Simulation of hyperfine-rotational spectrum of electromagnetic dipole transition rotation of BrF molecules

Chen Run; Shao Xu-Ping; Huang Yun-Xia; Yang Xiao-Hua

doi:10.7498/aps.72.20221957

Abstract

The transition dipole of the hyperfine-rotation spectrum of J = 1←0 within the vibronic ground (X¹Σ, v = 0) state of BrF molecule is derived, and thus, the transition selection rules are summarized as follows: ΔJ = ±1; ΔF₁ = 0, ±1 and ΔF = 0, ±1, and those of ΔF₁ = ΔF are intense while those of ΔF₁ ≠ ΔF are weak. Some spectral lines result from both the electric dipole transition and nuclear magnetic dipole transition due to perturbations, however, the magnetic dipole transition only contributes about one-billionth in the spectral intensity. The spectral linewidth is determined to be about 18 kHz by calculating the spectral transition probability. The obtained spectral linewidth and relative intensities are consistent with the experimental results. Additionally, the hyperfine-rotation spectral positions are determined by diagonalizing the Hamiltonian matrix in the basis of |JI₁F₁I₂F$\rangle $, which is also in good agreement with the experiments within 10^–8 (one-fiftieth of the spectral line width). Hence, the microwave hyperfine-rotation spectrum is simulated. In addition, we find that the nuclear spin-spin interaction not only slightly shifts the hyperfine-rotation spectral positions but also changes the sequence of the spectra. As to those unavailable constants of molecules, the fairly precise molecular constants can be achieved by quantum chemical calculation, say, by employing MOLPRO program, and then the simulated spectra can guide the spectral assignment. Besides the guidance of spectral assignment, our results are also helpful for other relevant applications such as in absolute single quantum state preparation.

Keywords:

Authors and contacts

School of Science, Nantong University, Nantong 226019, China

Corresponding author: Shao Xu-Ping, xuping1115@ntu.edu.cn ; Yang Xiao-Hua, xhyang@ntu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12004199).

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References

[1]	Bernath P F 2020 ????? (Oxford: Oxford University Press)
[2]	Kennedy C J, Oelker E, Robinson J M, Bothwell T, D. Kedar, Milner W R, Marti G E, Derevianko A, Ye J 2020 Phys. Rev. Lett. 125 201302 Google Scholar
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[4]	Denis M, Pi A, Timmermans R, Eliav E, Borschevsky A 2019 Phys. Rev. A 99 042512 Google Scholar
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[6]	Cairncross W B, Gresh D N, Grau M, Cossel K C, Roussy T S, Ni Y, Zhou Y, Ye J, Cornell E A 2017 Phys. Rev. Lett. 119 153001 Google Scholar
[7]	Bouchendira R, Cladé P, Biraben F 2011 Phys. Rev. Lett. 106 080801 Google Scholar
[8]	Webb J K, Flambaum V V, Churchill C W, Drinkwater M J, Barrow J D 1999 Phys. Rev. Lett. 82 884 Google Scholar
[9]	Liang Q, Chan Y C, Changala P B, Nesbitt D J, Ye J, Toscano J 2021 Proc. Natl. Acad. Sci. 118 e2105063118 Google Scholar
[10]	Kolkowitz S P I, Langellier N, Lukin M D, Walsworth R L and Ye J 2016 Phys. Rev. D 94 124043 Google Scholar
[11]	Valtolina G, Matsuda K, Tobias W G, Li J R, Marco L D, Ye J 2020 Nature 588 239 Google Scholar
[12]	William D, Phillips 1998 Rev. Mod. Phys. 70 721 Google Scholar
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[15]	Marco L D, Valtolina G, Matsuda K, Tobias W G, Covey J P, Ye J 2019 Science 363 853 Google Scholar
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[17]	Mccarron D J, Norrgard E B, Steinecker M H, Demille D 2015 New J. Phys. 17 035014 Google Scholar
[18]	Yeo M, Hummon M T, Collopy A L, Yan B, Hemmerling B, Chae E, Doyle J M, Ye J 2015 Phys. Rev. Lett. 114 223003 Google Scholar
[19]	Ni K K, Ospelkaus S, Miranda M, Pe'Er A, Neyenhuis B, Zirbel J J, Kotochigova S, Julienne P S, Jin D S, Ye J 2008 Science 322 231 Google Scholar
[20]	Peter, Molony K, Philip, Gregory D, Zhonghua, Ji, Bo, Lu, Michael, Köppinger P 2014 Phys. Rev. Lett. 113 255301 Google Scholar
[21]	Takekoshi T, Reichsoellner L, Schindewolf A, Hutson J M, Sueur C, Dulieu O, Ferlaino F, Grimm R, Naegerl H C 2014 Phys. Rev. Lett. 113 205301 Google Scholar
[22]	Park J W, Will S A, Zwierlein M W 2015 Phys. Rev. Lett. 114 205302 Google Scholar
[23]	Wang F, He X, Li X, Zhu B, Chen J, Wang D 2015 New J. Phys. 17 035003 Google Scholar
[24]	Matsuda K, Marco L D, Li J R, Tobias W G, Ye J 2020 Science 370 1324 Google Scholar
[25]	Gu Y, Chen K, Huang Y, Yang X 2019 Chin. Phys. B 28 43702 Google Scholar
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[34]	Yang Q S, Li S C, Yu Y, Gao T 2018 J Phys. Chem. A 122 3021 Google Scholar
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图 1 ⁷⁹BrF(上)和⁸¹BrF(下)振动基态(X¹Σ, v = 0)下的超精细能级. 图中还标明了各能级的能量值和量子数

Figure 1. Hyperfine-rotation energy levels of ⁷⁹BrF (upper) and ⁸¹BrF (lower) in the vibronic ground state (X¹Σ, v = 0). The quantum numbers and the values of the levels are labeled as well.

DownLoad: Full-Size Img PowerPoint

图 2 BrF振动基态(X¹Σ, v = 0)下J = 1←0转动超精细跃迁光谱模拟(下图), 红线代表⁷⁹BrF, 黑线代表⁸¹BrF. 两同位素丰度相差很小, 使得它们的光谱强度几乎相等. 超高分辨的光谱模拟见上图(⁷⁹BrF)和中图(⁸¹BrF), 其中, 谱线1.5, 1–1.5, 2, 1.5, 2–1.5, 1和2.5, 2–1.5, 2的相对强度极小, 导致它们无法观测到(蓝圈部分)

Figure 2. Simulated hyperfine-rotation spectra (lower) of the J = 1←0 transition within the vibronic ground state (X¹Σ, v = 0) of BrF of its two isotopes, ⁷⁹BrF in Red and ⁸¹BrF in black. Their spectral intensities are almost the same accordingly due to their nearly equal natural abundance of the two isotopes. Details of the spectra of ⁷⁹BrF (upper) and ⁸¹BrF (medium) of the unresolved spectra (lower) are plotted as well. Intensities of the spectra F₁, F = 1.5, 1–1.5, 2, 1.5, 2–1.5, 1 and 2.5, 2–1.5, 2 are too small to observe, as shown in the blue circles.

DownLoad: Full-Size Img PowerPoint

表 1 BrF(X¹Σ, v = 0)分子常数

Table 1. Molecular parameters of BrF(X¹Σ, v = 0)

	⁷⁹BrF	⁸¹BrF
B/MHz	10628.46302	10577.63957
D/kHz	12.028	11.956
eqQ/MHz	1086.89197	907.97681
C₁/kHz	89.051	95.818
C₂/kHz	–24.17	–24.54
C₃/kHz	–7.15	–7.71
C₄/kHz	4.86	5.24

DownLoad: CSV

表 2 BrF分子振动基态(X¹Σ, v = 0)中J = 1←0跃迁的转动超精细光谱计算值(单位: MHz), 同时列出了其与实验值的偏差和归一化光谱强度

Table 2. Calculated hyperfine-rotation spectra (in MHz) of the J = 1←0 transition in the vibronic ground state (X¹Σ, v = 0) of BrF molecule. Deviations (in MHz) from the experimental spectra and the normalized intensity are listed as well.

$F_1',F'\text{-}F''_1,F'' $	⁷⁹BrF		⁸¹BrF		强度 (归一化)
$F_1',F'\text{-}F''_1,F'' $	计算值	误差^a	计算值	误差^a	强度 (归一化)
0.5, 0–1.5, 1	20986.0744	0.0003	20928.7933	0	0.1428
0.5, 1–1.5, 1	20986.1035	–0.0011	20928.8236	0.0002	0.0917
1.5, 1–1.5, 1	21475.0918	0	21337.3854	0.0001	0.3571
1.5, 2–1.5, 1	21475.0730		21337.3660		0.0713
2.5, 2–1.5, 1	21203.1734	0.0001	21110.3358	0	0.6427
0.5, 1–1.5, 2	20986.0937	0	20928.8131	–0.0002	0.3570
1.5, 1–1.5, 2	21475.0820		21337.3749		0.0714
1.5, 2–1.5, 2	21475.0632	0	21337.3556	–0.0001	0.6427
2.5, 2–1.5, 2	21203.1636		21110.3253		0.0713
2.5, 3–1.5, 2	21203.1484	0	21110.3109	0	1
σ^b		0.0004		0.0001
^a 计算值减去参考文献中的实验值^[37], 误差缺失表示谱线强度太弱而实验无法观测到.
^b σ为计算总体方差.

DownLoad: CSV

表 3 BrF振动基态下的转动超精细跃迁偶极矩

Table 3. Hyperfine-rotation transition dipoles of BrF within its vibronic ground state.

$ (J' = 1)F_1', F' $	$(J'' = 0) F_1'', F''$
$ (J' = 1)F_1', F' $	0.5, 0	0.5, 1	1.5, 1	1.5, 2	2.5, 2	2.5, 3
1.5, 1	0.2247	0.1124	0.5616	0.1123	1.0110	0
1.5, 2	0	0.5617	0.1123	1.0110	0.1122	1.5728

DownLoad: CSV

[1]	Bernath P F 2020 ????? (Oxford: Oxford University Press)
[2]	Kennedy C J, Oelker E, Robinson J M, Bothwell T, D. Kedar, Milner W R, Marti G E, Derevianko A, Ye J 2020 Phys. Rev. Lett. 125 201302 Google Scholar
[3]	Changala P B, Weichman M L, Lee K F, Fermann M E, Ye J 2019 Science 363 49 Google Scholar
[4]	Denis M, Pi A, Timmermans R, Eliav E, Borschevsky A 2019 Phys. Rev. A 99 042512 Google Scholar
[5]	Hudson J J, Sauer B E, Tarbutt M R, Hinds E A 2002 Phys. Rev. Lett. 89 023003 Google Scholar
[6]	Cairncross W B, Gresh D N, Grau M, Cossel K C, Roussy T S, Ni Y, Zhou Y, Ye J, Cornell E A 2017 Phys. Rev. Lett. 119 153001 Google Scholar
[7]	Bouchendira R, Cladé P, Biraben F 2011 Phys. Rev. Lett. 106 080801 Google Scholar
[8]	Webb J K, Flambaum V V, Churchill C W, Drinkwater M J, Barrow J D 1999 Phys. Rev. Lett. 82 884 Google Scholar
[9]	Liang Q, Chan Y C, Changala P B, Nesbitt D J, Ye J, Toscano J 2021 Proc. Natl. Acad. Sci. 118 e2105063118 Google Scholar
[10]	Kolkowitz S P I, Langellier N, Lukin M D, Walsworth R L and Ye J 2016 Phys. Rev. D 94 124043 Google Scholar
[11]	Valtolina G, Matsuda K, Tobias W G, Li J R, Marco L D, Ye J 2020 Nature 588 239 Google Scholar
[12]	William D, Phillips 1998 Rev. Mod. Phys. 70 721 Google Scholar
[13]	Bethlem H L, Berden G, Meijer G 1999 Phys. Rev. Lett. 83 1558 Google Scholar
[14]	Barry F J, McCarron J D, Norrgard B E, Steinecker H M, DeMille D 2014 Nature 512 286 Google Scholar
[15]	Marco L D, Valtolina G, Matsuda K, Tobias W G, Covey J P, Ye J 2019 Science 363 853 Google Scholar
[16]	Hummon M T, Yeo M, Stuhl B K, Collopy A L, Xia Y, Ye J 2013 Phys. Rev. Lett. 110 143001 Google Scholar
[17]	Mccarron D J, Norrgard E B, Steinecker M H, Demille D 2015 New J. Phys. 17 035014 Google Scholar
[18]	Yeo M, Hummon M T, Collopy A L, Yan B, Hemmerling B, Chae E, Doyle J M, Ye J 2015 Phys. Rev. Lett. 114 223003 Google Scholar
[19]	Ni K K, Ospelkaus S, Miranda M, Pe'Er A, Neyenhuis B, Zirbel J J, Kotochigova S, Julienne P S, Jin D S, Ye J 2008 Science 322 231 Google Scholar
[20]	Peter, Molony K, Philip, Gregory D, Zhonghua, Ji, Bo, Lu, Michael, Köppinger P 2014 Phys. Rev. Lett. 113 255301 Google Scholar
[21]	Takekoshi T, Reichsoellner L, Schindewolf A, Hutson J M, Sueur C, Dulieu O, Ferlaino F, Grimm R, Naegerl H C 2014 Phys. Rev. Lett. 113 205301 Google Scholar
[22]	Park J W, Will S A, Zwierlein M W 2015 Phys. Rev. Lett. 114 205302 Google Scholar
[23]	Wang F, He X, Li X, Zhu B, Chen J, Wang D 2015 New J. Phys. 17 035003 Google Scholar
[24]	Matsuda K, Marco L D, Li J R, Tobias W G, Ye J 2020 Science 370 1324 Google Scholar
[25]	Gu Y, Chen K, Huang Y, Yang X 2019 Chin. Phys. B 28 43702 Google Scholar
[26]	Huang Y, Shao X, Yang X 2016 J. Phys. B 49 135101 Google Scholar
[27]	Chen K, Huang Y, Yang X 2017 Chin. J Chem. Phys. 30 418 Google Scholar
[28]	Smith D F, Tidwell M, Williams D V P 1950 Phys. Rev. 77 420 Google Scholar
[29]	Calder V, Hansen D, Hoffman D, Ruedenberg K 1972 J Chem. Phys. 49 5399
[30]	Nair K, Hoeft J, Tiemann E 1979 J Mol. Spectrosc. 78 506 Google Scholar
[31]	Clyne M A A, Curran A H, Coxon J A 1976 J Mol. Spectrosc. 63 43 Google Scholar
[32]	Aldegunde J, Hutson J M 2008 Phys. Rev. A 78 033434 Google Scholar
[33]	Wang D, Shao X, Huang Y, Li C, Yang X 2021 Chin. Phys. B 30 113301 Google Scholar
[34]	Yang Q S, Li S C, Yu Y, Gao T 2018 J Phys. Chem. A 122 3021 Google Scholar
[35]	Brown J M, Carrington A 2003 Cambridge University Press
[36]	Arima A, Horie H, Sano M 1957 Prog. Theor. Exp. Phys. 17 567 Google Scholar
[37]	Müller H S, Gerry M C 1995 J. Chem. Phys. 103 577 Google Scholar
[38]	Shao X, Gong T, Wu L, Yang X 2011 J. Quant. Spectrosc. Radiat. Transfer 112 1005 Google Scholar
[39]	Ospelkaus S, Ni K K, Quéméner G, Neyenhuis B, Wang D, Miranda M D, Bohn J, Ye J, Jin D 2010 Phys. Rev. Lett. 104 030402 Google Scholar

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