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We use an atomic fountain clock to measure quantum scattering phase shiftsprecisely through a series of narrow, low-field Feshbach resonances at averagecollision energies below $1\,\mu$K. Our low spread in collision energy yieldsphase variations of order $\pm \pi/2$ for target atoms in several $F,m_F$states. We compare them to a theoretical model and establish the accuracy ofthe measurements and the theoretical uncertainties from the fitted potential.We find overall excellent agreement, with small statistically significantdifferences that remain unexplained.

Atomic Clock Measurements of Quantum Scattering Phase Shifts Spanning Feshbach Resonances at Ultralow Fields