Non-Markovian quantum dynamics quantification in the Jaynes-Cummings model using principal component analisys

Recent advancements in quantum information science have led to an increased focus on the study of open quantum systems and their non-Markovian dynamics. In this paper, we present a novel approach to quantifying the non-Markovian dynamics of a n-dimensional quantum system using Principal Component Analysis (PCA). The motivation for this work stems from the growing interest in understanding the complex interplay between quantum systems and their environment, alongside the potential of machine learning techniques to provide new insights into such systems dynamics. We specifically apply our methodology to the Jaynes-Cummings (JC) model, which describes the interaction between a two-level atom and a quantized electromagnetic field mode, and a cornerstone in quantum non-Markovianity studies due to its characteristic collapse and revival phenomena. Our PCA-based method aims to capture the non-Markovian features of the system dynamics in a comprehensive and interpretable manner. This involves constructing a covariance matrix from the state vector of the system for a set of initial states and employing PCA to identify the dominant modes of variation. Subsequently, we analyze the temporal behavior of these principal components to quantify the non-Markovian characteristics of the system. Importantly, our method provides a more nuanced understanding of non-Markovian dynamics, revealing insights that may not be fully captured by conventional approaches.