Yang Yang

Optical lattice clocks are the prospective devices that can probe many subtle physics including temporal variation of the fine structure constant ($\alpha_e$). These studies necessitate high-precision measurements of atomic clock frequency ratios to unprecedented accuracy. In contrast to the earlier claimed highest sensitive coefficient ($K$) clock transition to $\alpha_e$ in Yb [Phys. Rev. Lett. $\textbf{120}$, 173001 (2018)], we found the $4f^{14}6s6p\,(^3P_2) - 4f^{13}5d6s^{2}\,(^3P_2^*)$ transition of this atom can serve as the clock transition with the largest $K$ value (about $-$25(2)). Moreover, we demonstrate a scheme to attain simultaneous magic trapping conditions for this clock transition with the other two proposed clock transitions $4f^{14}6s^2\,(^1S_0) - 4f^{14}6s6p\,(^3P_2)$ and $4f^{14}6s^2\,(^1S_0) - 4f^{13}5d6s^{2}\,(^3P_2^*)$; also exhibiting large $K$ values. This magic condition can be realized by subjecting Yb atoms to a bias magnetic field at a particular polarization angle along the quantization axis in an experimental set up. Upon realization, it will serve as the most potential optical lattice clock to probe $\alpha_e$ variation.

The roles of the fine-structure intramanifold resonances to the Zeeman shifts caused by the blackbody radiation (BBRz shifts) in the optical clock transitions are analyzed. The clock frequency measurement in the $^1S_0-^3P_0$ clock transition of the singly charged aluminium ion (Al$^+$) has already been reached the $10^{-19}$ level at which the BBRz effect can be significant in determining the uncertainty. In view of this, we probe first the BBRz shift in this transition rigorously and demonstrate the importance of the contributions from the intramanifold resonances explicitly. To carry out the analysis, we determine the dynamic magnetic dipole (M1) polarizabilities of the clock states over a wide range of angular frequencies by employing two variants of relativistic many-body methods. This showed the BBRz shift is highly suppressed due to blue-detuning of the BBR spectrum to the $^3P_0-^3P_1$ fine-structure intramanifold resonance in Al$^+$ and it fails to follow the usually assumed static M1 polarizability limit in the estimation of the BBRz shift. The resonance also leads to a reversal behavior of the temperature dependence and a cancellation in the shift. After learning this behavior, we extended our analyses to other optical clocks and found that these shifts are of the order of micro-hertz leading to fractional shifts in the clock transitions at the $10^{-20}$ level or below.