We measured the homogeneous linewidth $\Gamma_h$ of ytterbium atoms inside a whispering gallery mode ring resonator. Using two-pulse photon echoes, we looked at the temperature dependence of $...Show moreWe measured the homogeneous linewidth $\Gamma_h$ of ytterbium atoms inside a whispering gallery mode ring resonator. Using two-pulse photon echoes, we looked at the temperature dependence of $\Gamma_h$ for an applied external magnetic field of $B=0$ and $B=0.3$ T. We found a clear narrowing of the linewidth at each temperature. Furthermore, we found saturation of $\Gamma_h$ for $T<30$ mK for both $B=0$ and $B=0.3$ T. At $T=10$ mK and $B=0.3$ T, we have observed a linewidth of 22 kHz, which is very near the lifetime limit of 1 kHz. Our results for the homogeneous linewidth of ions in glasses show that current theories have to be reconsidered. In addition, our results for $T_2$ ensure that rare earth element-doped cavities are a candidate for AFC quantum memory.Show less