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Efficient quantum memory is of paramount importance for long-distance quantumcommunications, as well as for complex large-scale computing architectures. Weinvestigate the capability of Er$^{3+}$:Y$_2$SiO$_5$ crystal to serve as aquantum memory for the travelling microwave photons by employing techniquesdeveloped for dense optical ensembles. In our efforts to do so, we haveperformed high-resolution microwave spectroscopy of Er$^{3+}$:Y$_2$SiO$_5$,where we identified electronic spin as well as hyperfine transitions.Furthermore, we have explored spectral hole burning technique and studied thespin relaxation process at millikelvin temperatures, determined the mainrelaxation mechanisms, which lay the groundwork for further studies of thetopic.

Microwave cavity-free hole burning spectroscopy of Er$^{3+}$:Y$_2$SiO$_5$ at millikelvin temperatures