Time-series and network analysis in quantum dynamics: Comparison with classical dynamics

Abstract

Time-series analysis and network analysis are now used extensively in diverse areas of science. In this paper, we applythese techniques to quantum dynamics in an optomechanical system: specifically, the long-time dynamics of the mean photon number in an archetypal tripartite quantum system comprising a single-mode radiation field interacting with a two-level atom and an oscillating membrane. We also investigate a classical system of interacting Duffing oscillators which effectively mimics several of the features of tripartite quantum-optical systems. In both cases, we examine the manner in which the maximal Lyapunov exponent obtained from a detailed time-series analysis varies with changes in an appropriate tunable parameter of the system. Network analysis is employed in both the quantum and classical models to identify suitable network quantifiers which will reflect these variations with the system parameter. This is a novel approach towards (i) examining how a considerably smaller data set (the network) obtained from a long time series of dynamical variables captures important aspects of the underlying dynamics, and (ii) identifying the differences between classical and quantum dynamics.

arXiv comment8 pages, 8 plots

References in corpus (23)

• The structure and function of complex networks
• Cavity Optomechanics
• Quantum support vector machine for big data classification
• From time series to complex networks: the visibility graph
• Practical implementation of nonlinear time series methods: The TISEAN package
• Recurrence Plot Based Measures of Complexity and its Application to Heart Rate Variability Data
• Towards quantum superpositions of a mirror
• Complex network approaches to nonlinear time series analysis
• Complex Network Approach for Recurrence Analysis of Time Series
• Ground-state cooling of a micromechanical oscillator: generalized framework for cold damping and cavity-assisted cooling schemes
• Classical Analog of Electromagnetically Induced Transparency
• Quantum wave packet revivals
• Opto-mechanical transducers for long-distance quantum communication
• Laser cooling of a nanomechanical resonator mode to its quantum ground state
• Short-range force detection using optically-cooled levitated microspheres
• The Geometry of Chaotic Dynamics -- A Complex Network Perspective
• Identifying complex periodic windows in continuous-time dynamical systems using recurrence-based methods
• Quantum Theory of Transmission Line Resonator-Assisted Cooling of a Micromechanical Resonator
• Optomechanical scheme for the detection of weak impulsive forces
• Back-action ground state cooling of a micromechanical membrane via intensity-dependent interaction
• Interpolating Coherent States for Heisenberg-Weyl and Single-Photon SU(1,1) Algebras
• Nonclassical effects in optomechanics: Dynamics and collapse of entanglement
• Recurrence network analysis in a model tripartite quantum system