Direct Observation of the Difference of Scattering Phase Shifts

We directly observe the difference of s-wave scattering phase shifts of Cs atoms in a juggling atomic fountain clock. In our fountain clock, we launch two balls of atoms in rapid succession so that they collide with relative velocities between 5 and 20 cm/s. After launching, the atoms are optically-pumped and cooled to 500 nK with degenerate sideband cooling in a far-detuned optical lattice. One ball, via several microwave transitions and a stimulated Raman transition, is velocity-selected and prepared in a superposition of the two Cs m$_{F}$=0 clock states. This coherent superposition scatters off of the atoms in the other ball, which is prepared in an F=4, m$_{F}$ state. Each atomic state is phase shifted by the scattering. After a second $\pi $/2 pulse, we use a second velocity-selective stimulated-Raman transition to probe the scattered atoms. We vary the phase of the second $\pi $/2 pulse and detect the Ramsey fringes of the scattered atoms. To lowest order, the phase shift of the Ramsey fringes is independent of the atomic density and the interrogation time.