This book explores interesting possibilities of extracting information about quantum states
from data readily obtained from experiments, such as tomograms and expectation values of
appropriate observables. The procedures suggested for identifying nonclassical effects such
as wave packet revivals, squeezing and entanglement solely from tomograms circumvent
detailed state reconstruction. Several bipartite entanglement indicators are defined based
on tomograms, and their efficacy assessed in models of atom-field interactions and qubitsystems. Tools of classical ergodic theory such as time series and network analysis are
applied to quantum observables treated as dynamical variables. This brings out novel
aspects involving different time scales. The book is aimed at researchers in the areas of
quantum optics and quantum dynamics.
Author(s): S. Lakshmibala, V. Balakrishnan
Series: SpringerBriefs in Physics
Publisher: Springer
Year: 2022
Language: English
Pages: 137
City: Cham
Preface
Contents
Acronyms
1 Introduction
References
2 Revivals, Fractional Revivals and Tomograms
2.1 Introduction
2.2 Basic Mechanism of Wave Packet Revivals
2.3 An Illustrative Example
2.4 Signatures of Revivals in Expectation Values of Observables
2.5 Effect of an Imperfectly Coherent Initial State
2.6 Revivals in Single-Mode Systems: A Tomographic Approach
2.7 Decoherence Effects
2.8 A Tomographic Approach to the Double-Well BEC System
References
3 Tomographic Approach to Squeezing
3.1 Introduction
3.2 Entropic Squeezing from Optical Tomograms
3.3 Quadrature and Higher-Order Squeezing from Optical Tomograms
References
4 Entanglement at Avoided Level Crossings
4.1 Introduction
4.2 Entanglement Indicators from Optical and Qubit Tomograms
4.3 Entanglement Indicators and Squeezing in Spin Systems
4.4 Bipartite CV Models and Avoided Level Crossings
4.5 Avoided Crossings in Multipartite HQ Systems: The Tavis–Cummings Model
References
5 Dynamics and Entanglement Indicators in Bipartite CV Systems
5.1 Introduction
5.2 The Bipartite Atom-Field Interaction Model Revisited
5.2.1 Time Evolution
5.2.2 Entanglement Dynamics
5.2.3 Tomographic Entanglement Indicators During Time Evolution
5.3 The Double-Well BEC Model Revisited
5.3.1 Time Development
5.3.2 Decoherence Effects in the Double-Well BEC Model
References
6 Dynamics of Entanglement Indicators in Hybrid Quantum and Spin Systems
6.1 Introduction
6.2 The Double Jaynes-Cummings Model
6.2.1 Dynamics
6.2.2 Equivalent Circuit for the DJC Model and the IBM Q Platform
6.3 The Double Tavis-Cummings Model
6.3.1 The Model
6.3.2 Equivalent Circuit and the IBM Q Platform
6.4 Bipartite Entanglement in Tripartite Models
6.4.1 The Cavity Optomechanical System
6.4.2 Λ-Atom Interacting with Radiation Fields
6.5 Entanglement and Squeezing in NMR Experiments
6.5.1 NMR Experiment I
6.5.2 Blockade and Freezing in Nuclear Spins
6.6 Concluding Remarks
References
7 Dynamics of the Mean Photon Number: Time Series and Network Analysis
7.1 Introduction
7.2 Brief Overview of Time Series Analysis
7.3 The Bipartite Atom-Field Interaction Model: Time Series Analysis
7.3.1 Dynamics
7.3.2 Power Spectrum and Lyapunov Exponent
7.3.3 Recurrence Statistics
7.4 Three-Level Atom Interacting with Radiation Fields
7.5 The Tripartite HQ Model with Intensity-Dependent Couplings
7.5.1 The Model
7.5.2 Time Series Analysis with Large and Small Data Sets
7.5.3 Return Maps and Recurrence Time Distributions
7.5.4 Recurrence Plots and Recurrence Network
7.5.5 Network Analysis
7.6 Concluding Remarks
References
8 Conclusion and Outlook
