Fundamental Limitations of Cavity-assisted Atom Interferometry

TL;DR

This paper investigates the fundamental physical and design limitations of cavity-assisted atom interferometers, providing bounds on parameters like cavity length, temperature, and beam size to guide future experimental designs.

Contribution

It establishes theoretical upper and lower bounds on cavity parameters, revealing constraints on cavity length, bandwidth, and atomic ensemble temperature for effective atom interferometry.

Findings

Upper bounds on cavity length for symmetric two-mirror cavities.

Lower bound on cavity bandwidth to optimize power enhancement.

Upper limit on beam size based on cavity stability.

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.