Measuring the oscillations of a Foucault pendulum with a tall atom interferometer*

A Foucault pendulum hangs in an unused elevator shaft in the physics department of the U.S. Naval Postgraduate School in Monterey, CA. The quantum sensing team is building a 30-meter-tall atom interferometer in an elevator shaft to measure the pendulum's motion. Atom interferometers have proven to be highly capable instruments for capturing precision measurements. In this interferometer we use strontium atoms to take advantage of a low magnetic dipole moment and two cooling transitions. Between laser pulses, the cold strontium atoms evolve freely and collect information about their surroundings. We anticipate the sensitivity of the instrument will be sufficient to measure the small changes in the gravitational potential due to the oscillating mass of the pendulum. An additional constraint is that the measurements need to be completed within time scales that are operationally relevant in a defense context. In this talk we present an update on the construction efforts and review the pertinent theoretical calculations for this sensor. Specifically, we highlight the Feynman path integral formulation associated with closing the interferometer and time-dependent phase calculations. Additionally, we show how initial calculations in 1D are altered to fit the 3D geometry of the experiment. We also discuss the intermediate design of a smaller version of the interferometer to test our systems at a reduced scale. We also discuss the anticipated next steps and review our experimental methodology.