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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.-
Keywords:
- HD /
- hyperfine structure /
- Zeeman effect /
- ro-vibrational transition
[1] Miller C E, Brown L R, Toth R A, Benner D C, Devi V M 2005 C. R. Phys. 6 876
Google Scholar
[2] Salumbides E J, Dickenson G D, Ivanov T I, Ubachs W 2011 Phys. Rev. Lett. 107 043005
Google Scholar
[3] Puchalski M, Komasa J, Czachorowski P, Pachucki K 2016 Phys. Rev. Lett. 117 263002
Google Scholar
[4] Korobov V I, Hilico L, Karr J P 2017 Phys. Rev. Lett. 118 233001
Google Scholar
[5] Biesheuvel J, Karr J P, Hilico L, Eikema K S E, Ubachs W, Koelemeij J C J 2016 Nat. Commun. 7 10385
Google Scholar
[6] Shelkovnikov A, Butcher R J, Chardonnet C, Amy-Klein A 2008 Phys. Rev. Lett. 100 150801
Google 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 043108
Google 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 153001
Google Scholar
[9] Wang J, Sun Y R, Tao L G, Liu A W, Hu S M 2017 J. Chem. Phys. 147 091103
Google 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 210 111
Google 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 17
Google 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. 32 107
Google Scholar
[13] Cozijn F M J, Duprxe P, Salumbides E J, Eikema K S E, Ubachs W 2018 Phys. Rev. Lett. 120 153002
Google Scholar
[14] Diouf M L, Cozijn F M J, Darquié B, Salumbides E J, Ubachs W 2019 Opt. Lett. 44 4733
Google Scholar
[15] Hua T P, Sun Y R, Hu S M 2020 Opt. Lett. 45 4863
Google Scholar
[16] Quinn W E, Baker J M, LaTourrette J T, Ramsey N F 1958 Phys. Rev. 112 1929
Google Scholar
[17] Dupre P 2020 Phys. Rev. A 101 022504
Google Scholar
[18] Komasa J, Puchalski M, Pachucki K 2020 Phys. Rev. A 102 012814
Google Scholar
[19] Puchalski M, Komasa J, Pachucki K 2020 Phys. Rev. Lett. 125 253001
Google Scholar
[20] Breit G 1929 Phys. Rev. 34 553
Google Scholar
[21] Bowater I C, Brown J M, Carrington A 1973 Proc. R. Soc. London, Ser. A 333 265
Google Scholar
[22] Ramsey N F, Lewis H R 1957 Phys. Rev. 108 1246
Google Scholar
[23] Borde C, Hall J L, Kunasz C V, Hummer D G 1976 Phys. Rev. A 14 236
Google Scholar
[24] Hall J L, Borde C J, Uehara K 1976 Phys. Rev. Lett. 37 1339
Google Scholar
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图 1 在磁场中测定HD分子振转跃迁
Figure 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
Figure 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)
Figure 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)
Figure 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)
Figure 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
Figure 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
Figure 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 = + 1 a→A –56.3 0.3333 –106.9 0.3333 –208.0 0.3333 –561.9 0.3333 b1→B1 –56.3 0.0000 –100.6 0.1800 –216.4 0.1157 –656.9 0.0197 b1→B2 –1.4 0.2922 –33.3 0.1533 –146.5 0.2176 –516.3 0.3136 b1→B3 53.3 0.0411 323.4 0.0000 940.3 0.0000 3108.3 0.0000 b2→B1 –56.3 0.2000 –461.0 0.0019 –1297.6 0.0003 –4261.1 0.0000 b2→B2 –1.4 0.0164 –393.7 0.0018 –1227.7 0.0001 –4120.5 0.0000 b2→B3 53.3 0.1169 –37.0 0.3297 –141.0 0.3329 –495.9 0.3333 c1→C1 –114.1 0.1439 –165.4 0.1619 –286.0 0.1273 –776.7 0.0315 c1→C2 –56.3 0.0000 –93.4 0.0640 –222.5 0.0372 –699.2 0.0029 c1→C3 –1.4 0.0974 –2.2 0.1070 –129.5 0.1688 –528.6 0.2990 c1→C4 53.3 0.0137 298.6 0.0000 893.3 0.0000 2972.7 0.0000 c1→C5 179.3 0.0783 432.1 0.0004 1032.2 0.0000 3181.2 0.0000 c2→C1 –114.1 0.0196 –525.8 0.0018 –1367.3 0.0004 –4380.9 0.0000 c2→C2 –56.3 0.1000 –453.8 0.0025 –1303.8 0.0002 –4303.5 0.0000 c2→C3 –1.4 0.0219 –362.6 0.0015 –1210.8 0.0003 –4132.8 0.0000 c2→C4 53.3 0.1559 –61.9 0.1248 –188.0 0.0859 –631.6 0.0292 c2→C5 179.3 0.0360 71.7 0.2028 –49.1 0.2465 –423.0 0.3040 d→D1 –114.1 0.0587 –445.7 0.0018 –1309.3 0.0001 –4366.4 0.0000 d→D2 –56.3 0.0333 –353.7 0.0170 –1198.0 0.0018 –4198.3 0.0002 d→D3 –1.4 0.0164 –163.3 0.0232 –321.7 0.0236 –867.0 0.0083 d→D4 53.3 0.1169 –84.8 0.0197 –223.8 0.0063 –690.0 0.0002 d→D5 179.3 0.1079 45.6 0.2716 –73.9 0.3015 –442.1 0.3247 Δm =–1 a→C1 –114.1 0.0587 –34.7 0.0616 106.1 0.0884 530.4 0.2835 a→C2 –56.3 0.0333 37.3 0.0446 169.6 0.0865 607.9 0.0249 a→C3 –1.4 0.0164 128.5 0.2139 262.6 0.1567 778.5 0.0248 a→C4 53.3 0.1169 429.2 0.0046 1285.4 0.0006 4279.8 0.0001 a→C5 179.3 0.1079 562.8 0.0086 1424.3 0.0011 4488.3 0.0001 b1→D1 –114.1 0.1439 45.5 0.1473 164.2 0.1950 545.0 0.2888 b1→D2 –56.3 0.0000 137.5 0.1648 275.5 0.1368 713.1 0.0444 b1→D3 –1.4 0.0974 327.9 0.0085 1151.7 0.0003 4044.4 0.0000 b1→D4 53.3 0.0137 406.4 0.0081 1249.6 0.0008 4221.4 0.0001 b1→D5 179.3 0.0783 536.8 0.0045 1399.5 0.0004 4469.3 0.0000 b2→D1 –114.1 0.0196 –314.9 0.0001 –917.1 0.0000 –3059.2 0.0000 b2→D2 –56.3 0.1000 –222.9 0.0021 –805.8 0.0000 –2891.1 0.0000 b2→D3 –1.4 0.0219 –32.5 0.2496 70.4 0.2653 440.2 0.3123 b2→D4 53.3 0.1559 46.0 0.0372 168.4 0.0383 617.2 0.0125 b2→D5 179.3 0.0360 176.4 0.0442 318.3 0.0297 865.2 0.0085 c1→E1 –56.3 0.0000 55.2 0.3291 159.4 0.3329 514.4 0.3333 c1→E2 –1.4 0.2922 375.0 0.0019 1201.0 0.0001 4084.7 0.0000 c1→E3 53.3 0.0411 452.7 0.0023 1297.2 0.0003 4269.7 0.0000 c2→E1 –56.3 0.2000 –305.3 0.0003 –921.9 0.0000 –3089.9 0.0000 c2→E2 –1.4 0.0164 14.6 0.2593 119.7 0.2884 480.5 0.3223 c2→E3 53.3 0.1169 92.3 0.0737 215.9 0.0450 665.5 0.0110 d→F –56.3 0.3333 –5.8 0.3333 95.3 0.3333 449.3 0.3333 
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[1] Miller C E, Brown L R, Toth R A, Benner D C, Devi V M 2005 C. R. Phys. 6 876
Google Scholar
[2] Salumbides E J, Dickenson G D, Ivanov T I, Ubachs W 2011 Phys. Rev. Lett. 107 043005
Google Scholar
[3] Puchalski M, Komasa J, Czachorowski P, Pachucki K 2016 Phys. Rev. Lett. 117 263002
Google Scholar
[4] Korobov V I, Hilico L, Karr J P 2017 Phys. Rev. Lett. 118 233001
Google Scholar
[5] Biesheuvel J, Karr J P, Hilico L, Eikema K S E, Ubachs W, Koelemeij J C J 2016 Nat. Commun. 7 10385
Google Scholar
[6] Shelkovnikov A, Butcher R J, Chardonnet C, Amy-Klein A 2008 Phys. Rev. Lett. 100 150801
Google 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 043108
Google 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 153001
Google Scholar
[9] Wang J, Sun Y R, Tao L G, Liu A W, Hu S M 2017 J. Chem. Phys. 147 091103
Google 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 210 111
Google 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 17
Google 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. 32 107
Google Scholar
[13] Cozijn F M J, Duprxe P, Salumbides E J, Eikema K S E, Ubachs W 2018 Phys. Rev. Lett. 120 153002
Google Scholar
[14] Diouf M L, Cozijn F M J, Darquié B, Salumbides E J, Ubachs W 2019 Opt. Lett. 44 4733
Google Scholar
[15] Hua T P, Sun Y R, Hu S M 2020 Opt. Lett. 45 4863
Google Scholar
[16] Quinn W E, Baker J M, LaTourrette J T, Ramsey N F 1958 Phys. Rev. 112 1929
Google Scholar
[17] Dupre P 2020 Phys. Rev. A 101 022504
Google Scholar
[18] Komasa J, Puchalski M, Pachucki K 2020 Phys. Rev. A 102 012814
Google Scholar
[19] Puchalski M, Komasa J, Pachucki K 2020 Phys. Rev. Lett. 125 253001
Google Scholar
[20] Breit G 1929 Phys. Rev. 34 553
Google Scholar
[21] Bowater I C, Brown J M, Carrington A 1973 Proc. R. Soc. London, Ser. A 333 265
Google Scholar
[22] Ramsey N F, Lewis H R 1957 Phys. Rev. 108 1246
Google Scholar
[23] Borde C, Hall J L, Kunasz C V, Hummer D G 1976 Phys. Rev. A 14 236
Google Scholar
[24] Hall J L, Borde C J, Uehara K 1976 Phys. Rev. Lett. 37 1339
Google Scholar
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