Relativistic hyperpolarizabilities of atomic H, Li, and Be+ systems

doi:10.1088/1674-1056/ad9911

中国物理B ›› 2025, Vol. 34 ›› Issue (2): 23202-023202.doi: 10.1088/1674-1056/ad9911

Relativistic hyperpolarizabilities of atomic H, Li, and Be⁺ systems

Shan-Shan Lu(卢闪闪)^1,2, Hong-Yuan Zheng(郑弘远)^1,2, Zong-Chao Yan(严宗朝)^3,1, James F. Babb⁴, and Li-Yan Tang(唐丽艳)^1,†

1 State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China;
2 University of Chinese Academy of Sciences, Beijing 100049, China;
3 Department of Physics, University of New Brunswick, Fredericton, New Brunswick, E 3 B 5 A 3, Canada;
4 ITAMP, Center for Astrophysics|Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA

收稿日期:2024-10-06 修回日期:2024-11-13 接受日期:2024-12-02 出版日期:2025-02-15 发布日期:2025-01-15
通讯作者: Li-Yan Tang E-mail:lytang@apm.ac.cn
基金资助:
This work was supported by the National Natural Science Foundation of China (Grant Nos. 12174402 and 12393821), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant Nos. XDB0920100 and XDB0920101), and the Nature Science Foundation of Hubei Province (Grant Nos. 2019CFA058 and 2022CFA013). ZCY was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). JFB was supported in part by NSF grant PHY-2116679. All the calculations are finished on the APM-Theoretical Computing Cluster (APMTCC).

Relativistic hyperpolarizabilities of atomic H, Li, and Be⁺ systems

Shan-Shan Lu(卢闪闪)^1,2, Hong-Yuan Zheng(郑弘远)^1,2, Zong-Chao Yan(严宗朝)^3,1, James F. Babb⁴, and Li-Yan Tang(唐丽艳)^1,†

1 State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China;
2 University of Chinese Academy of Sciences, Beijing 100049, China;
3 Department of Physics, University of New Brunswick, Fredericton, New Brunswick, E 3 B 5 A 3, Canada;
4 ITAMP, Center for Astrophysics|Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA

Received:2024-10-06 Revised:2024-11-13 Accepted:2024-12-02 Online:2025-02-15 Published:2025-01-15
Contact: Li-Yan Tang E-mail:lytang@apm.ac.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (Grant Nos. 12174402 and 12393821), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant Nos. XDB0920100 and XDB0920101), and the Nature Science Foundation of Hubei Province (Grant Nos. 2019CFA058 and 2022CFA013). ZCY was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). JFB was supported in part by NSF grant PHY-2116679. All the calculations are finished on the APM-Theoretical Computing Cluster (APMTCC).

摘要/Abstract

摘要： For atoms in external electric fields, the hyperpolarizabilities are the coefficients describing the nonlinear interactions contributing to the induced energies at the fourth power of the applied electric fields. Accurate evaluations of these coefficients for various systems are crucial for improving precision in advanced atom-based optical lattice clocks and for estimating field-induced effects in atoms for quantum information applications. However, there is a notable scarcity of research on atomic hyperpolarizabilities, especially in the relativistic realm. Our work addresses this gap by establishing a novel set of alternative formulas for the hyperpolarizability based on the fourth-order perturbation theory. These formulas offer a more reasonable regrouping of scalar and tensor components compared to previous formulas, thereby enhancing their correctness and applicability. To validate our formulas, we perform the calculations for the ground and low-lying excited pure states of few-electron atoms H, Li, and Be$^+$. The highly accurate results obtained for the H atom could serve as benchmarks for further development of other theoretical methods.

关键词: hyperpolarizabilities, Stark effect, fourth-order perturbation, few-electron atoms

Abstract: For atoms in external electric fields, the hyperpolarizabilities are the coefficients describing the nonlinear interactions contributing to the induced energies at the fourth power of the applied electric fields. Accurate evaluations of these coefficients for various systems are crucial for improving precision in advanced atom-based optical lattice clocks and for estimating field-induced effects in atoms for quantum information applications. However, there is a notable scarcity of research on atomic hyperpolarizabilities, especially in the relativistic realm. Our work addresses this gap by establishing a novel set of alternative formulas for the hyperpolarizability based on the fourth-order perturbation theory. These formulas offer a more reasonable regrouping of scalar and tensor components compared to previous formulas, thereby enhancing their correctness and applicability. To validate our formulas, we perform the calculations for the ground and low-lying excited pure states of few-electron atoms H, Li, and Be$^+$. The highly accurate results obtained for the H atom could serve as benchmarks for further development of other theoretical methods.

Key words: hyperpolarizabilities, Stark effect, fourth-order perturbation, few-electron atoms

中图分类号: (Zeeman and Stark effects)

32.60.+i

32.10.Dk (Electric and magnetic moments, polarizabilities) 31.15.xp (Perturbation theory) 31.15.ac (High-precision calculations for few-electron (or few-body) atomic systems)

Shan-Shan Lu(卢闪闪), Hong-Yuan Zheng(郑弘远), Zong-Chao Yan(严宗朝), James F. Babb, and Li-Yan Tang(唐丽艳). Relativistic hyperpolarizabilities of atomic H, Li, and Be⁺ systems[J]. 中国物理B, 2025, 34(2): 23202-023202.

Shan-Shan Lu(卢闪闪), Hong-Yuan Zheng(郑弘远), Zong-Chao Yan(严宗朝), James F. Babb, and Li-Yan Tang(唐丽艳). Relativistic hyperpolarizabilities of atomic H, Li, and Be⁺ systems[J]. Chin. Phys. B, 2025, 34(2): 23202-023202.

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Relativistic hyperpolarizabilities of atomic H, Li, and Be⁺ systems

Relativistic hyperpolarizabilities of atomic H, Li, and Be⁺ systems

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