Quadrupole shifts for the 171Yb+ ion clocks: Experiments versus theories

Quadrupole shifts for three prominent clock transitions, [4f(14)6s]S-2(1/2) --> [4f(14)5d]D-2(3/2), [4f(14)6s]S-2(1/2) --> [4f(14)5d]D-2(5/2), and [4f(14)6s]S-2(1/2) --> [4f (13)6s(2)]F-2(7/2), in the Yb+ ion are investigated by calculating values of the quadrupole moment (Theta) for the 5d(3/2,5/2) and 4f(7/2) states using the relativistic coupled-cluster (RCC) methods. We find an order of magnitude difference in the Theta value of the 4f(7/2) state between our calculation and the experimental result, but our result concurs with that of other calculations carried out using many-body methods different from ours. However, our Theta value of the 5d(3/2) state is in good agreement with the available experimental result and is highly precise. This enables us to estimate the quadrupole shift of the [4f(14)6s]S-2(1/2) --> [4f(14)5d]D-2(3/2) clock transition more accurately. To justify the accuracies in our calculations, we evaluate the hyperfine structure constants of the 6s(1/2), 5d(3/2,5/2), and 4f(7/2,5/2) states of the Yb-171(+) ion using the same RCC methods and compare the results with the experimental values. We also determine the lifetime of the 5d(3/2) state to address a discrepancy between conflicting values given by recent experiments.