|
|
|
Theoretical calculations on Landé $g$-factors and quadratic Zeeman shift coefficients of $n$s$n$p $^{3} {P}^{o}_{0}$ clock states in Mg and Cd optical lattice clocks |
| Benquan Lu(卢本全)1 and Hong Chang(常宏)1,2,† |
1 National Time Service Center, Chinese Academy of Sciences, Xi'an 710600, China;
2 The University of Chinese Academy of Sciences, Beijing 100088, China |
|
|
|
|
Abstract The study of magnetic field effects on the clock transition of Mg and Cd optical lattice clocks is scarce. In this work, the hyperfine-induced Landé $g$-factors and quadratic Zeeman shift coefficients of the ${n{\rm s}n{\rm p}}$ $^3P^{\rm o}_0$ clock states for $^{111,113}$Cd and $^{25}$Mg were calculated by using the multi-configuration Dirac-Hartree-Fock theory. To obtain accurate values of these parameters, the impact of electron correlations and furthermore the Breit interaction and quantum electrodynamical effects on the Zeeman and hyperfine interaction matrix elements, and energy separations were investigated in detail. We also estimated the contributions from perturbing states to the Landé $g$-factors and quadratic Zeeman shift coefficients concerned so as to truncate the summation over the perturbing states without loss of accuracy. Our calculations provide important data for estimating the first- and second-order Zeeman shifts of the clock transition for the Cd and Mg optical lattice clocks.
|
Received: 13 July 2022
Revised: 29 August 2022
Accepted manuscript online: 09 September 2022
|
|
PACS:
|
31.15.aj
|
(Relativistic corrections, spin-orbit effects, fine structure; hyperfine structure)
|
| |
31.15.vj
|
(Electron correlation calculations for atoms and ions: excited states)
|
| |
32.60.+i
|
(Zeeman and Stark effects)
|
| |
95.55.Sh
|
(Auxiliary and recording instruments; clocks and frequency standards)
|
|
| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 61775220), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB21030100), and the Key Research Project of Frontier Science of the Chinese Academy of Sciences (Grant No. QYZDB-SSW-JSC004). |
Corresponding Authors:
Hong Chang
E-mail: changhong@ntsc.ac.cn
|
Cite this article:
Benquan Lu(卢本全) and Hong Chang(常宏) Theoretical calculations on Landé $g$-factors and quadratic Zeeman shift coefficients of $n$s$n$p $^{3} {P}^{o}_{0}$ clock states in Mg and Cd optical lattice clocks 2023 Chin. Phys. B 32 013101
|
[1] McGrew W F, Zhang X, Fasano R J, Schaffer S A, Beloy K, Nicolodi D, Brown R C, Hinkley N, Milani G, Schioppo M, Yoon T H and Ludlow A D 2018 Nature 564 87
[2] Oelker E, Hutson R B, Kennedy C J, Sonderhouse L, Bothwell T, Goban A, Kedar D, Sanner C, Robinson J M, Marti G E, Matei D G, Legero T, Giunta M, Holzwarth R, Riehle F, Sterr U and Ye J 2019 Nat. Photon. 13 714
[3] Le Targat R, Lorini L, Le Coq Y, Zawada M, Guna J, Abgrall M, Gurov M, Rosenbusch P, Rovera D G, Nagrny B, Gartman R, Westergaard P G, Tobar M E, Lours M, Santarelli G, Clairon A, Bize S, Laurent P, Lemonde P and Lodewyck J 2013 Nat. Commun. 4 2109
[4] Lisdat C, Grosche G, Quintin N, Shi C, Raupach S M F, Grebing C, Nicolodi D, Stefani F, Al-Masoudi A, Dorscher S, Hafner S, Robyr J L, Chiodo N, Bilicki S, Bookjans E, Koczwara A, Koke S, Kuhl A, Wiotte F, Meynadier F, Camisard E, Abgrall M, Lours M, Legero T, Schnatz H, Sterr U, Denker H, Chardonnet C, Le Coq Y, Santarelli G, Amy-Klein A, Le Targat R, Lodewyck J, Lopez O and Pottie P E 2016 Nat. Commun. 7 12443
[5] Takano T, Takamoto M, Ushijima I, Ohmae N, Akatsuka T, Yamaguchi A, Kuroishi Y, Munekane H, Miyahara B and Katori H 2016 Nat. Photon. 10 662
[6] Uzan J P 2003 Rev. Mod. Phys. 75 403
[7] Huntemann N, Lipphardt B, Tamm C, Gerginov V, Weyers S and Peik E 2014 Phys. Rev. Lett. 113 210802
[8] Derevianko A and Pospelov M 2014 Nat. Phys. 10 933
[9] Kolkowitz S, Pikovski I, Langellier N, Lukin M D, Walsworth R L and Ye J 2016 Phys. Rev. D 94 124043
[10] Jefferts S R, Heavner T P, Parker T E, Shirley J H, Donley E A, Ashby N, Levi F, Calonico D and Costanzo G A 2014 Phys. Rev. Lett. 112 050801
[11] Rosenband T, Hume D B, Schmidt P O, Chou C W, Brusch A, Lorini L, Oskay W H, Drullinger R E, Fortier T M, Stalnaker J E, Diddams S A, Swann W C, Newbury N R, Itano W M, Wineland D J and Bergquist J C 2008 Science 319 1808
[12] Huang Y, Zhang B L, Zeng M Y, Hao Y M, Ma Z X, Zhang H Q, Guan H, Chen Z, Wang M and Gao K L 2022 Phys. Rev. Appl. 17 034041
[13] Ushijima I, Takamoto M, Das M, Ohkubo T and Katori H 2015 Nat. Photon. 9 185
[14] Nemitz N, Ohkubo T, Takamoto M, Ushijima I, Das M, Ohmae N and Katori H 2016 Nat. Photon. 10 258
[15] Beloy K, Hinkley N, Phillips N B, Sherman J A, Schioppo M, Lehman J, Feldman A, Hanssen L M, Oates C W and Ludlow A D 2014 Phys. Rev. Lett. 113 260801
[16] McFerran J J, Yi L, Mejri S, Di Manno S, Zhang W, Guena J, Le Coq Y and Bize S 2012 Phys. Rev. Lett. 108 183004
[17] Yamanaka K, Ohmae N, Ushijima I, Takamoto M and Katori H 2015 Phys. Rev. Lett. 114 230801
[18] Kulosa A P, Fim D, Zipfel K H, Ruhmann S, Sauer S, Jha N, Gibble K, Ertmer W, Rasel E M, Safronova M S, Safronova U I and Porsev S G 2015 Phys. Rev. Lett. 115 240801
[19] Sukachev D, Fedorov S, Tolstikhina I, Tregubov D, Kalganova E, Vishnyakova G, Golovizin A, Kolachevsky N, Khabarova K and Sorokin V 2016 Phys. Rev. A 94 022512
[20] Golovizin A A, Tregubov D O, Fedorova E S, Mishin D A, Provorchenko D I, Khabarova K Yu, Sorokin V N and Kolachevsky N N 2021 Nat. Commun. 12 5171
[21] Kaneda Y, Yarborough J M, Merzlyak Y, Yamaguchi A, Hayashida K, Ohmae N and Katori H 2016 Opt. Lett. 41 705
[22] Chou C W, Hume D B, Koelemeij J C J, Wineland D J and Rosenband T 2010 Phys. Rev. Lett. 104 070802
[23] Huntemann N, Sanner C, Lipphardt B, Tamm C and Peik E 2016 Phys. Rev. Lett. 116 063001
[24] Ohtsubo N, Li Y, Matsubara K, Ido T and Hayasaka K 2017 Opt. Express 25 11725
[25] Arnold K J, Kaewuam R, Roy A, Tan T R and Barrett M D 2018 Nat. Commun. 9 1650
[26] Peik E and Tamm C 2003 Europhys. Lett. 61 181
[27] Campbell C J, Radnaev A G, Kuzmich A, Dzuba V A, Flambaum V V and Derevianko A 2012 Phys. Rev. Lett. 108 120802
[28] Dzuba V A, Flambaum V V and Katori H 2015 Phys. Rev. A 91 022119
[29] Kozlov M G, Safronova M S, Crespo Lopez-Urrutia J R and Schmidt P O 2018 Rev. Mod. Phys. 90 045005
[30] Garstang R H 1962 J. Opt. Soc. Am. 52 845
[31] Safronova M S, Porsev S G, Sanner C and Ye J 2018 Phys. Rev. Lett. 120 173001
[32] Porsev S G, Ludlow A D, Boyd M M and Ye J 2008 Phys. Rev. A 78 032508
[33] Porsev S G, Safronova U I and Safronova M S 2017 Phys. Rev. A 96 012509
[34] Yamaguchi A, Safronova M S, Gibble K and Katori H 2019 Phys. Rev. Lett. 123 113201
[35] Dzuba V A and Derevianko A 2019 J. Phys. B: At. Mol. Opt. Phys. 52 215005
[36] Porsev S G and Safronova M S 2020 Phys. Rev. A 102 012811
[37] Wu F F, Tang Y B, Shi T Y and Tang L Y 2020 Phys. Rev. A 101 053414
[38] Zhang T X, Lu B Q, Li J G, Li C. B, Chang H, Shi T. Y and Lu Z H 2021 J. Quantum Spectrosc. Radiat. Transfer 266 107562
[39] Lu B Q, Lu X T, Li J G and Chang H 2022 Chin. Phys. B 31 043101
[40] Taichenachev A V, Yudin V I, Oates C W, Hoyt C W, Barber Z W and Hollberg L 2006 Phys. Rev. Lett. 96 083001
[41] Lindgren I 1984 Rep. Prog. Phys. 47 345
[42] Jonsson P, Parpia F A and Froese Fischer C 1996 Comput. Phys. Commun. 96 301
[43] Cheng K T and Childs W J 1985 Phys. Rev. A 31 2775
[44] Andersson M and Jonsson P 2008 Comput. Phys. Commun. 178 156
[45] Boyd M M, Zelevinsky T, Ludlow A D, Blatt S, Zanon-Willette T, Foreman S M and Ye J 2007 Phys. Rev. A 76 022510
[46] Grant I P, McKenzie B J, Norrington P H, Mayers D F and Pyper N C 1980 Comput. Phys. Commun. 21 207
[47] Jonsson P, He X, Froese Fischer C and Grant I P 2007 Comput. Phys. Commun. 177 597
[48] Froese Fischer C, Brage T and Jonsson P 1997 Computational Atomic Structure — An MCHF Approach (London: Institute of Physics Publishing) p. 90
[49] Li J G, Godefroid M and Wang J G 2016 J. Phys. B: At. Mol. Opt. Phys. 49 115002
[50] Froese Fischer C, Gaigalas G, Jonsson P and Bieron J 2019 Comput. Phys. Commun. 237 184
[51] Lott S H, Roos C E and Ginter M L 1966 J. Opt. Soc. Am. 56 775
[52] Briand C and Solanki S K 1995 Astron. Astrophys. 299 596
[53] Li J G, Jonsson P, Godefroid M, Dong C Z and Gaigalas G 2012 Phys. Rev. A 86 052523
[54] Kramida A, Ralchenko Yu, Reader J and NIST ASD Team 2021 NIST Atomic Spectra Database (ver. 5.9),[Online]. Available: https://physics.nist.gov/asd[2022, March 1]. National Institute of Standards and Technology, Gaithersburg, MD.
[55] Andersson M, Zou Y, Hutton R and Brage T 2010 J. Phys. B: At. Mol. Opt. Phys. 43 095001
[56] Lurio A 1962 Phys. Rev. 126 1768
[57] Stone N J 2005 At. Data Nucl. Data Tables 90 75
[58] Kohler R and Thaddeus P 1964 Phys. Rev. 134 A1204
[59] Lurio A and Novick R 1964 Phys. Rev. 134 A608
[60] Kelly F M and Tomchuk E 1959 Proc. Phys. Soc. 74 689
[61] van der Veer W E, van Diest R J J, Donszelmann A and van Linden van den Heuvell H B 1992 Z. Phys. D: At., Mol. Clusters 24 365
[62] Masłowski P, Bielska K, Cygan A, Domysławska J, Lisak D, Ciuryło R, Bielski A and Trawinski R S 2009 Eur. Phys. J. D 51 295 |
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
