The frequency stability of lasers is limited by thermal noise in state-of-the-art frequency references. Further improvement requires operation at cryogenic temperature. In this context, we investigate a fiber-based ring resonator. Our system exhibits a first-order temperature-insensitive point around $3.55$ K, much lower than that of crystalline silicon. The observed low sensitivity with respect to vibrations ($<5cdot{10^{-11}},text{m}^{-1} text{s}^{2}$), temperature ($-22(1)cdot{10^{-9}},text{K}^{-2}$) and pressure changes ($4.2(2)cdot{10^{-11}},text{mbar}^{-2}$) makes our approach promising for future precision experiments.
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