Control of the systematic shifts of the strontium ion optical frequency standard at the 10 mHz level

An overview of the key methods used to reduce the uncertainty of the systematic shifts of the strontium ion optical frequency standard is presented. An uncertainty of 10 mHz at a clock frequency of 445 THz is obtained, limited by the uncertainty of the blackbody radiation shift. The uncertainty estimates of other shifts such as micromotion and electric quadrupole shifts are on the order of 1 mHz or less. The effectiveness of the methods used to reduce or cancel the shifts is illustrated with experiments comparing two ion traps. One has strong micromotion levels while the other, the reference trap, provides good control over the shifts. Despite nominal shifts of 70 Hz in the trap with large micromotion levels, the agreement with the reference trap is at the sub-Hz level.