Properties of a Rare-Earth-Ion-Doped Waveguide at Sub-Kelvin Temperatures for Quantum Signal Processing

We characterize the 795 nm $^3$H$_6$ to $^3$H$_4$ transition of Tm$^{3+}$ in a Ti$^{4+}$:LiNbO$_{3}$ waveguide at temperatures as low as 800 mK. Coherence and hyperfine population lifetimes -- up to 117 $\mu$s and 2.5 hours, respectively -- exceed those at 3 K at least ten-fold, and are equivalent to those observed in a bulk Tm$^{3+}$:LiNbO$_{3}$ crystal under similar conditions. We also find a transition dipole moment that is equivalent to that of the bulk. Finally, we prepare a 0.5 GHz-bandwidth atomic frequency comb of finesse $>$2 on a vanishing background. These results demonstrate the suitability of rare-earth-doped waveguides created using industry-standard Ti-indiffusion in LiNbO$_3$ for on-chip quantum applications.