Bifurcations, time-series analysis of observables, and network properties in a tripartite quantum system

Abstract

In a tripartite system comprising a $\Lambda$-atom interacting with two radiation fields in the presence of field nonlinearities and an intensity-dependent field-atom coupling, striking features have been shown to occur in the dynamics of the mean photon number $\aver{N_{i}(t)}$ ($i=1,2$) corresponding to either field. In this Letter, we carry out a detailed time-series analysis and establish an interesting correlation between the short-time and long-time dynamics of $\aver{N_{i}(t)}$. Lyapunov exponents, return maps, recurrence plots, recurrence-time statistics, as well as the clustering coefficient and the transitivity of networks constructed from the time series, are studied as functions of the intensity parameter $\kappa$. These are shown to carry signatures of a special value $\kappa =\bar{\kappa }$. Our work also exhibits how techniques from nonlinear dynamics help analyze the behavior of observables in multipartite quantum systems.

References in corpus (19)

• Quantum Machine Learning
• Recurrence Plots for the Analysis of Complex Systems
• Quantum support vector machine for big data classification
• Practical implementation of nonlinear time series methods: The TISEAN package
• Sudden Death of Entanglement
• Recurrence Plot Based Measures of Complexity and its Application to Heart Rate Variability Data
• Complex network approaches to nonlinear time series analysis
• Historical Review of Recurrence Plots
• Identifying complex periodic windows in continuous-time dynamical systems using recurrence-based methods
• Back-action ground state cooling of a micromechanical membrane via intensity-dependent interaction
• Nonlinear photon-atom coupling with 4Pi microscopy
• Signatures of nonclassical effects in optical tomograms
• Interpolating Coherent States for Heisenberg-Weyl and Single-Photon SU(1,1) Algebras
• Quantum algorithms for topological and geometric analysis of big data
• Estimation of squeezing properties of multiphoton coherent states from optical tomograms
• Nonclassical effects in optomechanics: Dynamics and collapse of entanglement
• Dynamics of an open quantum system interacting with a quantum environment
• Entanglement dynamics in a model tripartite quantum system
• Recurrence network analysis in a model tripartite quantum system

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