Progress towards a strontium single-ion optical clock with mHz uncertainty

The strontium ion clock developed at the National Research Council of Canada has reached an uncertainty level of 5 mHz in recent years. This low level of uncertainty was achieved in great part by using methods that harness specific properties of the clock transition that allow either a very high level of cancellation or a strong suppression of frequency shifts that would otherwise dominate the uncertainty budget. The shifts controlled by these methods are the electric quadrupole shift, the tensor Stark shifts, and the micromotion shifts. With these methods in place, the main limitation to the accuracy of the clock transition frequency is the uncertainty in the evaluation of blackbody radiation (BBR) field. In this paper, we review the methods used to control the shifts to the 5 mHz level and present our plans for the evaluation of the BBR field that is expected to reduce the total uncertainty to the mHz level.