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Rare-earth ion-doped crystals are of great interest for quantum memories, a central component in future quantum repeaters. To assess the promise of 1$\%$ Tm$^{3+}$-doped yttrium gallium garnet (Tm:YGG), we report measurements of optical coherence and energy-level lifetimes of its $^3$H$_6$ $\leftrightarrow$ $^3$H$_4$ transition at a temperature of around 500 mK and various magnetic fields. Using spectral hole burning, we find hyperfine ground-level (Zeeman level) lifetimes of several minutes at magnetic fields of less than 1000 G. We also measure coherence time exceeding one millisecond using two-pulse photon echoes. Three-pulse photon echo and spectral hole burning measurements reveal that due to spectral diffusion, the effective coherence time reduces to a few $\mu$s over a timescale of around two hundred seconds. Finally, temporal and frequency-multiplexed storage of optical pulses using the atomic frequency comb protocol is demonstrated. Our results suggest Tm:YGG to be promising for multiplexed photonic quantum memory for quantum repeaters.

Single quantum emitters embedded in solid-state hosts are an ideal platform for realizing quantum information processors and quantum network nodes. Among the currently-investigated candidates, Er$^{3+}$ ions are particularly appealing due to their 1.5 $\mu$m optical transition in the telecom band as well as their long spin coherence times. However, the long lifetimes of the excited state -- generally in excess of 1 ms -- along with the inhomogeneous broadening of the optical transition result in significant challenges. Photon emission rates are prohibitively small, and different emitters generally create photons with distinct spectra, thereby preventing multi-photon interference -- a requirement for building large-scale, multi-node quantum networks. Here we solve this challenge by demonstrating for the first time linear Stark tuning of the emission frequency of a single Er$^{3+}$ ion. Our ions are embedded in a lithium niobate crystal and couple evanescently to a silicon nano-photonic crystal cavity that provides an up to 143 increase of the measured decay rate. By applying an electric field along the crystal c-axis, we achieve a Stark tuning greater than the ion's linewidth without changing the single-photon emission statistics of the ion. These results are a key step towards rare earth ion-based quantum networks.

We argue that long optical storage times are required to establish entanglement at high rates over large distances using memory-based quantum repeaters. Triggered by this conclusion, we investigate the $^3$H$_6$ $\leftrightarrow$ $^3$H$_4$ transition at 795.325 nm of Tm:Y$_3$Ga$_5$O$_{12}$ (Tm:YGG). Most importantly, we show that the optical coherence time can reach 1.1 ms, and, using laser pulses, we demonstrate optical storage based on the atomic frequency comb protocol up to 100 $\mu$s as well as a memory decay time T$_M$ of 13.1 $\mu$s. Possibilities of how to narrow the gap between the measured value of T$_m$ and its maximum of 275 $\mu$s are discussed. In addition, we demonstrate quantum state storage using members of non-classical photon pairs. Our results show the potential of Tm:YGG for creating quantum memories with long optical storage times, and open the path to building extended quantum networks., Comment: 6 pages, 4 figures

We report the measurement of the inhomogeneous linewidth, homogeneous linewidth and spin state lifetime of Pr3+ ions in a novel waveguide architecture. The TeO2 slab waveguide deposited on a bulk Pr3+:Y2SiO5 crystal allows the 3H4 - 1D2 transition of Pr3+ ions to be probed by the optical evanescent field that extends into the substrate. The 2 GHz inhomogeneous linewidth, the optical coherence time of 70 +- 5 us, and the spin state lifetime of 9.8 +- 0.3 s indicate that the properties of ions interacting with the waveguide mode are consistent with those of bulk ions. This result establishes the foundation for large, integrated and high performance rare-earth-ion quantum systems based on a waveguide platform., Comment: 5 pages, 5 figures