Polarisation and Temperature Dependence of Er$^{3+}$:CaWO$_4$ -- Towards a Solid-State Rare-Earth Ion-Doped Quantum Memory

In the endeavour of developing quantum memories, Er$^{3+}$:CaWO$_4$ has emerged as a promising rare-earth ion-doped (REID) crystal platform due to its long optical coherence times and compatibility with the 1550 nm telecommunications band. This work investigates the effects of polarisation and temperature on the absorption strength, central wavelength, and linewidth of the $Z_1\to Y_1$ and $Z_1\to Y_2$ optical transitions, with light incident along the crystal $a$ and $c$ axes. It is found that the $Z_1\to Y_1$ transition at 1532.6 nm with the incident laser along the $c$-axis at cryogenic temperatures ($\sim$3 K) is particularly favourable. The transition exhibits a stable central wavelength, narrower linewidth, polarisation independence, larger absorption cross-section, and lies within the C-band -- attributes that make it highly suitable for quantum memory applications.