We present precise values of the dipole polarizabilities (α) of the ground [4f 14 6s] 2 S 1/2 and metastable [4f 14 5d] 2 D 3/2 states of Yb + , that are important in reducing systematics in the clock frequency of the [4f 14 6s] 2 S 1/2 → [4f 14 5d] 2 D 3/2 transition. The static values of α for the ground and [4f 14 5d] 2 D 3/2 states are estimated to be 9.8(1)×10 −40 Jm 2 V −2 and 17.6(5)×10 −40 Jm 2 V −2 , respectively, while the tensor contribution to the [4f 14 5d] 2 D 3/2 state as −12.3(3) × 10 −40 Jm 2 V −2 compared to the experimental value −13.6(2.2) × 10 −40 Jm 2 V −2 . This corresponds to the differential scalar polarizability value of the above transition as −7.8(5) × 10 −40 Jm 2 V −2 in contrast to the available experimental value −6.9(1.4) × 10 −40 Jm 2 V −2 . This results in the black-body radiation (BBR) shift of the clock transition as −0.44(3) Hz at the room temperature, which is large as compared to the previously estimated values. Using the dynamic α values, we report the tune-out and magic wavelengths that could be of interest to subdue systematics due to the Stark shifts and for constructing lattice optical clock using Yb + .
We propose a new ion-trap geometry to carry out accurate measurements of the quadrupole shifts in the 171 Yb-ion. This trap will produce nearly ideal harmonic potential where the quadrupole shifts due to the anharmonic components can be reduced by four orders of magnitude. This will be useful to reduce the uncertainties in the clock frequency measurements of the 6s 2 S 1/2 → 4f 13 6s 2 2 F 7/2 and 6s 2 S 1/2 → 5d 2 D 3/2 transitions, from which we can deduce precise values of the quadrupole moments (Θs) of the 4f 13 6s 2 2 F 7/2 and 5d 2 D 3/2 states. Moreover, it may be able to affirm validity of the measured Θ value of the 4f 13 6s 2 2 F 7/2 state where three independent theoretical studies defer almost by one order in magnitude from the measurement. We also perform calculations of Θs using the relativistic coupled-cluster (RCC) method. We use these Θ values to estimate quadrupole shift that can be measured in our proposed ion trap experiment.
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