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, $10\mu \mathrm{m}$ radius, and sphericity to within less than 1 Å. 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.

中文翻译：

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具有原子尺度公差的微球会产生超简并性

在精确的科学测量以及传感应用中，简并性起着至关重要的规则。球形谐振器由于其最高的对称性而具有高度的简并性。然而，制造完美的球体具有挑战性，因为即使固定球体的杆也会破坏对称性。在这里，我们制造了一个悬浮的球形谐振器，该谐振器与标准光纤e逝耦合。我们确定谐振器的光学品质因数超过十亿，$10\mu \mathrm{米}$半径和球形度在1Å以内。利用我们的高质量和球形性，我们通过实验将超过200的简并性提升，我们用超过1千万的光学精细度来解决。然后，我们在进行相应的理论计算后，给出了实验测量的简并模及其状态密度。我们的非接触式光子谐振器与标准电信光纤技术兼容，展现出（质量因数）/（模量）所定义的最高谐振增强，而填充我们腔体的模在任何研究过的系统中均显示出最高的简并度。与通常使用最低阶两倍简并性的其他设置相比。