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

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