Evaluation of blackbody radiation shift with temperature-associated fractional uncertainty at 10−18 level for 40Ca+ ion optical clock

In this paper, the blackbody radiation (BBR) temperature rise experienced by a 40Ca+ ion confined in a miniature Paul trap and its uncertainty have been evaluated via finite-element method (FEM) modelling. The FEM model was validated through comparisons with thermal camera measurements at several points on a dummy trap. Before the validation, the thermal camera was calibrated by using a PT1000 resistance thermometer. The input modelling parameters were analyzed carefully, and their contributions to the uncertainty of the trap environment temperature were evaluated using the validated FEM model. The result shows that the temperature rise experienced by the 40Ca+ ion is 1.72 K with an uncertainty of 0.46 K. It results in a contribution of 2.2 mHz to the systematic uncertainty of a 40Ca+ ion optical clock, corresponding to a fractional uncertainty 5.4 × 10−18. This is much smaller than the uncertainty caused by the BBR shift coefficient, which is evaluated to be 4.8 mHz and at the 10−17 level in fractional frequency units.