Microwave dielectric properties of LiNbO$_{\mathbf{3}}$ and AlN at millikelvin temperatures and single-photon power

Electro-optic materials are paramount to achieving efficient and

reliable signal transduction in the quantum regime.

It is of great interest to investigate the performance of these materials

at the quantum level and at cryogenic temperatures to assess their compatibility

with superconducting circuit-based quantum systems. This work presents a

detailed study of the electric properties of bulk, single-crystal LiNbO$_{3}$ and AlN at cryogenic

temperatures and at the single photon level. We characterize the

materials' dielectric loss tangent and dielectric tensor throughout a wide range of

electromagnetic power levels between temperatures from 35 to 700 mK. Our findings indicate that

both materials' loss tangent behavior is consistent with the two-level system model up

to a certain power threshold, beyond which it increases logarithmically with power. This suggests that

two-level system loss mechanisms dominate at the single-photon level, while additional loss mechanisms

become apparent at higher powers and temperatures.