Four Wave Mixing from Fe3+ Spins in Sapphire

Fe3+ ions in sapphire exhibit an Electron Spin Resonance (ESR) which interacts strongly with high-Q Whispering Gallery (WG) modes at microwave frequencies. We report the first observation of a third-order paramagnetic nonlinear susceptibility in such a resonator at cryogenic temperatures, and the first demonstration of four wave mixing (FWM) using this parametric nonlinearity. This observation of an all-microwave nonlinearity is an enabling step towards a host of quantum measurement and control applications which utilize spins in solids.