Microspheres with Atomic-Scale Tolerances Generate Hyperdegeneracy

Degeneracies play a crucial rule in precise scientific measurements as well as in sensing applications. Spherical resonators have a high degree of degeneracy thanks to their highest symmetry; yet, fabricating perfect spheres is challenging because even a stem to hold the sphere breaks the symmetry. Here we fabricate a levitating spherical resonator that is evanescently coupled to a standard optical fiber. We characterize the resonators to exhibit an optical quality factor exceeding a billion, 10 mu m radius, and sphericity to within less than 1 angstrom. Using our high quality and sphericity, we experimentally lift degeneracies of orders higher than 200, which we resolve with optical finesse exceeding 10 000 000. We then present our experimentally measured degenerate modes as well as their density of states next to our corresponding theoretical calculation. Our contactless photonic resonator is compatible with standard telecom fiber technology, exhibits the highest resonance enhancement as defined by (quality factor)/(mode volume), and the modes populating our cavity show the highest order of degeneracy reported in any system ever studied. This is in comparison with other settings that typically utilize the lowest-order twofold degeneracy.