Numerical analysis of motional mode coupling of sympathetically cooled two-ion crystals

doi:10.1088/1674-1056/abfc3e

中国物理B ›› 2021, Vol. 30 ›› Issue (7): 73702-073702.doi: 10.1088/1674-1056/abfc3e

Numerical analysis of motional mode coupling of sympathetically cooled two-ion crystals

Li-Jun Du(杜丽军)^1,2, Yan-Song Meng(蒙艳松)^1,2,†, Yu-Ling He(贺玉玲)^1,2, and Jun Xie(谢军)^2,3

1 China Academy of Space Technology(Xi'an), Xi'an 710100, China;
2 National Key Laboratory of Science and Technology on Space Microwave, China Academy of Space Technology(Xi'an), Xi'an 710100, China;
3 China Academy of Space Technology, Beijing 100094, China

收稿日期:2021-01-03 修回日期:2021-03-21 接受日期:2021-04-28 出版日期:2021-06-22 发布日期:2021-07-09
通讯作者: Yan-Song Meng E-mail:yansmeng@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11803023), the Equipment Pre-research Foundation (Grant No. 6142411196406), and Key Research and Development Program of Shaanxi Province, China (Grant No. 2017ZDXM-GY-113).

Numerical analysis of motional mode coupling of sympathetically cooled two-ion crystals

Li-Jun Du(杜丽军)^1,2, Yan-Song Meng(蒙艳松)^1,2,†, Yu-Ling He(贺玉玲)^1,2, and Jun Xie(谢军)^2,3

1 China Academy of Space Technology(Xi'an), Xi'an 710100, China;
2 National Key Laboratory of Science and Technology on Space Microwave, China Academy of Space Technology(Xi'an), Xi'an 710100, China;
3 China Academy of Space Technology, Beijing 100094, China

Received:2021-01-03 Revised:2021-03-21 Accepted:2021-04-28 Online:2021-06-22 Published:2021-07-09
Contact: Yan-Song Meng E-mail:yansmeng@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11803023), the Equipment Pre-research Foundation (Grant No. 6142411196406), and Key Research and Development Program of Shaanxi Province, China (Grant No. 2017ZDXM-GY-113).

摘要/Abstract

摘要： A two-ion pair in a linear Paul trap is extensively used in the research of the simplest quantum-logic system; however, there are few quantitative and comprehensive studies on the motional mode coupling of two-ion systems yet. This study proposes a method to investigate the motional mode coupling of sympathetically cooled two-ion crystals by quantifying three-dimensional (3D) secular spectra of trapped ions using molecular dynamics simulations. The 3D resonance peaks of the ⁴⁰Ca⁺-²⁷Al⁺ pair obtained by using this method were in good agreement with the 3D in- and out-of-phase modes predicted by the mode coupling theory for two ions in equilibrium and the frequency matching errors were lower than 2%. The obtained and predicted amplitudes of these modes were also qualitatively similar. It was observed that the strength of the sympathetic interaction of the ⁴⁰Ca⁺-²⁷Al⁺ pair was primarily determined by its axial in-phase coupling. In addition, the frequencies and amplitudes of the ion pair's resonance modes (in all dimensions) were sensitive to the relative masses of the ion pair, and a decrease in the mass mismatch enhanced the sympathetic cooling rates. The sympathetic interactions of the ⁴⁰Ca⁺-²⁷Al⁺ pair were slightly weaker than those of the ²⁴Mg⁺-²⁷Al⁺ pair, but significantly stronger than those of ⁹Be⁺-²⁷Al⁺. However, the Doppler cooling limit temperature of ⁴⁰Ca⁺ is comparable to that of ⁹Be⁺ but lower than approximately half of that of ²⁴Mg⁺. Furthermore, laser cooling systems for ⁴⁰Ca⁺ are more reliable than those for ²⁴Mg⁺ and ⁹Be⁺. Therefore, ⁴⁰Ca⁺ is probably the best laser-cooled ion for sympathetic cooling and quantum-logic operations of ²⁷Al⁺ and has particularly more notable comprehensive advantages in the development of high reliability, compact, and transportable ²⁷Al⁺ optical clocks. This methodology may be extended to multi-ion systems, and it will greatly aid efforts to control the dynamic behaviors of sympathetic cooling as well as the development of low-heating-rate quantum logic clocks.

关键词: sympathetic cooling, coupled oscillations, secular motion, radio-frequency ion traps

Abstract: A two-ion pair in a linear Paul trap is extensively used in the research of the simplest quantum-logic system; however, there are few quantitative and comprehensive studies on the motional mode coupling of two-ion systems yet. This study proposes a method to investigate the motional mode coupling of sympathetically cooled two-ion crystals by quantifying three-dimensional (3D) secular spectra of trapped ions using molecular dynamics simulations. The 3D resonance peaks of the ⁴⁰Ca⁺-²⁷Al⁺ pair obtained by using this method were in good agreement with the 3D in- and out-of-phase modes predicted by the mode coupling theory for two ions in equilibrium and the frequency matching errors were lower than 2%. The obtained and predicted amplitudes of these modes were also qualitatively similar. It was observed that the strength of the sympathetic interaction of the ⁴⁰Ca⁺-²⁷Al⁺ pair was primarily determined by its axial in-phase coupling. In addition, the frequencies and amplitudes of the ion pair's resonance modes (in all dimensions) were sensitive to the relative masses of the ion pair, and a decrease in the mass mismatch enhanced the sympathetic cooling rates. The sympathetic interactions of the ⁴⁰Ca⁺-²⁷Al⁺ pair were slightly weaker than those of the ²⁴Mg⁺-²⁷Al⁺ pair, but significantly stronger than those of ⁹Be⁺-²⁷Al⁺. However, the Doppler cooling limit temperature of ⁴⁰Ca⁺ is comparable to that of ⁹Be⁺ but lower than approximately half of that of ²⁴Mg⁺. Furthermore, laser cooling systems for ⁴⁰Ca⁺ are more reliable than those for ²⁴Mg⁺ and ⁹Be⁺. Therefore, ⁴⁰Ca⁺ is probably the best laser-cooled ion for sympathetic cooling and quantum-logic operations of ²⁷Al⁺ and has particularly more notable comprehensive advantages in the development of high reliability, compact, and transportable ²⁷Al⁺ optical clocks. This methodology may be extended to multi-ion systems, and it will greatly aid efforts to control the dynamic behaviors of sympathetic cooling as well as the development of low-heating-rate quantum logic clocks.

Key words: sympathetic cooling, coupled oscillations, secular motion, radio-frequency ion traps

中图分类号: (Ion trapping)

37.10.Ty

37.10.Rs (Ion cooling) 37.90.+j (Other topics in mechanical control of atoms, molecules, and ions) 31.15.xv (Molecular dynamics and other numerical methods)

Li-Jun Du(杜丽军), Yan-Song Meng(蒙艳松), Yu-Ling He(贺玉玲), and Jun Xie(谢军). Numerical analysis of motional mode coupling of sympathetically cooled two-ion crystals[J]. 中国物理B, 2021, 30(7): 73702-073702.

Li-Jun Du(杜丽军), Yan-Song Meng(蒙艳松), Yu-Ling He(贺玉玲), and Jun Xie(谢军). Numerical analysis of motional mode coupling of sympathetically cooled two-ion crystals[J]. Chin. Phys. B, 2021, 30(7): 73702-073702.

参考文献

[1] Safronova M S, Budker D, DeMille D, Kimball D F J, Derevianko A and Clark C W 2018 Rev. Mod. Phys. 90 025008
[2] Brewer S M, Chen J S, Hankin A M, Clements E R, Chou C W, Wineland D J, Hume D B and Leibrandt D R 2019 Phys. Rev. Lett. 123 033201
[3] Von der Wense L, Seiferle B, Laatiaoui M, Neumayr J B, Maier H J, Wirth H F, Mokry C, Runke J, Eberhardt K, Düllmann C E and Trautmann N G 2016 Nature 533 47
[4] Seiferle B, Von der Wense L, Bilous P V, Amersdorffer I, Lemell C, Libisch F, Stellmer S, Schumm T, Düllmann C E, Pálffy A and Thirolf P G 2019 Nature 573 243
[5] Dzuba V A, Flambaum V V and Katori H 2015 Phys. Rev. A 91 022119
[6] Yudin V I, Taichenachev A V and Derevianko A 2014 Phys. Rev. Lett. 113 233003
[7] Derevianko A, Dzuba V A and Flambaum V V 2012 Phys. Rev. Lett. 109 180801
[8] Chou C W, Hume D B, Rosenband T and Wineland D J 2010 Science 329 1630
[9] Chen J S, Brewer S M, Chou C W, Wineland D J, Leibrandt D R and Hume D B 2017 Phys. Rev. Lett. 118 053002
[10] Walz J, Ross S B, Zimmermann C, Ricci L, Prevedelli M and Hansch T W 1995 Phys. Rev. Lett. 75 3257
[11] Germann M, Tong X and Willitsch S 2014 Nat. Phys. 10 820
[12] Raghunandan M, Wolf F, Ospelkaus C, Schmidt P O and Weimer H 2020 Science Adv. 6 eaaw9268
[13] Monroe C, Meekhof D M, King B E, Itano W M and Wineland D J 1995 Phys. Rev. Lett. 75 4714
[14] Häffner H, Hänsel W, Roos C F, Benhelm J, Chwalla M, Körber T, Rapol U D, Riebe M, Schmidt P O, Becher C and Gühne O 2005 Nature 438 643
[15] Riebe M, Monz T, Kim K, Villar A S, Schindler P, Chwalla M, Hennrich M and Blatt R 2008 Nat. Phys. 4 839
[16] Home J P, Hanneke D, Jost J D, Amini J M, Leibfried D and Wineland D J 2009 Science 325 1227
[17] Wan Y, Gebert F, Wolf F and Schmidt P O 2015 Phys. Rev. A 91 043425
[18] Inlek I V, Crocker C, Lichtman M, Sosnova K, and Monroe C 2017 Phys. Rev. Lett. 118 250502
[19] Zhang J, Deng K, Luo J, Lu Z H 2017 Chin. Phys. Lett. 34 050601
[20] Du L J, Chen T, Song H F, Chen S L, Li H X, Huang Y, Tong X, Guan H and Gao K L 2015 Chin. Phys. B 24 083702
[21] Du L J, Song H F, Li H X, Chen S L, Chen T, Sun H Y, Huang Y, Tong X, Guan H and Gao K L 2015 Chin. Phys. B 24 113703
[22] James D F V 1998 Appl. Phys. B 66 181
[23] Wineland D J, Monroe C, Itano W M, Leibfried D, King B E and Meekhof D M 1998 J. Res. Natl. Inst. Stand. Technol. 103 259
[24] Kielpinski D, King B E, Myatt C J, Sackett C A, Turchette Q A, Itano W M, Monroe C, Wineland D J and Zurek W H 2000 Phys. Rev. A 61 032310
[25] Wübbena J B, Amairi S, Mandel O and Schmidt P O 2012 Phys. Rev. A 85 043412
[26] Bruzewicz C D, McConnell R, Stuart J, Sage J M and Chiaverini J 2019 npj Quantum Inf 5 1
[27] Verlet L 1967 Phys. Rev. 159 98
[28] Verlet L 1968 Phys. Rev. 165 201
[29] Zhang M Q and Skeel R D 1995 J. Comput. Chem. 16 365
[30] Berkeland D J, Miller J D, Bergquist J C, Itano W M and Wineland D J 1998 J. Appl. Phys. 83 5025
[31] Paul W, Osberghaus O and Fischer E 1958 Forschungsberichte des Wirtschafts und Verkehrsministeriums Nordrhein-Westfalen 415
[32] Brian C S, Joseph W B, and John J B 2014 Phys. Rev. A 89 033408
[33] Knünz S, Herrmann M, Batteiger V, Saathoff G, Hänsch T W, Vahala K, and Udem T 2010 Phys. Rev. Lett. 105 013004
[34] Removille S, Dubessy R, Dubost B, Glorieux Q, Coudreau T, Guibal S, Likforman J P and Guidon L 2009 J. Phys. B 42 154014
[35] Mulholland S, Klein H A, Barwood G P, Donnellan S, Gentle D, Huang G, Walsh G, Baird P E G and Gill P 2019 Appl. Phys. B 125 198
[36] Campbell C J, Radnaev A G, Kuzmich A, Dzuba V A, Flambaum V V and Derevianko A 2012 Phys. Rev. Lett. 108 120802
[37] Seiferle B, Wense L V D, Bilous P V, Amersdorffer I, Lemell C, Libisch F, Stellmer S, Schumm T, Christoph E D, Pálffy A and Thirolf P G 2019 Nature 573 243

Numerical analysis of motional mode coupling of sympathetically cooled two-ion crystals

Numerical analysis of motional mode coupling of sympathetically cooled two-ion crystals

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