Effects of mechanical processing and annealing on optical coherence properties of Er$^{3+}$:LiNbO$_3$ powders
Optical coherence lifetimes and decoherence processes in erbium-doped lithium niobate (Er$^{3+}$:LiNbO$_3$) crystalline powders are investigated for materials that underwent different mechanical and thermal treatments. Several complimentary methods are used to assess the coherence lifetimes for these highly scattering media. Direct intensity or heterodyne detection of two-pulse photon echo techniques was employed for samples with longer coherence lifetimes and larger signal strengths, while time-delayed optical free induction decays were found to work well for shorter coherence lifetimes and weaker signal strengths. Spectral hole burning techniques were also used to characterize samples with very rapid dephasing processes. The results on powders are compared to the properties of a bulk crystal, with observed differences explained by the random orientation of the particles in the powders combined with new decoherence mechanisms introduced by the powder fabrication. Modeling of the coherence decay shows that paramagnetic materials such as Er$^{3+}$:LiNbO$_3$ that have highly anisotropic interactions with an applied magnetic field can still exhibit long coherence lifetimes and relatively simple decay shapes even for a powder of randomly oriented particles. We find that coherence properties degrade rapidly from mechanical treatment when grinding powders from bulk samples, leading to the appearance of amorphous-like behavior and a broadening of up to three orders of magnitude for the homogeneous linewidth even when low-energy grinding methods are employed. Annealing at high temperatures can improve the properties in some samples, with homogeneous linewidths reduced to less than 10 kHz, approaching the bulk crystal linewidth of 3 kHz under the same experimental conditions.