Principal Component Analysis for Spatial Phase Reconstruction in Atom Interferometry

TL;DR

This paper introduces a PCA-based algorithm for extracting spatial phase patterns in atom interferometry, improving phase estimation accuracy without prior pattern knowledge, and demonstrating its effectiveness on simulated and experimental data.

Contribution

The paper presents a novel PCA-based method for characterizing spatial phase structures in atom interferometers without prior pattern assumptions.

Findings

Algorithm's reconstruction error scales inversely with the square root of the number of atoms or images.

Successfully applied to experimental data from an atom gravimeter.

Provides a foundation for understanding complex spatial phase patterns in interferometry.

Abstract

Atom interferometers are sensitive to a wide range of forces by encoding their signals in interference patterns of matter waves. To estimate the magnitude of these forces, the underlying phase shifts they imprint on the atoms must be extracted. Up until now, extraction algorithms typically rely on a fixed model of the patterns' spatial structure, which if inaccurate can lead to systematic errors caused by, for example, wavefront aberrations of the used lasers. In this paper we employ an algorithm based on Principal Component Analysis, which is capable of characterizing the spatial phase structure and per image phase offsets of an atom interferometer from a set of images. The algorithm does so without any prior knowledge about the specific spatial pattern as long as this pattern is the same for all images in the set. On simulated images with atom projection noise we show the algorithm's reconstruction performance follows distinct scaling laws, i.e., it is inversely-proportional to the square-root of the number atoms or the number of images respectively, which allows a projection of its performance for experiments. We also successfully extract the spatial phase patterns of two experimental data sets from an atom gravimeter. This algorithm is a first step towards a better understanding and complex spatial phase patterns, e.g., caused by inhomogeneous laser fields in atom interferometry.