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磁场中HD分子振转跃迁的超精细结构

唐家栋 刘乾昊 程存峰 胡水明

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磁场中HD分子振转跃迁的超精细结构

唐家栋, 刘乾昊, 程存峰, 胡水明

Hyperfine structure of ro-vibrational transition of HD in magnetic field

Tang Jia-Dong, Liu Qian-Hao, Cheng Cun-Feng, Hu Shui-Ming
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  • HD分子红外跃迁的精密测量被用以检验量子电动力学、确定质子-电子质量比等. 但HD分子的超精细结构分裂对于测量精度是一个很重要的限制因素, 并可能是实验中测得ν = 2—0谱带跃迁呈特殊线型的原因之一. 本文分别在耦合表象和非耦合表象下计算了HD分子振转跃迁的超精细结构, 并计算了不同外加磁场下HD分子(2–0)带中R(0), P(1), R(1)线的超精细结构, 模拟了10 K低温下对应的光谱结构. 结果表明, HD分子跃迁结构可随磁场发生明显变化. 这可能有助于分析HD分子跃迁特异线型产生的机制, 进一步获得其准确的跃迁中心频率, 用于基础物理学检验.
    The precise measurement of the infrared transition of hydrogen-deuterium (HD) molecule is used to test quantum electrodynamics and determine the proton-to-electron mass ratio. The saturated absorption spectrum of the R(1) line in the first overtone (2–0) band of HD molecule has been measured by the comb locked cavity ring-down spectroscopy (CRDS) method in Hefei [Tao L G, et al. 2018 Phys. Rev. Lett. 120 153001], and also by the noise-immune cavity-enhanced optical heterodyne molecular spectroscopy (NICE-OHMS) method in Amsterdam [Cozijn F M J, et al. 2018 Phys. Rev. Lett. 120 153002 ]. However, there is a significant difference between the line center positions obtained in these two studies. Later the discrepancy was found to be due to unexpected asymmetry in the line shape of the saturated absorption spectrum of the HD molecule. A possible reason is the superposition of multiple hyperfine splitting peaks in the saturated spectrum. However, this model strongly depends on the population transfer caused by intermolecular collisions, which is a lack of experimental and theoretical support. In this paper, the hyperfine structures of the ro-vibrational transition of HD are calculated in the coupled and uncoupled representations. The hyperfine structures of the R(0), P(1) and R(1) lines in the (2–0) band of HD molecule under different external magnetic fields are calculated. The corresponding spectral structures at a temperature of 10 K are simulated. The results show that the transition structure of HD molecule changes significantly with the externally applied magnetic field. The frequency shift of each hyperfine transition line also increases with the intensity of external magnetic field increasing. When the intensity of the external magnetic field is sufficiently high, the hyperfine lines are clearly divided into two branches, and they can be completely separated from each other. Because the dynamic effect of intermolecular collision and the energy level population transfer are very sensitive to the energy level structure, the comparison between experiment and theory will help us to analyze the mechanism of the observed special profiles. It will allow us to obtain accurate frequencies of these transitions, which can be used for testing the fundamental physics.
      通信作者: 胡水明, smhu@ustc.edu.cn
    • 基金项目: 中国科学院战略性先导科技专项(B类)(批准号: XDB21020100)和国家自然科学基金(批准号: 21688102)资助的课题
      Corresponding author: Hu Shui-Ming, smhu@ustc.edu.cn
    • Funds: Project supported by the Strategic Priority Research Program (B) of Chinese Academy of Sciences (Grant No. XDB21020100) and the National Natural Science Foundation of China (Grant No. 21688102)
    [1]

    Miller C E, Brown L R, Toth R A, Benner D C, Devi V M 2005 C. R. Phys. 6 876Google Scholar

    [2]

    Salumbides E J, Dickenson G D, Ivanov T I, Ubachs W 2011 Phys. Rev. Lett. 107 043005Google Scholar

    [3]

    Puchalski M, Komasa J, Czachorowski P, Pachucki K 2016 Phys. Rev. Lett. 117 263002Google Scholar

    [4]

    Korobov V I, Hilico L, Karr J P 2017 Phys. Rev. Lett. 118 233001Google Scholar

    [5]

    Biesheuvel J, Karr J P, Hilico L, Eikema K S E, Ubachs W, Koelemeij J C J 2016 Nat. Commun. 7 10385Google Scholar

    [6]

    Shelkovnikov A, Butcher R J, Chardonnet C, Amy-Klein A 2008 Phys. Rev. Lett. 100 150801Google Scholar

    [7]

    Wang J, Sun Y R, Tao L G, Liu A W, Hua T P, Meng F, Hu S M 2017 Rev. Sci. Instrum. 88 043108Google Scholar

    [8]

    Tao L G, Liu A W, Pachucki K, Komasa J, Sun Y R, Wang J, Hu S M 2018 Phys. Rev. Lett. 120 153001Google Scholar

    [9]

    Wang J, Sun Y R, Tao L G, Liu A W, Hu S M 2017 J. Chem. Phys. 147 091103Google Scholar

    [10]

    Tao L G, Hua T P, Sun Y R, Wang J, Liu A W, Hu S M 2018 J. Quant. Spectrosc. Radiat. Transfer 210 111Google Scholar

    [11]

    Liu G L, Wang J, Tan Y, Kang P, Bi Z, Liu A W, Hu S M 2019 J. Quant. Spectrosc. Radiat. Transfer 229 17Google Scholar

    [12]

    Hua T P, Sun Y R, Wang J, Hu C L, Tao L G, Liu A W, Hu S M 2019 Chin. J. Chem. Phys. 32 107Google Scholar

    [13]

    Cozijn F M J, Duprxe P, Salumbides E J, Eikema K S E, Ubachs W 2018 Phys. Rev. Lett. 120 153002Google Scholar

    [14]

    Diouf M L, Cozijn F M J, Darquié B, Salumbides E J, Ubachs W 2019 Opt. Lett. 44 4733Google Scholar

    [15]

    Hua T P, Sun Y R, Hu S M 2020 Opt. Lett. 45 4863Google Scholar

    [16]

    Quinn W E, Baker J M, LaTourrette J T, Ramsey N F 1958 Phys. Rev. 112 1929Google Scholar

    [17]

    Dupre P 2020 Phys. Rev. A 101 022504Google Scholar

    [18]

    Komasa J, Puchalski M, Pachucki K 2020 Phys. Rev. A 102 012814Google Scholar

    [19]

    Puchalski M, Komasa J, Pachucki K 2020 Phys. Rev. Lett. 125 253001Google Scholar

    [20]

    Breit G 1929 Phys. Rev. 34 553Google Scholar

    [21]

    Bowater I C, Brown J M, Carrington A 1973 Proc. R. Soc. London, Ser. A 333 265Google Scholar

    [22]

    Ramsey N F, Lewis H R 1957 Phys. Rev. 108 1246Google Scholar

    [23]

    Borde C, Hall J L, Kunasz C V, Hummer D G 1976 Phys. Rev. A 14 236Google Scholar

    [24]

    Hall J L, Borde C J, Uehara K 1976 Phys. Rev. Lett. 37 1339Google Scholar

  • 图 1  在磁场中测定HD分子振转跃迁

    Fig. 1.  Determination of the ro-vibrational transition of HD molecule in magnetic field.

    图 2  耦合表象下HD分子的角动量耦合示意图

    Fig. 2.  Angular momentums of the HD molecule in the coupled representation.

    图 3  计算得到的HD分子ν = 2—0带R(0)线的所有超精细跃迁谱线的频率偏移及其对应的相对线强度(有部分弱线在显示范围之外)

    Fig. 3.  Calculated frequency shifts of all hyperfine transition lines in the R(0) line in the ν = 2–0 band and their corresponding line intensities (some weak lines are outside the display range).

    图 4  计算得到的HD分子ν = 2—0带P(1)线的所有超精细跃迁谱线的频率偏移及其对应的相对线强度(有部分弱线在显示范围之外)

    Fig. 4.  Calculated frequency shifts of all hyperfine transition lines of ν = 2–0 band P (1) lines of HD molecule and their corresponding relative line intensities (some weak lines are outside the display range).

    图 5  计算得到的HD分子ν = 2—0带R(1)线的所有超精细跃迁谱线的频率偏移及其对应的相对线强度(有部分弱线在显示范围之外)

    Fig. 5.  Calculated frequency shifts of all hyperfine transition lines of HD molecule ν = 2–0 band R (1) line and their corresponding relative line intensities (some weak lines are outside the display range).

    图 6  HD分子R(0) (ν = 2—0)跃迁在轴向磁场下, Δm = + 1和Δm = –1两支超精细跃迁谱线光谱中心的频率偏移与磁场强度的关系

    Fig. 6.  Relationship between the magnetic field intensity and the frequency shift of the spectral center of the Δm = + 1 and Δm = – 1 hyperfine transitions of the R(0) (ν = 2–0) line of HD.

    图 7  在10 K的低温条件下, 分别在不同外加磁场下模拟的HD分子(2—0)带R(0)线、P(1)线、R(1)线的光谱

    Fig. 7.  Simulated spectra of R (0), P (1) and R (1) lines in the (2–0) band of HD under different magnetic fields at the temperature of 10 K.

    表 1  计算得到的R(0)线所有超精细跃迁谱线的频率偏移及其对应的相对线强度

    Table 1.  Calculated frequency shifts of all hyperfine transition lines in the R(0) line and their corresponding line intensities

    跃迁线0 G 100 G 300 G 1000 G
    频率偏移/kHz相对强度频率偏移/kHz相对强度频率偏移/kHz相对强度频率偏移/kHz相对强度
    Δm = + 1a→A–56.30.3333 –106.90.3333 –208.00.3333 –561.90.3333
    b1→B1–56.30.0000–100.60.1800–216.40.1157–656.90.0197
    b1→B2–1.40.2922–33.30.1533–146.50.2176–516.30.3136
    b1→B353.30.0411323.40.0000940.30.00003108.30.0000
    b2→B1–56.30.2000–461.00.0019–1297.60.0003–4261.10.0000
    b2→B2–1.40.0164–393.70.0018–1227.70.0001–4120.50.0000
    b2→B353.30.1169–37.00.3297–141.00.3329–495.90.3333
    c1→C1–114.10.1439–165.40.1619–286.00.1273–776.70.0315
    c1→C2–56.30.0000–93.40.0640–222.50.0372–699.20.0029
    c1→C3–1.40.0974–2.20.1070–129.50.1688–528.60.2990
    c1→C453.30.0137298.60.0000893.30.00002972.70.0000
    c1→C5179.30.0783432.10.00041032.20.00003181.20.0000
    c2→C1–114.10.0196–525.80.0018–1367.30.0004–4380.90.0000
    c2→C2–56.30.1000–453.80.0025–1303.80.0002–4303.50.0000
    c2→C3–1.40.0219–362.60.0015–1210.80.0003–4132.80.0000
    c2→C453.30.1559–61.90.1248–188.00.0859–631.60.0292
    c2→C5179.30.036071.70.2028–49.10.2465–423.00.3040
    d→D1–114.10.0587–445.70.0018–1309.30.0001–4366.40.0000
    d→D2–56.30.0333–353.70.0170–1198.00.0018–4198.30.0002
    d→D3–1.40.0164–163.30.0232–321.70.0236–867.00.0083
    d→D453.30.1169–84.80.0197–223.80.0063–690.00.0002
    d→D5179.30.107945.60.2716–73.90.3015–442.10.3247
    Δm =–1a→C1–114.10.0587–34.70.0616106.10.0884530.40.2835
    a→C2–56.30.033337.30.0446169.60.0865607.90.0249
    a→C3–1.40.0164128.50.2139262.60.1567778.50.0248
    a→C453.30.1169429.20.00461285.40.00064279.80.0001
    a→C5179.30.1079562.80.00861424.30.00114488.30.0001
    b1→D1–114.10.143945.50.1473164.20.1950545.00.2888
    b1→D2–56.30.0000137.50.1648275.50.1368713.10.0444
    b1→D3–1.40.0974327.90.00851151.70.00034044.40.0000
    b1→D453.30.0137406.40.00811249.60.00084221.40.0001
    b1→D5179.30.0783536.80.00451399.50.00044469.30.0000
    b2→D1–114.10.0196–314.90.0001–917.10.0000–3059.20.0000
    b2→D2–56.30.1000–222.90.0021–805.80.0000–2891.10.0000
    b2→D3–1.40.0219–32.50.249670.40.2653440.20.3123
    b2→D453.30.155946.00.0372168.40.0383617.20.0125
    b2→D5179.30.0360176.40.0442318.30.0297865.20.0085
    c1→E1–56.30.000055.20.3291159.40.3329514.40.3333
    c1→E2–1.40.2922375.00.00191201.00.00014084.70.0000
    c1→E353.30.0411452.70.00231297.20.00034269.70.0000
    c2→E1–56.30.2000–305.30.0003–921.90.0000–3089.90.0000
    c2→E2–1.40.016414.60.2593119.70.2884480.50.3223
    c2→E353.30.116992.30.0737215.90.0450665.50.0110
    d→F–56.30.3333–5.80.333395.30.3333449.30.3333
    下载: 导出CSV
  • [1]

    Miller C E, Brown L R, Toth R A, Benner D C, Devi V M 2005 C. R. Phys. 6 876Google Scholar

    [2]

    Salumbides E J, Dickenson G D, Ivanov T I, Ubachs W 2011 Phys. Rev. Lett. 107 043005Google Scholar

    [3]

    Puchalski M, Komasa J, Czachorowski P, Pachucki K 2016 Phys. Rev. Lett. 117 263002Google Scholar

    [4]

    Korobov V I, Hilico L, Karr J P 2017 Phys. Rev. Lett. 118 233001Google Scholar

    [5]

    Biesheuvel J, Karr J P, Hilico L, Eikema K S E, Ubachs W, Koelemeij J C J 2016 Nat. Commun. 7 10385Google Scholar

    [6]

    Shelkovnikov A, Butcher R J, Chardonnet C, Amy-Klein A 2008 Phys. Rev. Lett. 100 150801Google Scholar

    [7]

    Wang J, Sun Y R, Tao L G, Liu A W, Hua T P, Meng F, Hu S M 2017 Rev. Sci. Instrum. 88 043108Google Scholar

    [8]

    Tao L G, Liu A W, Pachucki K, Komasa J, Sun Y R, Wang J, Hu S M 2018 Phys. Rev. Lett. 120 153001Google Scholar

    [9]

    Wang J, Sun Y R, Tao L G, Liu A W, Hu S M 2017 J. Chem. Phys. 147 091103Google Scholar

    [10]

    Tao L G, Hua T P, Sun Y R, Wang J, Liu A W, Hu S M 2018 J. Quant. Spectrosc. Radiat. Transfer 210 111Google Scholar

    [11]

    Liu G L, Wang J, Tan Y, Kang P, Bi Z, Liu A W, Hu S M 2019 J. Quant. Spectrosc. Radiat. Transfer 229 17Google Scholar

    [12]

    Hua T P, Sun Y R, Wang J, Hu C L, Tao L G, Liu A W, Hu S M 2019 Chin. J. Chem. Phys. 32 107Google Scholar

    [13]

    Cozijn F M J, Duprxe P, Salumbides E J, Eikema K S E, Ubachs W 2018 Phys. Rev. Lett. 120 153002Google Scholar

    [14]

    Diouf M L, Cozijn F M J, Darquié B, Salumbides E J, Ubachs W 2019 Opt. Lett. 44 4733Google Scholar

    [15]

    Hua T P, Sun Y R, Hu S M 2020 Opt. Lett. 45 4863Google Scholar

    [16]

    Quinn W E, Baker J M, LaTourrette J T, Ramsey N F 1958 Phys. Rev. 112 1929Google Scholar

    [17]

    Dupre P 2020 Phys. Rev. A 101 022504Google Scholar

    [18]

    Komasa J, Puchalski M, Pachucki K 2020 Phys. Rev. A 102 012814Google Scholar

    [19]

    Puchalski M, Komasa J, Pachucki K 2020 Phys. Rev. Lett. 125 253001Google Scholar

    [20]

    Breit G 1929 Phys. Rev. 34 553Google Scholar

    [21]

    Bowater I C, Brown J M, Carrington A 1973 Proc. R. Soc. London, Ser. A 333 265Google Scholar

    [22]

    Ramsey N F, Lewis H R 1957 Phys. Rev. 108 1246Google Scholar

    [23]

    Borde C, Hall J L, Kunasz C V, Hummer D G 1976 Phys. Rev. A 14 236Google Scholar

    [24]

    Hall J L, Borde C J, Uehara K 1976 Phys. Rev. Lett. 37 1339Google Scholar

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出版历程
  • 收稿日期:  2021-03-16
  • 修回日期:  2021-04-15
  • 上网日期:  2021-06-07
  • 刊出日期:  2021-09-05

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