Measurement of a helium tune-out frequency: an independent test of quantum electrodynamics

Henson, B. M.; Ross, J. A.; Thomas, Kieran F.; Kuhn, Carlos Noschang; Shin, D. K.; Hodgman, Sean; Zhang, Yong-Hui; Tang, Li-Yan; Drake, G. W. F.; Bondy, Aaron; Truscott, A. G.; Baldwin, K. G. H.

doi:10.1126/science.abk2502

Cited by 18 publications

(5 citation statements)

References 66 publications

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“…It can be seen from Table VII that the C-BSBF can determine the accuracy of the 2 3 S − 2 1 S transition frequency (up to mα 5 -order correction) to the kHz level, which is consistent with the Recently, Mitroy and Tang suggested testing the QED theory using tune-out wavelength, which opens a new way to test fundamental atomic structure theory [48]. The 413 nm tune-out wavelengths for the helium atom 2 3 S 1 state discrepancies in the latest experiments by Baldwin's team and theoretical values by Drake based on the Hylleraas basis set with the NRQED method [49], in which the calculation only estimates the electric-field dependence of the Bethe logarithm [50]. The precision of the experiment is expected to improve further, and the QED theory will be tested at higher precision.…”

Section: Discussionsupporting

confidence: 75%

Application of the correlated B-spline basis functions to the leading relativistic and QED corrections of helium

Hao¹,

Zhang²,

Zhang³

et al. 2023

Preprint

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B-spline functions have been widely used in computational atomic physics. Different from the traditional B-spline basis (a simple product of two B-splines), the recently developed correlated B-spline basis functions(C-BSBF), in which the interelectronic coordinate r12 is included explicitly, have greatly improved the computational accuracy of polarizability [S. J. Yang et al., Phys. Rev. A 95, 062505 (2017)] and bethe logarithm [ S. J. Yang et al., Phys. Rev. A 100, 042509 (2019)] for singlet states of helium. Here, we report the extension of the C-BSBF to the leading relativistic and QED correction calculations for energy levels of the 1 1 S, 2 1 S, 2 3 S, and 3 3 S states of helium. The relativistic kinetic term p 4 1 , contact potential δ 3 (r1), δ 3 (r12) and Araki-Sucher correction 1/r 3 12 are calculated by using the global operator method, in which r n 12 and r n 12 ln r12 involved are calculated with the generalization of Laplace's expansions. The obtained values for the ground state are δE rel /α 2 = −1.951 754 7(2) and δEQED/α 3 =57.288 165(2), consistent with previous results, which opens the possibility of calculating higher-order relativistic and QED effects using the C-BSBF.

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Section: Discussionsupporting

confidence: 75%

Application of the correlated B-spline basis functions to the leading relativistic and QED corrections of helium

Hao¹,

Zhang²,

Zhang³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…The non-relativistic quantum electrodynamics framework, which systematically includes all relativistic and quantum electrodynamics (QED) corrections to the non-relativistic energy with increasing powers of the α fine structure constant is the current state of the art for small and light atomic and molecular systems [1][2][3][4][5][6][7][8][9][10]. Higher precision or higher charge numbers assume the derivation and evaluation of high-order perturbative corrections.…”

Section: Introductionmentioning

confidence: 99%

Variational vs perturbative relativistic energies for small and light atomic and molecular systems

Ferenc

Jeszenszki

Mátyus

2022

The Journal of Chemical Physics

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Variational and perturbative relativistic energies are computed and compared for two-electron atoms and molecules with low nuclear charge numbers. In general, good agreement of the two approaches is observed. Remaining deviations can be attributed to higher-order relativistic, also called non-radiative quantum electrodynamics (QED), corrections of the perturbative approach that are automatically included in the variational solution of the no-pair Dirac--Coulomb--Breit (DCB) equation to all orders of the $\alpha$ fine-structure constant. The analysis of the polynomial $\alpha$ dependence of the DCB energy makes it possible to determine the leading-order relativistic correction to the non-relativistic energy to high precision without regularization. Contributions from the Breit--Pauli Hamiltonian, for which expectation values converge slowly due the singular terms, are implicitly included in the variational procedure. The $\alpha$ dependence of the no-pair DCB energy shows that the higher-order ($\alpha^4 E_\mathrm{h}$) non-radiative QED correction is 5~\% of the leading-order ($\alpha^3 E_\mathrm{h}$) non-radiative QED correction for $Z=2$ (He), but it is 40~\% already for $Z=4$ (Be$^{2+}$), which indicates that resummation provided by the variational procedure is important already for intermediate nuclear charge numbers.

show abstract

Section: Introductionmentioning

confidence: 99%

Variational versus perturbative relativistic energies for small and light atomic and molecular systems

Ferenc¹,

Jeszenszki²,

Mátyus³

2022

Preprint

View full text Add to dashboard Cite

Variational and perturbative relativistic energies are computed and compared for two-electron atoms and molecules with low nuclear charge numbers. In general, good agreement of the two approaches is observed. Remaining deviations can be attributed to higher-order relativistic, also called nonradiative quantum electrodynamics (QED), corrections of the perturbative approach that are automatically included in the variational solution of the no-pair Dirac-Coulomb-Breit (DCB) equation to all orders of the α fine-structure constant. The analysis of the polynomial α dependence of the DCB energy makes it possible to determine the leading-order relativistic correction to the nonrelativistic energy to high precision without regularization. Contributions from the Breit-Pauli Hamiltonian, for which expectation values converge slowly due the singular terms, are implicitly included in the variational procedure. The α dependence of the no-pair DCB energy shows that the higher-order (α 4 E h ) non-radiative QED correction is 5 % of the leading-order (α 3 E h ) non-radiative QED correction for Z = 2 (He), but it is 40 % already for Z = 4 (Be 2+ ), which indicates that resummation provided by the variational procedure is important already for intermediate nuclear charge numbers.

show abstract

Measurement of a helium tune-out frequency: an independent test of quantum electrodynamics

Cited by 18 publications

References 66 publications

Application of the correlated B-spline basis functions to the leading relativistic and QED corrections of helium

Application of the correlated B-spline basis functions to the leading relativistic and QED corrections of helium

Variational vs perturbative relativistic energies for small and light atomic and molecular systems

Variational versus perturbative relativistic energies for small and light atomic and molecular systems

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