Imaging the collective excitations of an ultracold gas using statistical correlations

TL;DR

This paper demonstrates that principal component analysis can effectively extract and characterize collective excitations in ultracold gases from noisy images, providing detailed mode information.

Contribution

The authors introduce a novel application of PCA to ultracold gas images, enabling identification and analysis of collective modes from noisy data.

Findings

Successfully identified collective modes and their frequencies

Determined mode populations and eigenfunctions

Method is robust against noise and data sampling variations

Abstract

Advanced data analysis techniques have proved to be crucial for extracting information from noisy images. Here we show that principal component analysis can be successfully applied to ultracold gases to unveil their collective excitations. By analyzing the correlations in a series of images we are able to identify the collective modes which are excited, determine their population, image their eigenfunction, and measure their frequency. Our method allows to discriminate the relevant modes from other noise components and is robust with respect to the data sampling procedure. It can be extended to other dynamical systems including cavity polariton quantum gases or trapped ions.