Generalized Independent Component Analysis for Extracting Eigen-Modes of a Quantum System

TL;DR

This paper introduces an unsupervised machine learning method inspired by independent component analysis to extract eigenmode frequencies from noisy quantum system data, especially when short measurement times limit Fourier analysis.

Contribution

The authors develop a generalized ICA-based algorithm tailored for quantum eigenmode extraction, addressing challenges of noise and limited measurement durations.

Findings

Successfully applied to cold atom collective mode data

Outperforms traditional Fourier analysis in short-time measurements

Demonstrates broad applicability to quantum dynamical experiments

Abstract

In many dynamical probes of a quantum system, quite often multiple eigenmodes are excited. Therefore, the experimental data can be quite messy due to the mixing of different modes, as well as the background noise, despite that each mode manifests itself as a single frequency oscillation. Here we develop an unsupervised machine learning algorithm to extract the frequencies of these oscillations from such measurement data, that is, the eigenenergies of these modes. This method is particularly useful when the measurement time is not long enough to perform the Fourier transformation. Our method is inspired by the independent component analysis method and its application to the cocktail party problem. In that problem, the goal is to recover each voice from detectors that detect signals of many mixed voices, and the principle is to find out signals that possess features and are away from a Gaussian distribution. Instead, our generalization is to find out signals that are close to a single frequency oscillation. We demonstrate the advantage of our method by an example of analyzing the collective mode of cold atoms. We believe this method can find broad applications in analyzing data from dynamical experiments in quantum systems.