Measuring a Foucault pendulum oscillation period with an atom interferometer

At the NPS physics department in Monterey, CA, a Foucault pendulum hangs in an unused elevator shaft. We are constructing a 30-meter atom interferometer in an adjacent elevator shaft, anticipating sufficient sensitivity to detect the motion of the pendulum by measuring the minute changes in the gravitational potential caused by the oscillating mass. In this talk, we will present some of the theoretical calculations, based on Feynman path integrals, associated with this experiment. In particular, for a simple 1D geometry, we derive an expression for the time-dependent phase to be measured and further demonstrate that the atom interferometer closes in position and momentum. We then modify those initial calculations to account for the geometry of the experiment. We will highlight that the main goal of the experiments is not so much to count pendulum swings as to detect extremely weak signals in an operationally relevant environment and relevant time scales. Our interferometer is based on cold Strontium atoms. The status of the apparatus construction and experiments will be presented.