Title: Fundamental Limitations of Cavity-assisted Atom Interferometry,
Abstract: Atom interferometers employing optical cavities to enhance the beam splitter
pulses promise significant advances in science and technology, notably for
future gravitational wave detectors. Long cavities, on the scale of hundreds of
meters, have been proposed in experiments aiming to observe gravitational waves
with frequencies below 1 Hz, where laser interferometers, such as LIGO, have
poor sensitivity. Alternatively, short cavities have also been proposed for
enhancing the sensitivity of more portable atom interferometers. We explore the
fundamental limitations of two-mirror cavities for atomic beam splitting, and
establish upper bounds on the temperature of the atomic ensemble as a function
of cavity length and three design parameters: the cavity g-factor, the
bandwidth, and the optical suppression factor of the first and second order
spatial modes. A lower bound to the cavity bandwidth is found which avoids
elongation of the interaction time and maximizes power enhancement. An upper
limit to cavity length is found for symmetric two-mirror cavities, restricting
the practicality of long baseline detectors. For shorter cavities, an upper
limit on the beam size was derived from the geometrical stability of the
cavity. These findings aim to aid the design of current and future
cavity-assisted atom interferometers.