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

doi:10.1088/1674-1056/abfc3e

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.

Keywords: sympathetic cooling coupled oscillations secular motion radio-frequency ion traps

Received: 03 January 2021
Revised: 21 March 2021
Accepted manuscript online: 28 April 2021

PACS:	37.10.Ty	(Ion trapping)
	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)

Fund: 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).

Corresponding Authors: Yan-Song Meng
E-mail: yansmeng@163.com

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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 2021 Chin. Phys. B 30 073702

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

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