Concentration dependence of the optical and spin inhomogeneous linewidth in Europium-doped yttrium orthosilicate crystals

The transportable quantum memory is a viable solution for realizing the long-distance quantum communication, which requires a storage lifetime of the order of hours. The isotope-enriched $^{151}$Eu$^{3+}$:Y$_2$SiO$_5$ crystals are promising candidates for this application. However, their optical storage efficiency and spin storage lifetime is limited by the wide inhomogeneous linewidth. In this work, we successfully cultivated isotope-enriched $^{151}$Eu$^{3+}$:Y$_2$SiO$_5$ crystals with varying doping concentrations utilizing the Czochralski method. The optical inhomogeneous broadening and spin inhomogeneous broadening are measured by the optical absorption spectroscopy and optically detected magnetic resonance tests, respectively. Notably, in the undoped samples, we identified a baseline level of inhomogeneous broadening linewidths, registering at 390 $\pm$ 15 MHz for optical inhomogeneous broadening and 4.6 $\pm$ 0.2 kHz for spin inhomogeneous broadening. Our findings reveal that point defects, induced by the doping ions, significantly contribute to the inhomogeneous broadening, at a rate of 0.97 MHz/ppm for optical broadening and 0.014 kHz/ppm for spin broadening. Furthermore, we discussed the impact of dislocations on inhomogeneous broadening and proposed potential strategies to further mitigate these effects. Such advancements hold promise for fostering the development of ultra-long-lifetime transportable quantum memory applications. The optical inhomogeneous linewidth fitted as a function of $^{151}$Eu$^{3+}$ concentrations. $[^{151}$Eu$^{3+}]$ is the concentration of $^{151}$Eu$^{3+}$ ions. $\Gamma_{\rm opt-inh}$ is the optical inhomogeneous linewidth. Black squares stand for the data points. The red and blue lines represent linear fits of 0 ppm to 100 ppm and 100 ppm to 1000 ppm, respectively. The fitting equations are depicted in the graph, accompanied by arrows indicating their corresponding lines. (b) The fitting curve of concentration-dependent variation in the spin inhomogeneous broadening. $[^{151}$Eu$^{3+}]$ stands for the concentration of $^{151}$Eu$^{3+}$ ions. $\Gamma_{\rm spin-inh}$ represents the spin inhomogeneous linewidth. Black squares are the data points. The red and blue lines represent linear fits ranging from 0 ppm to 100 ppm and from 100 ppm to 1000 ppm, respectively. The fitted equations are illustrated in the graph, pointing to their respective lines by arrows.