Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Hamiltonians for Quantum Optics

Z. Ficek, Mohamed Ridza Wahiddin

Published Apr 19, 2016• 0 citations
Publisher

Abstract

We often hear at seminars and presentations ‘Show me the Hamiltonian of your problem and I will tell you what problem you are talking about’. Therefore, to understand what quantum optics is about, we start from the description of a standard Hamiltonian of the problems considered in quantum optics. We illustrate the method of derivation of the explicit form of the Hamiltonian for a simple system that is composed of two subsystems that interact (communicate) with each other. As we shall see, the explicit form of the Hamiltonian is essential to explicitly calculate energy levels of a given combined system and the temporal evolution of an arbitrary operator representing the system.

DOI
10.1201/b16875-4

Related papers

Effective Hamiltonian Approach to the Master Equation

X. X. Yi, Sixia Yu

A method of exactly solving the master equation is presented in this letter. The explicit form of the solution is determined by the time evolution of a composite system including an auxiliary system and the open system in question. The effective Hamiltonian governing the time evolution of the composed system are derived from the master equation. Two examples, the dissipative two-level system and the damped harmonic oscillator, are presented to illustrate the solving procedure. PACS number(s): 05.30.-d, 05.40.+j, 42.50.Ct Typeset using REVTEX 1 The problem of open quantum systems has been around since the beginnings of quantum mechanics [1]. Important contributions to this general area have been made by researchers working in fields as diverse as cosmology [2], condensed matter [3], quantum optics [4,5], particle physics [6], quantum measurement [7], and quantum computation [8]. The problem can be described generally as interest in the effective dynamics of the open system surrounded

•Jan 1, 2000•15 citations

The quantum theory of light

Stephen Mark Barnett, John Jeffers

We present a brief introduction to the quantum theory of light as it is understood in the field of quantum optics. Our aim is not to review the topic, which would require a very extensive article (or even a book of several volumes) but rather to provide sufficient background to set the ideas in the following papers in their correct context.This article is part of the theme issue 'The quantum theory of light'.

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Dec 24, 2024•2 citations

Quantum Optics

Marlan O. Scully, Muhammad Suhail Zubairy

The field of quantum optics has witnessed significant theoretical and experimental developments in recent years. This book provides an in-depth and wide-ranging introduction to the subject, emphasising throughout the basic principles and their applications. The book begins by developing the basic tools of quantum optics, and goes on to show the application of these tools in a variety of quantum optical systems, including lasing without inversion, squeezed states and atom optics. The final four chapters are devoted to a discussion of quantum optical tests of the foundations of quantum mechanics, and to particular aspects of measurement theory. Assuming only a background of standard quantum mechanics and electromagnetic theory, and containing many problems and references, this book will be invaluable to graduate students of quantum optics, as well as to researchers in this field.

Cambridge University Press eBooks•Sep 4, 1997•6,586 citations

Dicke model investigations in the framework of reduced description method

Alexander I. Sokolovsky, Sergiy F. Lyagushyn

The reduced description method proceeds from Bogolyubov’s idea that at large times the non-equilibrium system evolution can be described with the limited number of parameters and principle of correlation weakening. The way to the right choice of such parameters and constructing the time evolution equations for them was opened by the works of Kharkiv school in statistical physics. A quarter of a century ago at Dnipropetrovsk National University the developed method was first applied to the Dicke system of two-level emitters interacting via electromagnetic field. The paper presents a short review of the results obtained. They include the analysis of Dicke Hamiltonian structure, the choice of reduced description parameters satisfying the Peletminskii – Yatsenko scheme conditions, the realization of this scheme for concentrated and prolonged Dicke systems resulting in the temporal equation for emitter subsystemstatistical operator. The reduced description method possibilities are illustrated with using the effective Hamiltonian concept, in particular taking into account emitter motion and higher correlations. Reformulating the theory in terms of electromagnetic field allowed to construct the electrodynamics of medium formed by two-level emitters with considering binary correlations of field variables and to put forward the problem of correlation development picture. A new method of investigating correlations in quasispin subsystem with using ferromagnetism theory approach was also proposed.

Journal of Physics and Electronics•Dec 30, 2024•0 citations

Single‐Atom Entanglement for a System of Directly Linked Two Cavities in the Presence of an External Classical Field: Effect of Atomic Coherence

Sadek Ahmed Hanoura, M. M. A. Ahmed, Eied Mahmoud Khalil +1 more

Abstract The Hamiltonian of a system composed of two standard Jaynes‐Cummings cells connected by the overlap of evanescent cavity fields, which allows photons to hop from the first cavity to the second and vice versa, and interacting with an external classical field, is simplified in the framework of unitary canonical transformations. James's method of the effective Hamiltonian is used in the derivation of two effective Hamiltonians with two completely dispersive regimes. Analytical expressions for the time dependent wavefunction and the elements of the reduced atomic operators for the different Hamiltonians are derived. The temporal evolution of atomic quantum entropy is calculated when the fields are initially in their vacuum states with various forms of the atomic initial states. Effects of the photon hopping strength, detuning and the various forms of the atomic initial states on the evolution of the von Neumann entropies are analyzed. The impact of the time‐average technique on the features resulting due to involving the controlling parameters and their influences on the considered functions is discussed. Damping is taken into account through a non‐Hermitian Hamiltonian and results are discussed. General conclusions reached are illustrated by numerical results.

Fortschritte der Physik•May 28, 2019•4 citations

Quantum Optics for Experimentalists

Z. Y. Ou

This book on quantum optics is from the point of view of an experimentalist. It approaches the theory of quantum optics with the language of optical modes of classical wave theory, with which experimentalists are most familiar.

WORLD SCIENTIFIC eBooks•Feb 6, 2017•58 citations
We often hear at seminars and presentations ‘Show me the Hamiltonian of your problem and I will tell you what problem you are talking about’. Therefore, to understand what quantum optics is about, we start from the description of a standard Hamiltonian of the problems considered in quantum optics. We illustrate the method of derivation of the explicit form of the Hamiltonian for a simple system that is composed of two subsystems that interact (communicate) with each other. As we shall see, the explicit form of the Hamiltonian is essential to explicitly calculate energy levels of a given combined system and the temporal evolution of an arbitrary operator representing the system.
A method of exactly solving the master equation is presented in this letter. The explicit form of the solution is determined by the time evolution of a composite system including an auxiliary system and the open system in question. The effective Hamiltonian governing the time evolution of the composed system are derived from the master equation. Two examples, the dissipative two-level system and the damped harmonic oscillator, are presented to illustrate the solving procedure. PACS number(s): 05.30.-d, 05.40.+j, 42.50.Ct Typeset using REVTEX 1 The problem of open quantum systems has been around since the beginnings of quantum mechanics [1]. Important contributions to this general area have been made by researchers working in fields as diverse as cosmology [2], condensed matter [3], quantum optics [4,5], particle physics [6], quantum measurement [7], and quantum computation [8]. The problem can be described generally as interest in the effective dynamics of the open system surrounded
The field of quantum optics has witnessed significant theoretical and experimental developments in recent years. This book provides an in-depth and wide-ranging introduction to the subject, emphasising throughout the basic principles and their applications. The book begins by developing the basic tools of quantum optics, and goes on to show the application of these tools in a variety of quantum optical systems, including lasing without inversion, squeezed states and atom optics. The final four chapters are devoted to a discussion of quantum optical tests of the foundations of quantum mechanics, and to particular aspects of measurement theory. Assuming only a background of standard quantum mechanics and electromagnetic theory, and containing many problems and references, this book will be invaluable to graduate students of quantum optics, as well as to researchers in this field.
The reduced description method proceeds from Bogolyubov’s idea that at large times the non-equilibrium system evolution can be described with the limited number of parameters and principle of correlation weakening. The way to the right choice of such parameters and constructing the time evolution equations for them was opened by the works of Kharkiv school in statistical physics. A quarter of a century ago at Dnipropetrovsk National University the developed method was first applied to the Dicke system of two-level emitters interacting via electromagnetic field. The paper presents a short review of the results obtained. They include the analysis of Dicke Hamiltonian structure, the choice of reduced description parameters satisfying the Peletminskii – Yatsenko scheme conditions, the realization of this scheme for concentrated and prolonged Dicke systems resulting in the temporal equation for emitter subsystemstatistical operator. The reduced description method possibilities are illustrated with using the effective Hamiltonian concept, in particular taking into account emitter motion and higher correlations. Reformulating the theory in terms of electromagnetic field allowed to construct the electrodynamics of medium formed by two-level emitters with considering binary correlations of field variables and to put forward the problem of correlation development picture. A new method of investigating correlations in quasispin subsystem with using ferromagnetism theory approach was also proposed.
Abstract The Hamiltonian of a system composed of two standard Jaynes‐Cummings cells connected by the overlap of evanescent cavity fields, which allows photons to hop from the first cavity to the second and vice versa, and interacting with an external classical field, is simplified in the framework of unitary canonical transformations. James's method of the effective Hamiltonian is used in the derivation of two effective Hamiltonians with two completely dispersive regimes. Analytical expressions for the time dependent wavefunction and the elements of the reduced atomic operators for the different Hamiltonians are derived. The temporal evolution of atomic quantum entropy is calculated when the fields are initially in their vacuum states with various forms of the atomic initial states. Effects of the photon hopping strength, detuning and the various forms of the atomic initial states on the evolution of the von Neumann entropies are analyzed. The impact of the time‐average technique on the features resulting due to involving the controlling parameters and their influences on the considered functions is discussed. Damping is taken into account through a non‐Hermitian Hamiltonian and results are discussed. General conclusions reached are illustrated by numerical results.