We scan the collision energy of two clouds of cesium atoms between 12 and 50 μK in atomic fountain clock. By directly detecting the difference of s-wave scattering phase shifts, we observe a rapid variation of a scattering phase shift through a series of Feshbach resonances. At the energies we use, resonances that overlap at threshold become resolved. Our statistical phase uncertainty of 8 mrad can be improved in future precision measurements of Feshbach resonances to accurately determine the Cs-Cs interactions, which may provide stringent limits on the time variation of fundamental constants. PACS: 34.50.Cx, ρ06.30.Ft Feshbach scattering resonances occur when the continuum state of two colliding particles couples to a bound state (Fig. 1) [1]. Feshbach resonances have found wide applicability in dilute, ultracold, atomic and molecular gases because they provide an accessible control of the inter-particle interactions [2-6]. Feshbach's elegant treatment of scattering resonances showed that scattering phase shifts, and hence cross sections, change rapidly as the collision energy tunes through resonance. The rapid phase change is a general feature of resonance phenomena and the resonant energy dependence of cross sections has been observed in a variety of experiments, including neutron and electron scattering and photodetachment [7][8][9]. In ultracold gases, so far magnetic fields have been used to tune resonances to threshold, changing the energy of the bound state by vertically translating the grey potential in Fig. 1, instead of tuning the collision energy [3][4][5][6][7][8][9][10][11]. Here, we scan the collision energy between two ultracold clouds of cesium atoms in an atomic clock and directly observe the scattering phase shift [12] through a series of scattering resonances. Increasing the collision energy allows us to resolve resonances that overlap at threshold. Precise measurements of scattering phase shifts through a resonance will very accurately determine the resonance position, giving a highly precise determination of the atomic interactions [5] and a potential route to stringent limits on the time variation of fundamental constants [13,14].We directly measure scattering phase shifts by preparing cesium atoms in coherent superpositions of the two clock states and detecting the phase shift of these coherences after the clock atoms scatter off atoms prepared in a pure 'target' state ( Fig. 2 inset) [12]. When the ⎜F=3,m F =0Ú (⎜40Ú) clock state scatters off the target atoms, it acquires a scattering phase shift δ 3 (δ 4 ). The phase of the clock coherence, the superposition of ⎜30Ú and ⎜40Ú, precesses as hands on a clock. The scattering causes the phase of the coherence to jump by the difference of the scattering phase shifts, Φ=δ 4 −δ 3 [12], represented by the time difference between the ring of scattered clocks and the unscattered clock in the Fig. 2 inset. We directly detect Φ as a phase shift of the clock's Ramsey fringes as in Fig. 2(b). To be sensitive to the s-wave phase shifts, we detect at...

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 µK. Our low spread in collision energy yields phase variations of order ±π/2 for target atoms in several F, mF 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.