 11 L₄ = 60 mm, 不同r_d和L₅下的原子纯度和利用率　(a) 原子纯度; (b) 原子利用率

Figure 11. Atomic purity and utilization under different r_d and L₅at L₄ = 60 mm: (a) Atomic purity; (b) atomic utilization.

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图 12 L₄ = 70 mm, 不同r_d和L₅下的原子纯度和利用率　(a)原子纯度; (b)原子利用率

Figure 12. At L₄ = 70 mm, atomic purity and utilization under different r_d and L₅: (a) Atomic purity; (b) atomic utilization on the right.

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图 13 L₄ = 75 mm, 不同r_d和L₅下的原子纯度和利用率　(a) 原子纯度; (b) 原子利用率

Figure 13. At L₄ = 75 mm, atomic purity and utilization under different r_d and L₅: (a) Atomic purity; (b) atomic utilization.

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图 14 L₄ = 80 mm, 不同r_d和L₅下的原子纯度和利用率　(a) 原子纯度; (b) 原子利用率

Figure 14. At L₄ = 80 mm, atomic purity and utilization under different r_d and L₅: (a) Atomic purity; (b) atomic utilization.

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图 15 在储存泡口截面处原子点密度图

Figure 15. Point density diagram of atoms at entrance of storage bulb.

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图 16 在一对线圈电流I_x = –0.5 mA的固定值下, 氢原子钟输出功率与I_y的依赖关系

Figure 16. The Hydrogen atomic clock’s output power dependence on the current of the transverse pair I_y under fixed value of the another pair’s current I_x = –0.5 mA.

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图 17 改变两对线圈电流, 氢原子钟输出功率变化

Figure 17. The Hydrogen atomic clock’s output power dependence on the both coil pair’s currents.

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表 1 磁场梯度与磁极间距对应关系

Table 1. Correspondence between magnetic field gradient and magnetic pole spacing.

磁极间距/mm	0.8	1	1.2	1.3	1.4	1.5	1.6	1.8	2
$ \dfrac{B}{{{r_{\text{d}}}}} $/(T·mm^–1)	1.167	0.850	0.625	0.557	0.510	0.456	0.405	0.367	0.303

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表 2 L₄ = 60 mm时, 不同L₅和r_d原子偏转概率

Table 2. Different L₅ and r_d atomic deflection probabilities at L₄ = 60 mm.

r_d/mm	L₅/mm
r_d/mm	60	70	80	90	100	110	120	130	140	150
1.2	80.1%	84.2%	88.5%	96.8%	99.4%	100.0%	100.0%	100.0%	100.0%	100.0%
1.3	71.2%	75.0%	76.0%	85.9%	91.0%	98.8%	100.0%	100.0%	100.0%	100.0%
1.4	65.5%	70.5%	72.5%	75.2%	85.7%	91.2%	95.2%	99.7%	100.0%	100.0%
1.5	61.5%	64.2%	65.2%	69.6%	75.0%	81.7%	88.2%	93.9%	96.5%	99.4%
1.6	57.2%	58.6%	61.2%	67.5%	69.5%	73.4%	77.5%	83.0%	88.3%	93.0%

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表 3 L₄ = 70 mm时, 不同L₅和r_d原子偏转概率

Table 3. Different L₅ and r_d atomic deflection probabilities at L₄ = 70 mm.

r_d/mm	L₅/mm
r_d/mm	60	70	80	90	100	110	120	130	140	150
1.2	94.5%	96.1%	100.0%	100.0%	92.3%	97.6%	99.7%	100.0%	100.0%	100.0%
1.3	86.7%	88.0%	96.8%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%
1.4	76.0%	79.0%	88.2%	96.1%	99.5%	100.0%	100.0%	100.0%	100.0%	100.0%
1.5	71.2%	73.6%	76.6%	84.8%	91.3%	97.6%	99.7%	100.0%	100.0%	100.0%
1.6	66.2%	67.2%	71.2%	79.7%	84.8%	88.3%	93.1%	97.4%	100.0%	100.0%

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表 4 L₄ = 80 mm时, 不同L₅和r_d原子偏转概率

Table 4. Different L₅ and r_d atomic deflection probabilities at L₄ = 80 mm.

r_d/mm	L₅/mm
r_d/mm	60	70	80	90	100	110	120	130	140	150
1.2	99.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%
1.3	97.8%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%
1.4	89.5%	92.3%	97.2%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%
1.5	82.9%	83.5%	87.8%	93.4%	98.7%	100.0%	100.0%	100.0%	100.0%	100.0%
1.6	76.2%	78.2%	82.3%	90.1%	95.4%	98.2%	100.0%	100.0%	100.0%	100.0%

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