Fundamental limitations of cavity-assisted atom interferometry

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.