Sub-Hertz Optical Frequency Comparisons between Two Trapped 171Yb+ Ions

We compare the frequencies of the 6s 2S1/2(F=0)→5d 2D3/2(F=2) reference transition in 171Yb+ for two single ions stored in independent traps. The quadrupole moment of the 5d 2D3/2 state is measured to be 9.32(48)x10-40 C m2 and from the quadratic Stark shift the relevant scalar and tensor polarizabilities are determined to be αS(S1/2)-αS(D3/2)=-6.9(1.4)x10-40 J m2/V2 and αT(D3/2)=-13.6(2.2)x10-40 J m2/V2, respectively. In the absence of external perturbations we find a mean frequency difference between the two trapped ions of 0.26(42) Hz, corresponding to a relative difference of 3.8(6.1)x10-16. This is comparable to the agreement found in the most accurate comparisons between cesium fountain clocks