Linear and nonlinear effects of electron paramagnetic resonance in high-Q cryogenic sapphire microwave resonators

Abstract

Cryogenic sapphire resonators operating in Whispering Gallery Modes have very high Q-factors (> 10 9 ) at microwave frequencies . Such a property makes them useful for a host of applications, which are only possible due to the additional inclusion of residual paramagnetic impurities that annul the frequency-temperature dependence of sapphire. More recently, residual Fe 3+ impurities with parts-per-billion concentration within the lattice have been shown to create a three level system corresponding to the spin states of the ion. By pumping at 31.3 GHz, a stable 12.04 GHz maser signal (stability of parts in 10 1 4) has been created without any stabilization circuitry. In addition, we have observed the fundamental thermal noise limit near 4 K by operating such masers in a bimodal configuration. Annealing one resonator in air has led to conversion of Fe 2+ ions in the lattice to Fe 3+ , leading to an orders of magnitude increase in active ion concentration. At the post-annealing Fe 3+ concentration of 150 ppb , we observe nonlinear effects such as a degenerate four-wave mixing due to a χ (3) magnetic nonlinearity as well as stable frequency comb generation.