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We present precise values of the dipole polarizabilities ($alpha$) of the ground $rm [4f^{14}6s] ~ ^2S_{1/2}$ and metastable $rm [4f^{14} 5d] ~ ^2D_{3/2}$ states of Yb$^+$, that are %vital {bf important} in reducing systematics in the clock frequency of the $rm[4f^{14}6s] ~ ^2S_{1/2} rightarrow [4f^{14}5d] ~ ^2D_{3/2}$ transition. The static values of $alpha$ for the ground and $rm [4f^{14} 5d] ~ ^2D_{3/2}$ states are estimated to be $9.8(1) times 10^{-40} ,,rm Jm^2V^{-2}$ and $17.6(5) times 10^{-40},, rm Jm^2V^{-2}$, respectively, while the tensor contribution to the $rm [4f^{14} 5d] ~ ^2D_{3/2}$ state as $- 12.3(3) times 10^{-40},, rm Jm^2V^{-2}$ compared to the experimental value $-13.6(2.2) times 10^{-40},,rm Jm^2V^{-2}$. This corresponds to the differential scalar polarizability value of the above transition as $-7.8$(5)$,times, 10^{-40},rm Jm^2 V^{-2}$ in contrast to the available experimental value $-6.9$(1.4)$,times, 10^{-40}$,, $rm Jm^2V^{-2}$. 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 $alpha$ values, we report the tune-out and magic wavelengths that could be of interest to subdue %major systematics due to the Stark shifts and for constructing lattice optical clock using Yb$^+$.
The Stark shift of the ytterbium optical clock transition due to room temperature blackbody radiation is dominated by a static Stark effect, which was recently measured to high accuracy [J. A. Sherman et al., Phys. Rev. Lett. 108, 153002 (2012)]. How
The blackbody radiation shift of the Ga$^+$ $4s^2 ^1S^e_0 to 4s4p ^3P^o_0$ clock transition is computed to be $-$$0.0140 pm 0.0048$ Hz at 300 K. The small shift is consistent with the blackbody shifts of the clock transitions of other group III ion
The frequency dependent polarizabilities of the francium atom are calculated from the available data of energy levels and transition rates. Magic wavelengths for the state insensitive optical dipole trapping are identified from the calculated light s
The workhorse of atomic physics, quantum electrodynamics, is one of the best-tested theories in physics. However recent discrepancies have shed doubt on its accuracy for complex atomic systems. To facilitate the development of the theory further we a
We present additional magic wavelengths ($lambda_{rm{magic}}$) for the clock transitions in the alkaline-earth metal ions considering circular polarized light aside from our previously reported values in [J. Kaur et al., Phys. Rev. A {bf 92}, 031402(