Dimitri Kalincev

We investigate the normal mode spectrum of a trapped ion chain at the symmetry-breaking linear to zigzag transition and at finite temperatures. For this purpose we modulate the amplitude of the Doppler cooling laser in order to excite and measure mode oscillations. The expected mode softening at the critical point, a signature of the second-order transition, is not observed. Numerical simulations show that this is mainly due to the finite temperature of the chain. Inspection of the trajectories suggest that the thermal shifts of the normal-mode spectrum can be understood by the ions collectively jumping between the two ground state configurations of the symmetry broken phase. We develop an effective analytical model, which allows us to reproduce the low-frequency spectrum as a function of the temperature and close to the transition point. In this model the frequency shift of the soft mode is due to the anharmonic coupling with the high frequency modes of the spectrum, acting as an averaged effective thermal environment. Our study could prove important for implementing ground-state laser cooling close to the critical point.

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$^+$.