Progress towards an ultracold atomic Sagnac gyroscope

   Precise, accurate inertial navigation relies upon the rotation rate measurements of a
sensitive gyroscope. State of the art fiber optic gyroscopes measure rotation via the Sagnac
effect, which causes a phase shift proportional to the angular velocity of a rotating interferometer
whose beam path encloses an area. Gyroscopes using interfering atoms have a much greater
Sagnac phase shift for the same enclosed area than optical gyroscopes, and therefore promise
much greater sensitivity. However, an atom Sagnac gyroscope has not yet been demonstrated
in a compact device.
   This dissertation describes work towards the demonstration of a compact Sagnac gyroscope
using interfering ultracold atoms, which can be guided around suitably large areas using
magnetic potentials generated by micro-scale "atom chips". We first present the results of a
sequence of preliminary Bose-Einstein condensate (BEC) Michelson interferometry experiments.
In these experiments, BECs confined to a waveguide interfere, but the path does not enclose
area. We present the application of statistical image analysis techniques to data from our experiments.
We analyze the lessons learned about both apparatus design and the physics of BEC
interferometry. We describe the design of a new atom chip that should allow us to translate the
waveguide during the interferometry experiment, thus turning Michelson into Sagnac interferometry.
Finally, we explain the design of a new compact BEC apparatus that incorporates the
gyroscope chip. The apparatus is built on a rotary table so that we may truly test the gyroscope
when it is complete. We report on experimental progress towards the achievement of BEC in
this apparatus.