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  1. We have characterized the effects of thermal phase fluctuations in narrow rings of ultracold Fermi superfluids in the unitary regime and demonstrated that matter-wave interference may be reliably used to measure angular variations in the phase difference between two concentric, coplanar superfluid rings. When one of the rings is cut with a barrier, we find that phase fluctuations around that ring can be large enough to degrade the reliability of protocols for control of quantized circulation states. The effect is greatest when the one-dimensional density is low and the coupling between rings is negligible. In this limit, our measurements are consistent with a correlation length smaller than the system size, as expected from theory. These results establish the crucial role of phase fluctuations for experiments involving ultracold superfluids in elongated circuit-like geometries. 
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    Free, publicly-accessible full text available August 1, 2026