Figure 5: Mid-IR multiphonon absorption in crystalline microcavities.

(a) Measurements for different fluoride crystals of the XF₂ family (where X=Ca, Mg, Ba and Sr) prove the possibility of attaining the ultra-high-Q regime in the mid-IR. Except for MgF₂, for which we reach the theoretical limit imposed by multiphonon absorption (orange shaded region) at room temperature, other materials offer Q≥10⁸ around 4.5 μm. The lines represent the theoretical multiphonon absorption limit of Q with respect to the wavelength. The circles represent our experimental values. Despite the clear differences with the near-IR region, mid-IR cavities are able to overcome the high-Q regime achieving Q>10⁸. Measurements around 2 μm show typical level of impurities and defects that limits quality factors when they are not limited by Rayleigh scattering (short wavelengths) or multiphonon absorption (long wavelengths). Measurements around 3 μm highlight that OH absorption can strongly degrade the intrinsic Q factor of crystalline materials and constitutes a lower bound of Q limitation due to impurities and defects. The dashed grey line is a guide to the eye depicting bulk water absorption Q limitation (from ref. 50). Note that 1.5 μm represents the less-affected wavelength by OH absorption (by a few orders of magnitude compared with any other wavelengths). (b) Experimental proof of multiphonon absorption in a microresonator made out of an ionic crystal. Temperature sweeps of the microresonator reveal a typical temperature dependence of intrinsic multiphonon absorption for MgF₂ (fitted slopes of ∼4 × 10⁻² MHz K⁻¹) and consistently no temperature dependence for extrinsic absorption limited SrF₂ (fitted slope of 10⁻³ MHz K⁻¹). Sweep with increasing (up) and decreasing (down) temperatures corroborate the temperature dependence of the intrinsic losses. From the theoretical slope (see Discussion) we infer that two-phonon (N=2) processes contribute mostly to the temperature dependence.