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

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(3 D)secular spectra of trapped ions using molecular dynamics simulations.The 3 D resonance peaks of the^(40)Ca^(+)–^(27)Al^(+)pair obtained by using this method were in good agreement with the 3 D 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^(40)Ca^(+)–^(27)Al^(+)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^(40)Ca^(+)–^(27)Al^(+)pair were slightly weaker than those of the^(24)Mg^(+)–^(27)Al^(+)pair,but significantly stronger than those of^(9)Be^(+)–^(27)Al^(+).However,the Doppler cooling limit temperature of^(40)Ca^(+)is comparable to that of^(9)Be^(+)but lower than approximately half of that of^(24)Mg^(+).Furthermore,laser cooling systems for^(40)Ca^(+)are more reliable than those for^(24)Mg^(+)and^(9)Be^(+).Therefore,^(40)Ca^(+)is probably the best laser-cooled ion for sympathetic cooling and quantum-logic operations of^(27)Al^(+)and has particularly more notable comprehensive advantages in the development of high reliability,compact,and transportable^(27)Al^(+)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.

Towards High Molecular Weight Poly(bisphenol A carbonate) with Excellent Thermal Stability and Mechanical Properties by Solid-State Polymerization

Poly（bisphenol A carbonate） （BPA-PC） was post-polymerized by solid-state polymerization （SSP） after supercritical CO2-induced crystallization in low molecular weight particles prepolymerized via melt transesterification reaction. The effects of the crystallization conditions on melting behavior and SSP of BPA-PC were investigated with differential scanning calorimetry （DSC）, Ubbelohde viscosity method and gel permeation chromatography （GPC）. The reaction kinetics of the SSP of crystallized prepolymers was studied as a function of reaction temperatures for various reaction periods. As a result, the viscosity average molecular weight of BPA-PC particles （2 mm） increased from 1.9 × 10^4 g/mol to 2.8 × 10^4 g/mol after SSP. More importantly, the significantly enhanced thermal stability and mechanical properties of solid-state polymerized BPA-PC, compared with those of melt transesterification polymerized BPA-PC with the same molecular weight, can be ascribed to the substantial avoidance of undergoing high temperature during polymerization. Our work provides a useful method to obtain practical product of BPA-PC with high quality and high molecular weight.