Further investigation of a prototype microwave frequency standard based on trapped 171Yb+ ions

The compare the frequency of the ¹⁷¹Yb⁺ 12.6 GHz M_F=0→0 ground state hyperfine `clock´ transition in buffer gas-cooled ion clouds confined in two similar, but not identical, lineal Paul traps. After correction for the known differences between the two ion traps, including significantly different second-order Doppler shifts, the frequencies agree within an uncertainty of less than 2 parts in 10¹³. The frequency of the clock transition in an isolated ion at zero temperature, velocity, electric field and magnetic field, was found to be 12 642 812 118.468±0.0016 Hz