Theoretical study of laser cooling of potassium chloride anion

Wan Ming-Jie; Luo Hua-Feng; Yuan Di; Li Song

doi:10.7498/aps.68.20190869

Abstract

The potential energy curves and transition dipole moments (TDMs) for three Λ-S states (X²Σ⁺, A²Π, and B²Σ⁺) of potassium chloride anion (KCl^–) are investigated by using multi-reference configuration interaction (MRCI) method. The def2-AQZVPP-JKFI of K atom and AV5Z-DK all-electron basis set of Cl atom are used in all calculations. The Davidson correction, core-valence (CV) correction, and spin-orbit coupling effect (SOC) are also considered. In the complete active self-consistent field (CASSCF) calculations, eight molecular orbitals are selected as active orbitals, which includ K 4s4p and Cl 3s3p shells; K 3p shell is closed orbital, and the remaining shells (K 1s2s3s and Cl 1s2s2p) are frozen orbitals. In the MRCI+Q calculations, K 3p shell is used for the CV correction. There are 15 electrons in the correlation energy calculations. Then, their spectroscopic parameters, Einstein coefficients, Franck-Condon factors, and radiative lifetimes are obtained by solving the radial Schrödinger equation. The spectroscopic properties and transition properties for the Ω states are predicted. Highly diagonally distributed Franck-Condon factor f₀₀ values for the (2)1/2↔(1)1/2 and (1)3/2↔(1)1/2 transition are 0.8816 and 0.8808, respectively. And the short radiative lifetimes for the (2)1/2 and (1)3/2 excited states are also obtained, i.e. τ[(2)1/2] = 45.7 ns and τ[(1)3/2] = 45.5 ns, which can ensure laser cooling of KCl^– anion rapidly. The results indicate that the (2)1/2↔(1)1/2 and (1)3/2↔(1)1/2 quasicycling transitions are suitable to the building of laser cooling projects. For driving the (2)1/2↔(1)1/2 transition, a main pump laser (λ₀₀) and two repumping lasers (λ₁₀ and λ₂₁) are required. Their wavelengths are λ₀₀ = 1065.77 nm, λ₁₀ = 1090.13 nm and λ₂₁ = 1087.76 nm. For driving the (1)3/2↔(1)1/2 transition, the wavelengths are λ₀₀ = 1064.24 nm, λ₁₀ = 1088.54 nm, and λ₂₁ = 1086.17 nm. The cooling wavelengths of KCl^- anion for two transitions are both deep in the infrared range. Finally, the Doppler temperature and recoil temperature for two transitions are also calculated, respectively. The Doppler temperatures for (2)1/2↔(1)1/2 and (1)3/2(1)1/2 transitions are 83.57 μK and 83.93 μK, and the recoil temperatures for two transitions are 226 nK and 227 nK, respectively. for two transitions are 226 nK and 227 nK, respectively.

Keywords:

Authors and contacts

1.
School of Physics and Electronic Engineering, Yibin University, Yibin 644007, China
2.
College of Chemistry & Chemical Engineering, Yibin University, Yibin 644007, China
3.
School of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou 434023, China

Corresponding author: Wan Ming-Jie, wanmingjie1983@sina.com

Funds: Project supported by the Special Foundation for Theoretical Physics Research Program of China (Grant No. 11647075) and the Open Research Fund of Computational Physics Key Laboratory of Sichuan Province, Yibin University, China (Grant No. JSWL2018KFZ03).

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References

[1]	van Veldhoven J, Küpper J, Bethlem H L, Sartakov B, van Roij A J A, Meijer G 2004 Eur. Phys. J. D 31 337 Google Scholar
[2]	Micheli A, Brennen G K, Zoller P 2006 Nat. Phys. 2 341 Google Scholar
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图 1 KCl^-阴离子的势能曲线　(a) Λ-S态; (b) Ω态

Figure 1. Potential energy curves of KCl^– anion: (a) Λ-S states; (b) Ω states.

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图 2 KCl^-阴离子的偶极矩

Figure 2. Dipole moments (DMs) of KCl^- anion.

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图 3 KCl^–阴离子的跃迁偶极矩

Figure 3. Transition dipole moments (TDMs) of KCl^– anion

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图 4 激光冷却KCl^–阴离子的方案　(a) (2)1/2↔(1)1/2准闭合循环跃迁系统; (b) (1)3/2↔(1)1/2准闭合循环跃迁系统

Figure 4. Proposed laser cooling scheme of KCl^– anion: (a) Using (2)1/2↔(1)1/2 transition; (b) using (1)3/2↔(1)1/2 transition.

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表 1 KCl^–阴离子Ω电子态的离解极限

Table 1. The dissociation relationship for the Ω states of KCl^– anion.

原子态	Ω态	ΔE/cm^–1
原子态	Ω态	计算值	实验值^[33]
K(²S_1/2) + Cl^–(¹S₀)	(1)1/2	0	0
K(²P_1/2) + Cl^–(¹S₀)	(2)1/2	12997.94	12985.17
K(²P_3/2) + Cl^–(¹S₀)	(3)1/2, (1)3/2	13046.23	13042.89

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表 2 KCl^–阴离子的Ω态的光谱常数

Table 2. Spectroscopic parameters for the Ω states of KCl^– anion.

Ω态	对应的Λ-S态	R_e/Å	ω_e/cm^–1	B_e/cm^–1	D_e/eV	T_e/cm^–1
(1)1/2	X²Σ⁺	2.8290	212.34	0.1143	1.3483	0
(2)1/2	A²Π	2.7839	229.64	0.1180	1.7976	9375.30
(1)3/2	A²Π	2.7836	229.65	0.1180	1.8018	9388.68
(3)1/2	B²Σ⁺	2.7550	235.48	0.1205	1.3865	12746.21

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表 3 (2)1/2↔(1)1/2和(1)3/2↔(1)1/2跃迁的FCFs, A_{ν′ν′′}和τ

Table 3. FCFs, spontaneous emission rates A_{ν′ν′′} and spontaneous radiative lifetime τ for the (2)1/2↔(1)1/2 and (1)3/2↔(1)1/2 transitions.

跃迁		ν′′	0	1	2	3
(2)1/2↔(1)1/2		A_{ν′ν′′}/s^–1	1.9384(7)^a	2.3044(6)	1.7867(5)	1.1906(4)
	ν′ = 0	f_{ν′ν′′}	0.8816	0.1090	0.0088	0.0006
		τ/ns	45.7
		A_{ν′ν′′}/s^–1	2.5793(6)	1.4757(7)	4.0633(6)	5.0295(5)
	ν′ = 1	f_{ν′ν′′}	0.1128	0.6687	0.1914	0.0246
		τ/ns	45.5
		A_{ν′ν′′}/s^–1	1.3368(5)	4.7122(6)	1.0816(7)	5.3057(6)
	ν′ = 2	f_{ν′ν′′}	0.0056	0.2052	0.4883	0.2490
		τ/ns	45.4
(1)3/2↔(1)1/2		A_{ν′ν′′}/s^–1	1.9451(7)	2.3276(6)	1.8184(5)	1.2242(4)
	ν′ = 0	f_{ν′ν′′}	0.8808	0.1096	0.0089	0.0006
		τ/ns	45.5
		A_{ν′ν′′}/s^–1	2.6063(6)	1.4777(7)	5.1089(5)	4.7631(4)
	ν′ = 1	f_{ν′ν′′}	0.1134	0.6668	0.1924	0.0249
		τ/ns	45.4
		A_{ν′ν′′}/s^–1	1.3578(5)	4.7578(6)	1.0803(7)	5.3483(6)
	ν′ = 2	f_{ν′ν′′}	0.0057	0.2063	0.4857	0.2499
		τ/ns	45.2
注: ^a1.9384(7)表示1.9384 × 10⁷.

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表 4 (3)1/2↔(1)1/2, (3)1/2↔(2)1/2和(3)1/2↔(1)3/2跃迁的FCF, 总辐射速率A₀和辐射寿命

Table 4. FCFs, total emission rates A₀ and τ for the (3)1/2↔(1)1/2, (3)1/2↔(2)1/2 and (3)1/2↔(1)3/2 transitions.

跃迁	f₀₀	A₀/s^–1	τ₀/s
(3)1/2↔(1)1/2	0.7122	2.6535(7)	3.77(–8)
(3)1/2↔(2)1/2	0.9484	2.3716(5)	4.22(–6)
(3)1/2↔(1)3/2	0.9490	2.3435(5)	4.27(–6)
注: ^a1.9384(7)表示1.9384 × 10⁷.

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[1]	van Veldhoven J, Küpper J, Bethlem H L, Sartakov B, van Roij A J A, Meijer G 2004 Eur. Phys. J. D 31 337 Google Scholar
[2]	Micheli A, Brennen G K, Zoller P 2006 Nat. Phys. 2 341 Google Scholar
[3]	Willitsch S, Bell M T, Gingell A D, Procter S R, Softley T P 2008 Phys. Rev. Lett. 100 043203 Google Scholar
[4]	Shuman E S, Barry J F, de Mille D 2010 Nature 467 820 Google Scholar
[5]	Hummon M T, Yeo M, Stuhl B K, Collopy A L, Xia Y, Ye J 2013 Phys. Rev. Lett. 110 143001 Google Scholar
[6]	Zhelyazkova V, Cournol A, Wall T E, Matsushima A, Hudson J J, Hinds E A, Tarbutt M R, Sauer B E 2014 Phys. Rev. A 89 053416 Google Scholar
[7]	Gao Y, Gao T 2014 Phys. Rev. A 90 052506 Google Scholar
[8]	张云光, 张华, 窦戈, 徐建刚 2017 物理学报 66 233101 Google Scholar Zhang Y G, Zhang H, Dou G, Xu J G 2017 Acta Phys. Sin. 66 233101 Google Scholar
[9]	Cui J, Xu J G, Qi J X, Dou G, Zhang Y G 2018 Chin. Phys. B 27 103101 Google Scholar
[10]	Yzombard P, Hamamda M, Gerber S, Doser M, Comparat D 2015 Phys. Rev. Lett. 114 213001 Google Scholar
[11]	Wan M, Huang D, Yu Y, Zhang Y 2017 Phys. Chem. Chem. Phys. 19 27360 Google Scholar
[12]	万明杰, 李松, 金成国, 罗华锋 2019 物理学报 68 063103 Google Scholar Wan M J, Li S, Jin C G, Luo H F 2019 Acta Phys. Sin. 68 063103 Google Scholar
[13]	Zhang Q, Yang C, Wang M, Ma X, Liu W 2017 Spectrochim. Acta, Part A 182 130 Google Scholar
[14]	Zhang Q, Yang C, Wang M, Ma X, Liu W 2017 Spectrochim. Acta, Part A 185 365 Google Scholar
[15]	Huber K P, Herzberg G 1979 Constants of Diatomic Molecules (Vol. IV): Molecular Spectra and Molecular Structure (New York: Van Nostrand Reinhold) p358
[16]	Ram R S, Dulick M, Guo B, Zhang K Q, Bernath P F 1997 J. Mol. Spectrosc. 183 360 Google Scholar
[17]	Seth M, Pernpointner M, Bowmaker G A, Schwerdtfeger P 1999 Mol. Phys. 96 1767
[18]	Wan M J, Shao J X, Huang D H, Jin C G, Yu Y, Wang F H 2015 Phys. Chem. Chem. Phys. 17 26731 Google Scholar
[19]	Wan M J, Shao J X, Gao Y F, Huang D H, Yang J S, Cao Q L, Jin C G, Wang F H 2015 J. Chem. Phys. 143 024302 Google Scholar
[20]	Fu M K, Ma H T, Cao J W, Bian W S 2016 J. Chem. Phys. 144 184302 Google Scholar
[21]	Wan M J, Yuan D, Jin C G, Wang F H, Yang Y J, Yu Y, Shao J X 2016 J. Chem. Phys. 145 024309 Google Scholar
[22]	Yuan X, Yin S, Shen Y, Liu Y, Lian Y, Xu H F, Yan B 2018 J. Chem. Phys. 149 094306 Google Scholar
[23]	Werner H J, Knowles P J, Lindh R, et al. 2010 MOLPRO, version 2010.1, A Package of ab initio Programs, http://www.molpro.net
[24]	Knowles P J, Werner H J 1985 J. Chem. Phys. 82 5053 Google Scholar
[25]	Werner H J, Knowles P J 1988 J. Chem. Phys. 89 5803 Google Scholar
[26]	Xiao K L, Yang C L, Wang M S, Ma X G, Liu W W 2013 J. Chem. Phys. 139 074305 Google Scholar
[27]	Weigend F 2008 J. Comput. Chem. 29 167 Google Scholar
[28]	Woon D E, Dunning Jr T H 1993 J. Chem. Phys. 98 1358 Google Scholar
[29]	Berning A, Schweizer M, Werner H J, Knowles P J, Palmieri P 2000 Mol. Phys. 98 1823 Google Scholar
[30]	Le Roy R J Level 8.0: A Computer Program for Solving the Radial Schrödinger Equation for Bound and Quasibound Levels, University of Waterloo Chemical Physics Research Report CP-663. http://leroy.uwaterloo.ca/programs
[31]	Hotop H, Lineberger 1985 J. Phys. Chem. Ref. Data 14 731 Google Scholar
[32]	Berzinsh U, Gustafsson M, Hanstorp D, Klinkmueller A E, Ljungblad U, Maartensson-Pendrill A M 1995 Phys. Rev. A 51 231 Google Scholar
[33]	Moore C E 1971 Atomic Energy Levels (Vol. 1) Natl. Stand Ref. Data Ser. Natl. Bur. Stand. No. 35 (Washington, DC: U.S. GPO) p228
[34]	Kobayashi J, Aikawa K, Oasa K, Inouye S 2014 Phys. Rev. A 89 021401 Google Scholar
[35]	Cohen-Tannoudji C N 1998 Rev. Mod. Phys. 70 707 Google Scholar

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