Chih-Han Yeh

In attempts to unify the four known fundamental forces in a single quantum-consistent theory, it is suggested that Lorentz symmetry may be broken at the Planck scale. Here we search for Lorentz violation at the low-energy limit by comparing orthogonally oriented atomic orbitals in a Michelson-Morley-type experiment. We apply a robust radiofrequency composite pulse sequence in the $^2F_{7/2}$ manifold of an Yb$^+$ ion, extending the coherence time from 200 $μ$s to more than 1 s. In this manner, we fully exploit the high intrinsic susceptibility of the $^2F_{7/2}$ state and take advantage of its exceptionally long lifetime. We match the stability of the previous best Lorentz symmetry test nearly an order of magnitude faster and improve the constraints on the symmetry breaking coefficients to the 10$^{-21}$ level. These results represent the most stringent test of this type of Lorentz violation. The demonstrated method can be further extended to ion Coulomb crystals.

We report on the first coherent excitation of the highly forbidden $^2S_{1/2}\rightarrow{}^2F_{7/2}$ electric octupole (E3) transition in a single trapped ${}^{172}$Yb$^+$ ion, an isotope without nuclear spin. Using the transition in ${}^{171}$Yb$^+$ as a reference, we determine the transition frequency to be $642\,116\,784\,950\,887.6(2.4)\,$Hz. We map out the magnetic field environment using the forbidden $^2S_{1/2} \rightarrow{}^2D_{5/2}$ electric quadrupole (E2) transition and determine its frequency to be $729\,476\,867\,027\,206.8(4.4)\,$Hz. Our results are a factor of $1\times10^5$ ($3\times10^{5}$) more accurate for the E2 (E3) transition compared to previous measurements. The results open up the way to search for new physics via precise isotope shift measurements and improved tests of local Lorentz invariance using the metastable $^2F_{7/2}$ state of Yb$^+$.