Characterizing the Potential Energy of an Atom Trap Through Tomographic Fluorescence Imaging

We have developed a technique to fully characterize an arbitrary potential energy of an atom trap. The characterization allows one to measure the symmetry of the trap, a determining factor in many trapped atom applications. Created through a magneto-optical trap and evaporative cooling, a cold atom cloud is first loaded into our weakly-confined time-orbiting potential (TOP) trap. The whole atom cloud is then optically pumped into a dark state, an energy level that does not interact with the probe laser light. A selected part of the atom cloud is reactivated by a repump light which optically pump the atoms back into a state that can be probed. The repump light is shaped into a light sheet 168 $\mu$m thick. The reactivated region interacts with the probe laser light to create a fluorescence image. Since the light sheet is much thinner than the atom cloud, which is roughly 2 mm wide, the fluorescence image obtained is a cross-section of the atom cloud. A movable light sheet allows us to generate cross-section images of the cloud at different positions. A composite image of all the cross-section images shows the complete potential profile of our atom trap. This is similar to tomographic imaging used in medical imaging. We have verified the technique with two other methods: direct oscillation measurement at varying amplitude and numerical simulation of the atom trap. The technique is able to measure the potential up to the fourth-order terms in spatial coordinates. A complete characterization of the atom trap's symmetry will allow us to develop an atomic Foucault pendulum, a novel application for trapped atoms.