Microwave-optical double resonance in a erbium-doped whispering-gallery-mode resonator

Abstract: We showcase an erbium-doped whispering-gallery-mode resonator with optical modes that display intrinsic quality factors better than $10^8$ (linewidths less than 2 MHz), and coupling strengths to collective erbium transitions of up to 2$\pi\times$1.2 GHz - enough to reach the ensemble strong coupling regime. Our optical cavity sits inside a microwave resonator, allowing us to probe the spin transition which is tuned by an external magnetic field. We show a modified optically detected magnetic resonance measurement that measures population transfer by a change in coupling strength rather than absorption coefficient. This modification was enabled by the strong coupling to our modes, and allows us to optically probe the spin transition detuned by more than the inhomogeneous linewidth. We contrast this measurement with electron paramagnetic resonance to experimentally show that our optical modes are confined in a region of large microwave magnetic field and we explore how such a geometry could be used for coherent microwave-optical transduction.