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## 留言板

Stark structure of atomic gallium

## Stark structure of atomic gallium

Dong Hui-Jie, Wang Xin-Yu, Li Chang-Yong, Jia Suo-Tang
• #### Abstract

The Stark effect in Rydberg atoms has potential applications in the areas of dipole-dipole interaction, quantum information, quantum control, and so on. Many reflevant theoretical calculations and experimental studies about the Stark effect of alkali metal and alkali earth metals have been reported, but the other atom’s Stark effect is studied still relatively less. Our goal in this paper is to reflearch the third main group atom’s Stark effect in a large electric field. First, according to the level data of gallium atom in zero-field, we obtain the quantum defects from the modified Ritz formula in each state by using a nonlinear least-squares-fitting algorithm. The quantum defects as a function of the principal quantum number are analyzed in detail. Influences of both the core polarization and the penetrating valence electron on the quantum defect are discussed according to the fitting results. Then we use the Numerov algorithm to calculate the radial wave functions of atomic gallium. Finally, the Stark structures of Rydberg states around n=7 and n=18 are numerically calculated by matrix diagonalization. Results show that at the levels above n=7 manifold states, (n+1)P is higher than nD state, and it is in contrast to the levels below the n=7 manifold states. This phenomenon is different from the usual Stark structure of alkali metal atoms, the level’s order of which does not change with the principal quantum number. The Stark levels with the identical |m| anti-cross each other, and those with different |m| cross. Our results give an important reflerence for related reflearches, and are of great significance for insight into the atomic structure and the interaction between the atomic core and the highly excited electrons.

#### Authors and contacts

• Funds: Project supported by the National Basic Research Program of China (Grant No. 2012CB921603), the National Natural Science Foundation of China (Grant Nos. 61378039, 61078013, 61178009, 11274209), the Program for Changjiang Scholars and Innovative Research Team in University of Ministry of Education of China (Grant No. IRT13076), the Fund for Fostering Talents in Basic Science of the National Natural Science Foundation of China (Grant No. J1210036), and the Natural Science Foundation of Shanxi Province, China (Grant No. 2012011003-2).

#### References

 [1] Silverstone H J 1978 Phys. Rev. A 18 1853 [2] Zimmerman M L, Littman M G, Kash M M, Kleppner D 1979 Phys. Rev. A 20 2251 [3] Hu Z F, Zhao H T, Zhou S K, Gong S S, Shan M S 2000 Chin. Phys. B 9 805 [4] Wang L M, Zhang H, Li C Y, Zhao J M, Jia S T 2013 Acta Phys. Sin. 62 013201 (in Chinese) [王丽梅, 张好, 李昌勇, 赵建明, 贾锁堂 2013 物理学报 62 013201] [5] Zhu X B, Zhang H, Feng Z G, Zhang L J, Li C Y, Zhao J M, Jia S T 2010 Acta Phys. Sin. 59 2405 (in Chinese) [朱兴波, 张好, 冯志刚, 张临杰, 李昌勇, 赵建明, 贾锁堂 2010 物理学报 59 2405] [6] Singer K, Reetz-Lamour M, Amthor T, Folling S, Tscherneck M, Weidemuller M 2005 J. Phys. B 38 S321 [7] Zhi M C, Dai C J, Li S B 2001 Chin. Phys. B 10 929 [8] Yang H F, Gao W, Cheng H, Liu X J, Liu H P 2013 Chin. Phys. B 22 013202 [9] Kampschulte T, Schulze J, Luggenholscher D, Bowden M, Czarnetzki U 2007 New J. Phys. 9 18 [10] Li C Y, Hao T, Zhang H, Zhu X B, Tao G Q, Zhang L J, Zhao J M, Jia S T 2012 J. Phys. Soc. Jpn. 81 044302 [11] Li C Y, Zhang L J, Zhao J M, Jia S T 2012 Acta Phys. Sin. 61 163202 (in Chinese) [李昌勇, 张临杰, 赵建明, 贾锁堂 2012 物理学报 61 163202] [12] Dong H J, Wang T, Li C Y, Zhao J M, Zhang L J 2013 Chin. Phys. B 22 073201 [13] Dong H J, Huang K S, Zhao J M, Zhang L J, Jia S T 2014 Chin. Phys. B 23 093202 [14] Tao G Q, Li C Y, Zhang L J, Zhao J M, Jia S T 2009 Acta Sinica Quantum Optica 15 185 (in Chinese) [陶冠奇, 李昌勇, 张临杰, 赵建明, 贾锁堂 2009 量子光学学报 15 185] [15] Weber K H, Sansonnetti C J 1987 Phys. Rev. A 1987 35 4650

#### Cited By

•  [1] Silverstone H J 1978 Phys. Rev. A 18 1853 [2] Zimmerman M L, Littman M G, Kash M M, Kleppner D 1979 Phys. Rev. A 20 2251 [3] Hu Z F, Zhao H T, Zhou S K, Gong S S, Shan M S 2000 Chin. Phys. B 9 805 [4] Wang L M, Zhang H, Li C Y, Zhao J M, Jia S T 2013 Acta Phys. Sin. 62 013201 (in Chinese) [王丽梅, 张好, 李昌勇, 赵建明, 贾锁堂 2013 物理学报 62 013201] [5] Zhu X B, Zhang H, Feng Z G, Zhang L J, Li C Y, Zhao J M, Jia S T 2010 Acta Phys. Sin. 59 2405 (in Chinese) [朱兴波, 张好, 冯志刚, 张临杰, 李昌勇, 赵建明, 贾锁堂 2010 物理学报 59 2405] [6] Singer K, Reetz-Lamour M, Amthor T, Folling S, Tscherneck M, Weidemuller M 2005 J. Phys. B 38 S321 [7] Zhi M C, Dai C J, Li S B 2001 Chin. Phys. B 10 929 [8] Yang H F, Gao W, Cheng H, Liu X J, Liu H P 2013 Chin. Phys. B 22 013202 [9] Kampschulte T, Schulze J, Luggenholscher D, Bowden M, Czarnetzki U 2007 New J. Phys. 9 18 [10] Li C Y, Hao T, Zhang H, Zhu X B, Tao G Q, Zhang L J, Zhao J M, Jia S T 2012 J. Phys. Soc. Jpn. 81 044302 [11] Li C Y, Zhang L J, Zhao J M, Jia S T 2012 Acta Phys. Sin. 61 163202 (in Chinese) [李昌勇, 张临杰, 赵建明, 贾锁堂 2012 物理学报 61 163202] [12] Dong H J, Wang T, Li C Y, Zhao J M, Zhang L J 2013 Chin. Phys. B 22 073201 [13] Dong H J, Huang K S, Zhao J M, Zhang L J, Jia S T 2014 Chin. Phys. B 23 093202 [14] Tao G Q, Li C Y, Zhang L J, Zhao J M, Jia S T 2009 Acta Sinica Quantum Optica 15 185 (in Chinese) [陶冠奇, 李昌勇, 张临杰, 赵建明, 贾锁堂 2009 量子光学学报 15 185] [15] Weber K H, Sansonnetti C J 1987 Phys. Rev. A 1987 35 4650
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•  Citation:
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• Abstract views:  932
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##### Publishing process
• Received Date:  09 October 2014
• Accepted Date:  16 December 2014
• Published Online:  05 May 2015

## Stark structure of atomic gallium

• 1. State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China
Fund Project:  Project supported by the National Basic Research Program of China (Grant No. 2012CB921603), the National Natural Science Foundation of China (Grant Nos. 61378039, 61078013, 61178009, 11274209), the Program for Changjiang Scholars and Innovative Research Team in University of Ministry of Education of China (Grant No. IRT13076), the Fund for Fostering Talents in Basic Science of the National Natural Science Foundation of China (Grant No. J1210036), and the Natural Science Foundation of Shanxi Province, China (Grant No. 2012011003-2).

Abstract: The Stark effect in Rydberg atoms has potential applications in the areas of dipole-dipole interaction, quantum information, quantum control, and so on. Many reflevant theoretical calculations and experimental studies about the Stark effect of alkali metal and alkali earth metals have been reported, but the other atom’s Stark effect is studied still relatively less. Our goal in this paper is to reflearch the third main group atom’s Stark effect in a large electric field. First, according to the level data of gallium atom in zero-field, we obtain the quantum defects from the modified Ritz formula in each state by using a nonlinear least-squares-fitting algorithm. The quantum defects as a function of the principal quantum number are analyzed in detail. Influences of both the core polarization and the penetrating valence electron on the quantum defect are discussed according to the fitting results. Then we use the Numerov algorithm to calculate the radial wave functions of atomic gallium. Finally, the Stark structures of Rydberg states around n=7 and n=18 are numerically calculated by matrix diagonalization. Results show that at the levels above n=7 manifold states, (n+1)P is higher than nD state, and it is in contrast to the levels below the n=7 manifold states. This phenomenon is different from the usual Stark structure of alkali metal atoms, the level’s order of which does not change with the principal quantum number. The Stark levels with the identical |m| anti-cross each other, and those with different |m| cross. Our results give an important reflerence for related reflearches, and are of great significance for insight into the atomic structure and the interaction between the atomic core and the highly excited electrons.

Reference (15)

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