Modified independent component analysis for extracting Eigen-Modes of a quantum system

Abstract

Dynamical probes are popular experimental tools for studying quantum systems nowadays. Though a well-defined eigen-mode will manifest itself as a single frequency oscillation in the dynamical probe, the real experimental data can be quite messy because a probe usually excites multiple modes which are also mixed together with random white noise. Moreover, the oscillations usually quickly damp out due to finite decoherence time. These make it difficult to extract the frequencies of these oscillation measurement data, that is, the eigen-energies of these eigen-modes. Here we develop an unsupervised machine learning algorithm to solve this problem. Our method is inspired by the independent component analysis method and its application to the 'cocktail party problem', where the goal is to recover each voice from detectors that detect signals of many mixed voices. We demonstrate the advantage of our method by an example of analyzing the collective mode of a Bose-Einstein condensate of atomic gases. We believe that this method can find broad applications in analyzing data of dynamical experiments in quantum systems of different fields.