A comparison of two 40Ca+ single-ion optical frequency standards at the 5 × 10−17 level and an evaluation of systematic shifts

Abstract

A comparison of two optical frequency standards and a detailed study of the systematic frequency shifts of each 40Ca+ single-ion optical frequency standard is presented. The methods used for the systematic shift evaluation of the comparison measurements are also provided. One of the ion traps runs at a chosen operating frequency of 24.7 MHz, determined by the differential scalar polarizability of the clock transition, at which frequency the rf-induced Stark shifts and second-order Doppler shifts cancel each other, yielding a great suppression in the combined micromotion shifts. After compensating for the micromotion, the two optical frequency standards both reach an uncertainty level of a few parts in 10−17, which is more than an order of magnitude smaller compared to a few years ago. The dominant source of uncertainty is the blackbody radiation shift after minimizing the micromotion-induced shifts. The blackbody radiation shift is evaluated by controlling and measuring the temperature at the trap center. With a measurement over one month, the frequency difference between the two clocks is measured to be 3.2 × 10−17 with a measurement uncertainty of 5.5 × 10−17, considering both the statistical (1.9 × 10−17) and the systematic (5.1 × 10−17) uncertainties. Due to improvement of the clock laser and better control of the optical and electromagnetic field geometry and the laboratory conditions, a fractional stability of 7 × 10−17 in 20,000 s of averaging time is achieved. The absolute frequency of the 40Ca+ 4 s2S1/2–3d 2D5/2 clock transition is measured as 411 042 129 776 401.7 (1.1) Hz, with a fractional uncertainty of 2.7 × 10−15 using the GPS satellites as a link to the SI second. Details of the method used for the systematic shift evaluation of the measurements are given.