Sympathetic cooling of $^{113}$Cd$^+$ by laser-cooled $^{40}$Ca$^+$ in a linear Paul trap for Microwave Ion Clocks

Abstract

We report sympathetic cooling of 113 Cd + by laser-cooled 40 Ca + in a linear Paul trap for microwave clocks. Long-term low-temperature confinement of 113 Cd + ions was achieved. The temperature of these ions was measured at 90(10) mK, and the corresponding uncertainty arising from the secondorder Doppler shifts was estimated to a level of 2 × 10 −17 . Up to 4.2 × 10 5 Cd + ions were confined in the trap, and the confinement time constant was measured to be 84 hours. After three hours of confinement, there were still 10 5 Cd + ions present, indicating that this Ca + -Cd + dual ion system is surprisingly stable. The ac Stark shift was induced by the Ca + lasers and fluorescence, which was carefully estimated to an accuracy of 5.4(0.5) × 10 −17 using a high-accuracy ab initio approach. The Dick-effect-limited Allan deviation was also deduced because deadtimes were shorter. These results indicate that a microwave clock based on this sympathetic cooling scheme holds promise in providing ultra-high frequency accuracy and stability.

Research on the ions’ axial temperature of a sympathetically-cooled 113Cd+ ion crystal*

“…Typically, increasing RF voltage and end-cap voltage lead to substantial compression and extension on the radial distribution of the ion system, respectively. Because the effect of laser force is significant, [24][25][26] during the simulation process, the laser force is set as a constant value, verified by Subsection 2.2.…”