  Rare-earth (RE) ion doped nano-materials are promising candidates for a range
of quantum technology applications. Among RE ions, the so-called Kramers' ions
possess spin transitions in the GHz range at low magnetic fields, which allows
for high-bandwidth multimode quantum storage, fast qubit operations as well as
interfacing with superconducting circuits. They also present relevant optical
transitions in the infrared. In particular, Er$^{3+}$ has an optical transition
in the telecom band, while Nd$^{3+}$ presents a high-emission-rate transition
close to 890 nm. In this paper, we measure spectroscopic properties that are of
relevance to using these materials in quantum technology applications. We find
the inhomogeneous linewidth to be 10.7 GHz for Er$^{3+}$ and 8.2 GHz for
Nd$^{3+}$, and the excited state lifetime T$_1$ to be 13.68 ms for Er$^{3+}$
and 540 $\mu$s for Nd$^{3+}$. We study the dependence of homogeneous linewidth
on temperature for both samples, with the narrowest linewidth being 379 kHz
(T$_2$ = 839 ns) for Er$^{3+}$ measured at 3 K, and 62 kHz (T$_2$ = 5.14
$\mu$s) for Nd$^{3+}$ measured at 1.6 K. Further, we investigate time-dependent
homogeneous linewidth broadening due to spectral diffusion and the dependence
of homogeneous linewidth on magnetic field, in order to get additional clarity
of mechanisms that can influence the coherence time. In light of our results,
we discuss two applications: single qubit-state readout and a Fourier-limited
single photon source.
