Suppressing Inhomogeneous Broadening in a Lutetium Multi-ion Optical Clock

We demonstrate precision measurement and control of inhomogeneous broadening in a multi-ion clock consisting of three ${}^{176}{\mathrm{Lu}}^{+}$ ions. Microwave spectroscopy between hyperfine states in the ${}^3{D}_1$ level is used to characterize differential systematic shifts between ions, most notably those associated with the electric quadrupole moment. By appropriate alignment of the magnetic field, we demonstrate suppression of these effects to the $\sim {10}^{-17}$ level relative to the ${{}^{1}S}_0\leftrightarrow {{}^{3}D}_1$ optical transition frequency. Correlation spectroscopy on the optical transition demonstrates the feasibility of a 10-s Ramsey interrogation in the three ion configuration with a corresponding projection noise limited stability of $\sigma (\tau )=8.2\times {10}^{-17}/\sqrt{\tau }$.

Figure 1

Relevant energy level diagram of a ${}^{176}{\mathrm{Lu}}^{+}$ ion showing the ${{}^{1}S}_0\leftrightarrow {{}^{3}D}_1$ clock transition at 848 nm, the ${{}^{3}D}_1\leftrightarrow {{}^{3}P}_0$ transition at 646 nm used for Doppler cooling and detection, and optical pumping transitions at 350, 622, and 895 nm to initialize population to the ${}^3{D}_1$ level.

Figure 2

Schematic of the experimental setup showing laser beam configurations relative to the trap. (a),(b) Views along the $y$ (vertical) and $x$ (horizontal) axes, respectively. The $B$ field defines the quantization axis and is rotated in the $x\text{−}z$ plane to minimize tensor shifts. Raman beams in (a) and a near-resonant 646-nm beam with $\mathit{k}$ vector of $(1/\sqrt{2})(\widehat{y}-\widehat{z})$ in (b) are used to assess EMM.

Figure 3

(a),(b) Microwave Ramsey spectroscopy on the $|{{}^{3}D}_1,7,0⟩\leftrightarrow |{{}^{3}D}_1,8,0⟩$ transition with EMM minimized as described in the main text. Frequencies on the horizontal axes are relative to an offset near to the hyperfine splitting of $\sim 10.49\mathrm{GHz}$. For (a), a Ramsey time of 1 s is used with the $B$ field aligned approximately 20° from ${\theta }_0$. Similarly, (b) has a Ramsey time of 5 s with the $B$ field aligned to within 0.4° of ${\theta }_0$. (c) Correlation spectroscopy of the $|{{}^{3}D}_1,7,0⟩\leftrightarrow |{{}^{3}D}_1,8,1⟩$ transition. The oscillation period corresponds to a differential field of $\simeq 1.15\mathrm{nT}$ between the outer ions. (d)–(f) Correlation spectroscopy on the $|{{}^{1}S}_0,7,1⟩\leftrightarrow |{{}^{3}D}_1,7,0⟩$ transition: (d) and (e) have field alignments as for (a) and (b), and (f) has the $B$ field misaligned as in (a) and no EMM compensation.