Linear quantum measurement theory of matter-wave interferometry

Abstract: The theory of linear quantum measurement has been developed for analysing the sensitivities of experimental devices that measure extremely weak signals, such as gravitational waves. It has successfully contributed to the theoretical understanding of laser interferometer gravitational-wave detectors (used by LIGO, VIRGO and KaGRA) and helped many important experimental upgrades. In this work, we establish a linear quantum measurement theory for another kind of measurement device--- matter wave interferometers, which has been widely discussed as an important platform for many high-precision experiments. This theory allows us to account for both atom and light fluctuations, and leads to a detailed analysis of back-action in matter-wave interferometry (action of light back onto the atoms) and its effect on dynamics and measurement noise. From this analysis, we obtain a Standard Quantum Limit (SQL) for matter-wave interferometry. A comparison between the LIGO detector and matter wave interferometer is also given from the perspective of quantum measurement.