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Heydarizadmotlagh F, Skinner TDG, Kato K, George MC, Hessels EA. Precision Measurement of the n=2 Triplet P J=1 to J=0 Fine Structure of Atomic Helium Using Frequency-Offset Separated Oscillatory Fields. PHYSICAL REVIEW LETTERS 2024; 132:163001. [PMID: 38701455 DOI: 10.1103/physrevlett.132.163001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2023] [Accepted: 02/28/2024] [Indexed: 05/05/2024]
Abstract
Increasing accuracy of the theory and experiment of the n=2 ^{3}P fine structure of helium has allowed for increasingly precise tests of quantum electrodynamics (QED), determinations of the fine-structure constant α, and limitations on possible beyond the standard model physics. Here we present a 2 ppb measurement of the J=1 to J=0 interval. The measurement is performed using frequency-offset separated-oscillatory fields. Our result of 29 616 955 018(60) Hz represents a landmark for helium fine-structure measurements, and, for the first time, will allow for a 1-ppb determination of the fine-structure constant when QED theory for the interval is improved.
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Affiliation(s)
- F Heydarizadmotlagh
- Department of Physics and Astronomy, York University, Toronto, Ontario M3J 1P3, Canada
| | - T D G Skinner
- Department of Physics and Astronomy, York University, Toronto, Ontario M3J 1P3, Canada
| | - K Kato
- Department of Physics and Astronomy, York University, Toronto, Ontario M3J 1P3, Canada
| | - M C George
- Department of Physics and Astronomy, York University, Toronto, Ontario M3J 1P3, Canada
| | - E A Hessels
- Department of Physics and Astronomy, York University, Toronto, Ontario M3J 1P3, Canada
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2
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Abstract
The technique of quantum electrodynamics (QED) calculations of energy levels in the helium atom is reviewed. The calculations start with the solution of the Schrödinger equation and account for relativistic and QED effects by perturbation expansion in the fine structure constant α. The nonrelativistic wave function is represented as a linear combination of basis functions depending on all three interparticle radial distances, r1, r2 and r = |r→1−r→2|. The choice of the exponential basis functions of the form exp(−αr1−βr2−γr) allows us to construct an accurate and compact representation of the nonrelativistic wave function and to efficiently compute matrix elements of numerous singular operators representing relativistic and QED effects. Calculations of the leading QED effects of order α5m (where m is the electron mass) are complemented with the systematic treatment of higher-order α6m and α7m QED effects.
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Sun YR, Hu SM. Precision spectroscopy of atomic helium. Natl Sci Rev 2020; 7:1818-1827. [PMID: 34691519 PMCID: PMC8288801 DOI: 10.1093/nsr/nwaa216] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2019] [Revised: 12/15/2019] [Accepted: 03/13/2020] [Indexed: 11/13/2022] Open
Abstract
Helium is a prototype three-body system and has long been a model system for developing quantum mechanics theory and computational methods. The fine-structure splitting in the 23P state of helium is considered to be the most suitable for determining the fine-structure constant α in atoms. After more than 50 years of efforts by many theorists and experimentalists, we are now working toward a determination of α with an accuracy of a few parts per billion, which can be compared to the results obtained by entirely different methods to verify the self-consistency of quantum electrodynamics. Moreover, the precision spectroscopy of helium allows determination of the nuclear charge radius, and it is expected to help resolve the 'proton radius puzzle'. In this review, we introduce the latest developments in the precision spectroscopy of the helium atom, especially the discrepancies among theoretical and experimental results, and give an outlook on future progress.
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Affiliation(s)
- Yu R Sun
- Hefei National Laboratory for Physical Sciences at Microscale, iChem Center, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Shui-Ming Hu
- Hefei National Laboratory for Physical Sciences at Microscale, iChem Center, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
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Chen S, Liang S, Sun W, Huang Y, Guan H, Gao K. Saturated fluorescence spectroscopy measurement apparatus based on metastable Li + beam with low energy. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2019; 90:043112. [PMID: 31043027 DOI: 10.1063/1.5088187] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2019] [Accepted: 03/23/2019] [Indexed: 06/09/2023]
Abstract
The apparatus for fluorescence spectroscopy measurement is developed to determine the fine structure (FS)/hyperfine structure (HFS) splittings of 1s2p 3PJ(J=0,1,2) states of Li+. The instrument is composed of a low energy Li+ ion source and a saturated fluorescence spectroscopic probing system. A low energy Li+ ion source, containing 1.8(7)% of 1s2s 3S1 metastable ions with an energy of ∼500 eV, is obtained by an electron bombardment process. The ion current can stay more than 250 h with the variation of ∼0.3%, and the divergence of ion beam is ∼0.5 mrad. The symmetric profile of Lamb dip signals of 1s2s 3S1--1s2p 3PJ transitions with linewidths of ∼50 MHz are obtained after subtracting Doppler background from the saturated fluorescence signals. A back-and-forth scan method is adopted to determine the FS/HFS splittings of 1s2p 3PJ states. Under these conditions, as a preliminary test, several splittings of 7Li+ are measured. The statistical uncertainties of the FS/HFS splittings are estimated to be less than 50 kHz, and the results are one order of magnitude better than previous results. The apparatus is feasible to precisely determine the splittings of energy levels of alkali and alkaline earth ions.
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Affiliation(s)
- Shaolong Chen
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
| | - Shiyong Liang
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
| | - Wei Sun
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
| | - Yao Huang
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
| | - Hua Guan
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
| | - Kelin Gao
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
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Kato K, Skinner TDG, Hessels EA. Ultrahigh-Precision Measurement of the n=2 Triplet P Fine Structure of Atomic Helium Using Frequency-Offset Separated Oscillatory Fields. PHYSICAL REVIEW LETTERS 2018; 121:143002. [PMID: 30339449 DOI: 10.1103/physrevlett.121.143002] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2018] [Indexed: 06/08/2023]
Abstract
For decades, improved theory and experiment of the n=2 ^{3}P fine structure of helium have allowed for increasingly precise tests of quantum electrodynamics, determinations of the fine-structure constant α, and limitations on possible beyond-the-standard-model physics. Here we use the new frequency-offset separated-oscillatory-fields technique to measure the 2^{3}P_{2}→2^{3}P_{1} interval. Our result of 2 291 176 590(25) Hz represents a major step forward in precision for helium fine-structure measurements.
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Affiliation(s)
- K Kato
- Department of Physics and Astronomy, York University, Toronto, Ontario M3J 1P3, Canada
| | - T D G Skinner
- Department of Physics and Astronomy, York University, Toronto, Ontario M3J 1P3, Canada
| | - E A Hessels
- Department of Physics and Astronomy, York University, Toronto, Ontario M3J 1P3, Canada
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7
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Li J, Holzmann M, Duchemin I, Blase X, Olevano V. Helium Atom Excitations by the GW and Bethe-Salpeter Many-Body Formalism. PHYSICAL REVIEW LETTERS 2017; 118:163001. [PMID: 28474954 DOI: 10.1103/physrevlett.118.163001] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2016] [Indexed: 06/07/2023]
Abstract
The helium atom is the simplest many-body electronic system provided by nature. The exact solution to the Schrödinger equation is known for helium ground and excited states, and it represents a benchmark for any many-body methodology. Here, we check the ab initio many-body GW approximation and the Bethe-Salpeter equation (BSE) against the exact solution for helium. Starting from the Hartree-Fock method, we show that the GW and the BSE yield impressively accurate results on excitation energies and oscillator strength, systematically improving the time-dependent Hartree-Fock method. These findings suggest that the accuracy of the BSE and GW approximations is not significantly limited by self-interaction and self-screening problems even in this few electron limit. We further discuss our results in comparison to those obtained by time-dependent density-functional theory.
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Affiliation(s)
- Jing Li
- Université Grenoble Alpes, 38000 Grenoble, France
- CNRS, Institut Néel, 38042 Grenoble, France
| | - Markus Holzmann
- Université Grenoble Alpes, 38000 Grenoble, France
- CNRS, LPMMC, 38042 Grenoble, France
- European Theoretical Spectroscopy Facility (ETSF), 38000 Grenoble, France
| | - Ivan Duchemin
- Université Grenoble Alpes, 38000 Grenoble, France
- CEA, INAC-MEM L_Sim, 38054 Grenoble, France
| | - Xavier Blase
- Université Grenoble Alpes, 38000 Grenoble, France
- CNRS, Institut Néel, 38042 Grenoble, France
| | - Valerio Olevano
- Université Grenoble Alpes, 38000 Grenoble, France
- CNRS, Institut Néel, 38042 Grenoble, France
- European Theoretical Spectroscopy Facility (ETSF), 38000 Grenoble, France
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Zheng X, Sun YR, Chen JJ, Jiang W, Pachucki K, Hu SM. Laser Spectroscopy of the Fine-Structure Splitting in the 2^{3}P_{J} Levels of ^{4}He. PHYSICAL REVIEW LETTERS 2017; 118:063001. [PMID: 28234532 DOI: 10.1103/physrevlett.118.063001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2016] [Indexed: 06/06/2023]
Abstract
The fine-structure splitting in the 2^{3}P_{J} (J=0, 1, 2) levels of ^{4}He is of great interest for tests of quantum electrodynamics and for the determination of the fine-structure constant α. The 2^{3}P_{0}-2^{3}P_{2} and 2^{3}P_{1}-2^{3}P_{2} intervals are measured by laser spectroscopy of the ^{3}P_{J}-2^{3}S_{1} transitions at 1083 nm in an atomic beam, and are determined to be 31 908 130.98±0.13 kHz and 2 291 177.56±0.19 kHz, respectively. Compared with calculations, which include terms up to α^{5}Ry, the deviation for the α-sensitive interval 2^{3}P_{0}-2^{3}P_{2} is only 0.22 kHz. It opens the window for further improvement of theoretical predictions and an independent determination of the fine-structure constant α with a precision of 2×10^{-9}.
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Affiliation(s)
- X Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale, iChem Center, University of Science and Technology of China, Hefei 230026, China
| | - Y R Sun
- Hefei National Laboratory for Physical Sciences at the Microscale, iChem Center, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - J-J Chen
- Hefei National Laboratory for Physical Sciences at the Microscale, iChem Center, University of Science and Technology of China, Hefei 230026, China
| | - W Jiang
- School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230026, China
| | - K Pachucki
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - S-M Hu
- Hefei National Laboratory for Physical Sciences at the Microscale, iChem Center, University of Science and Technology of China, Hefei 230026, China
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Puchalski M, Pachucki K. Quantum electrodynamics corrections to the 2P fine splitting in Li. PHYSICAL REVIEW LETTERS 2014; 113:073004. [PMID: 25170705 DOI: 10.1103/physrevlett.113.073004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2014] [Indexed: 06/03/2023]
Abstract
We consider quantum electrodynamics (QED) corrections to the fine splitting E(2P_{3/2})-E(2P_{1/2}) in the Li atom. We derive complete formulas for the mα^{6} and mα^{7}lnα contributions and calculate them numerically using highly optimized, explicitly correlated basis functions. The obtained results are in agreement with the most recent measurement, helping to resolve discrepancies between former ones and lay the foundation for the investigation of QED effects in light, many-electron atoms.
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Affiliation(s)
- Mariusz Puchalski
- Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland
| | - Krzysztof Pachucki
- Faculty of Physics, University of Warsaw, Hoża 69, 00-681 Warsaw, Poland
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12
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Smiciklas M, Shiner D. Determination of the fine structure constant using helium fine structure. PHYSICAL REVIEW LETTERS 2010; 105:123001. [PMID: 20867632 DOI: 10.1103/physrevlett.105.123001] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2010] [Indexed: 05/29/2023]
Abstract
We measure 31,908,131.25(30) kHz for the 2(3)}P J=0 to 2 fine structure interval in helium. The difference between this and theory to order mα7 (20 Hz numerical uncertainty) implies 0.22(30) kHz for uncalculated terms. The measurement is performed by using atomic beam and electro-optic laser techniques. Various checks include a 3He 2{3}S hyperfine measurement. We can obtain an independent value for the fine structure constant α with a 5 ppb experimental uncertainty. However, dominant mα8 terms (potentially 1.2 kHz) limit the overall uncertainty to a less competitive 20 ppb in α.
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Affiliation(s)
- Marc Smiciklas
- Department of Physics, University of North Texas, Denton, Texas 76203, USA
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13
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Pachucki K, Yerokhin VA. Fine structure of heliumlike ions and determination of the fine structure constant. PHYSICAL REVIEW LETTERS 2010; 104:070403. [PMID: 20366863 DOI: 10.1103/physrevlett.104.070403] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2010] [Indexed: 05/29/2023]
Abstract
We report a calculation of the fine-structure splitting in light heliumlike atoms, which accounts for all quantum electrodynamical effects up to order alpha{5} Ry. For the helium atom, we resolve the previously reported disagreement between theory and experiment and determine the fine-structure constant with an accuracy of 31 ppb. The calculational results are extensively checked by comparison with the experimental data for different nuclear charges and by evaluation of the hydrogenic limit of individual corrections.
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Affiliation(s)
- Krzysztof Pachucki
- Institute of Theoretical Physics, University of Warsaw, Hoza 69, 00-681 Warsaw, Poland
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14
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DeVore TR, Crosby DN, Myers EG. Improved measurement of the 1s2s 1S0-1s2p 3P1 interval in heliumlike silicon. PHYSICAL REVIEW LETTERS 2008; 100:243001. [PMID: 18643579 DOI: 10.1103/physrevlett.100.243001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2008] [Indexed: 05/26/2023]
Abstract
Using colinear fast-beam laser spectroscopy with copropagating and counter-propagating beams we have measured the 1s2s 1S0-1s2p 3P1 intercombination interval in 28Si12+ with the result 7230.585(6) cm{-1}. The experiment made use of a dual-wavelength, high-finesse, power build-up cavity excited by single-frequency lasers at 1319 and 1450 nm. The result will provide a precision test of ab initio relativistic many-body atomic theory at moderate Z.
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Affiliation(s)
- Thomas R DeVore
- Department of Physics, Florida State University, Tallahassee, Florida 32306-4350, USA
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15
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Precision Laser Spectroscopy of Li+ and Neutral Lithium. ACTA ACUST UNITED AC 2008. [DOI: 10.1007/978-3-540-75479-4_7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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16
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Pachucki K. Improved theory of helium fine structure. PHYSICAL REVIEW LETTERS 2006; 97:013002. [PMID: 16907371 DOI: 10.1103/physrevlett.97.013002] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2006] [Indexed: 05/11/2023]
Abstract
Improved theoretical predictions for the fine-structure splitting of 2(3)PJ levels in helium are obtained by the calculation of contributions of order alpha5 Ry. New results for transition frequencies nu(01) = 29616943.01(17) kHz and nu(12) = 2291161.13(30) kHz disagree significantly with the experimental values, indicating an outstanding problem in bound state QED.
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Affiliation(s)
- Krzysztof Pachucki
- Institute of Theoretical Physics, Warsaw University, Hoza 69, 00-681 Warsaw, Poland
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Mueller P, Wang LB, Drake GWF, Bailey K, Lu ZT, O'Connor TP. Fine structure of the 1s3p 3PJ level in atomic 4He: theory and experiment. PHYSICAL REVIEW LETTERS 2005; 94:133001. [PMID: 15903989 DOI: 10.1103/physrevlett.94.133001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2004] [Indexed: 05/02/2023]
Abstract
The fine structure intervals in helium have been the focus of many theoretical and experimental studies in recent years with most of them concentrating on the 1s2p (3)P(J) levels. Here, we report on a theoretical calculation and an experimental determination of the 1s2p (3)P(J) fine structure intervals. The values from the theoretical calculation are 8113.730(6) and 658.801(6) MHz for the nu(01) and nu(12) intervals, respectively. The laser spectroscopic measurement reported here yields 8113.714(28) and 658.810(18) MHz for these intervals and is in excellent agreement with the theoretical calculation. Both, however, disagree significantly with the previous most precise experimental results.
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Affiliation(s)
- P Mueller
- Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA.
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High Precision Measurements on Helium at 1083 nm. ACTA ACUST UNITED AC 2001. [DOI: 10.1007/3-540-45395-4_15] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/07/2023]
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20
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Yan ZC. Calculations of magnetic moments for three-electron atomic systems. PHYSICAL REVIEW LETTERS 2001; 86:5683-5686. [PMID: 11415332 DOI: 10.1103/physrevlett.86.5683] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2001] [Indexed: 05/23/2023]
Abstract
The first fully correlated calculations of the magnetic moment in lithium are presented. Relative to the free-electron value, the Zeeman gJ factor for the ground state lithium gJ/g(e)-1 is calculated to a computational accuracy of 200 parts in 10(9), including relativistic and radiative corrections of orders alpha2, alpha2m/M, and alpha3. The isotope shifts in gJ are predicted precisely for various isotopes. The extensions to the first excited S state of lithium and the ground state of Be+ are made.
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Affiliation(s)
- Z C Yan
- Department of Physics, University of New Brunswick, P.O. Box 4400, Fredericton, New Brunswick, Canada E3B 5A3
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Castillega J, Livingston D, Sanders A, Shiner D. Precise measurement of the J = 1 to J = 2 fine structure interval in the 2( 3)P state of helium. PHYSICAL REVIEW LETTERS 2000; 84:4321-4324. [PMID: 10990676 DOI: 10.1103/physrevlett.84.4321] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/1999] [Indexed: 05/23/2023]
Abstract
We measure the J = 1 to J = 2 fine structure interval in the ( 3)2P state of helium to be 2 291 175.9(1.0) kHz. We use laser excitation of an atomic beam along with an integrated electro-optic modulator technique to obtain this result. The result is consistent (2.9+/-3.2 kHz) with what could be considered an earlier version of this experiment but is not in good agreement ( 20+/-5 kHz and 22+/-8 kHz) with the two other precision determinations of this interval. The current theoretical prediction lies between and overlaps the experiments.
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Affiliation(s)
- J Castillega
- Department of Physics, University of North Texas, Denton, Texas 76203, USA
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Zhang T, Drake GW. Corrections to O( alpha 7mc2) fine-structure splittings in helium. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1996; 54:4882-4922. [PMID: 9914055 DOI: 10.1103/physreva.54.4882] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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