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

Quadrupole shifts for three prominent clock transitions, [4f146s]2S1/2→[4f145d]2D3/2,[4f146s]2S1/2→[4f145d]2D5/2, and [4f146s]2S1/2→[4f136s2]2F7/2, in the Yb+ ion are investigated by calculating values of the quadrupole moment (Θ) for the 5d3/2,5/2 and 4f7/2 states using the relativistic coupled-cluster (RCC) methods. We find an order of magnitude difference in the Θ value of the 4f7/2 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 Θ value of the 5d3/2 state is in good agreement with the available experimental result and is highly precise. This enables us to estimate the quadrupole shift of the [4f146s]2S1/2→[4f145d]2D3/2 clock transition more accurately. To justify the accuracies in our calculations, we evaluate the hyperfine structure constants of the 6s1/2,5d3/2,5/2, and 4f7/2,5/2 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 5d3/2 state to address a discrepancy between conflicting values given by recent experiments.