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

arXiv:1009.5593

Integrals of motion and Robertson-Schrödinger correlated states of electromagnetic field in time-dependent linear media

Andrey K. Angelow, D. A. Trifonov

Published Sep 28, 2010• 0 citations
arXivHTMLPDF

Abstract

Integrals of motion and statistical properties of quantized electromagnetic field (e.-m. field) in time-dependent linear dielectric and conductive media are considered, using Choi-Yeon quantization, based on Caldirola-Kanai type Hamiltonian. Eigenstates of quadratic and linear invariants are constructed, the solutions being expressed in terms of a complex parametric function that obeys classical oscillator equation with time-varying frequency. The time evolutions of initial Glauber coherent states and Fock states are considered. The medium conductivity and the time-dependent electric permeability are shown to generate squeezing and non-vanishing covariances. In the time-evolved coherent and squeezed states all the second statistical moments of the electric and magnetic field components are calculated and shown to mminimize the Robertson-Schrödinger uncertainty relation.

DOI
10.48550/arxiv.1009.5593

Related papers

Dynamical Invariants and Robertson-Schrodinger Correlated States of Electromagnetic Field in Nonstationary Linear Media

D. A. Trifonov, Andrey K. Angelow, Kouei Sekigawa +3 more

Dynamical invariants and statistical properties of the quantized electromagnetic field in nonstationary linear media (dielectric and/or conductive) are considered in the framework of Choi‐Yeon quantization scheme. It is shown that in the eigenstates of linear dynamical invariant the Robertson‐Schrödinger uncertainty relation is minimized, both for the photon annihilation operator quadratures and for the electric and magnetic field components. The time evolution of initial Glauber coherent states and Fock (photon number) states is considered. On an initial coherent state the medium conductivity and the time‐dependent electric permeability both are shown to act as squeezing and correlating factors.

AIP conference proceedings•Jan 1, 2011•2 citations

Dynamical Invariants and Robertson-Schrodinger Correlated States of Electromagnetic Field in Nonstationary Linear Media

D. A. Trifonov, Andrey K. Angelow

Dynamical invariants and statistical properties of the quantized electromagnetic field in nonstationary linear media (dielectric and/or conductive) are considered in the framework of Choi‐Yeon quantization scheme. It is shown that in the eigenstates of linear dynamical invariant the Robertson‐Schrödinger uncertainty relation is minimized, both for the photon annihilation operator quadratures and for the electric and magnetic field components. The time evolution of initial Glauber coherent states and Fock (photon number) states is considered. On an initial coherent state the medium conductivity and the time‐dependent electric permeability both are shown to act as squeezing and correlating factors.

AIP conference proceedings•Jan 1, 2011•4 citations

On the quantization of the electromagnetic field in conducting media

Alberes Lopes de Lima, Alexandre Rosas, I. A. Pedrosa

In this work we investigate the quantization of electromagnetic waves propagating through homogeneous conducting linear media with no charge density. We use Coulomb's gauge to reduce the problem to that of a time-dependent harmonic oscillator, which is described by the Caldirola–Kanai Hamiltonian. Furthermore, we obtain the corresponding exact wave functions with the help of quadratic invariants and of the dynamic invariant method. These wave functions are written in terms of a particular solution of the Milne–Pinney equation. We also construct coherent and squeezed states for the quantized electromagnetic waves and evaluate the quantum fluctuations in coordinates and momentum as well as the uncertainty product for each mode of the electromagnetic field.

Journal of Modern Optics•Dec 17, 2008•7 citations

Generalized Coherent States for Quantized Electromagnetic Fields in Time-varying Linear Media

Jeong Ryeol Choi, Mustapha Maamache

If the parameters of the materials, such as electric permittivity, magnetic perme- ability, and conductivity, vary explicitly with time, the corresponding Hamiltonian is a time- dependent form and such materials are classifled as the time-varying media of light. The quan- tization of electromagnetic flelds in time-varying linear media is well described by means of the invariant operator theory of Lewis-Riesenfeld. The Coulomb gauge is chosen in the development of theory, which allows us to evaluate quantized electric and magnetic flelds by expanding only the vector potential in charge free space, since the scalar potential in this situation vanishes. The generalized coherent state, i.e., Gaussian-Klauder state, of electromagnetic flelds conflned inside a cavity fllled with a nontrivial conductive medium is investigated. The Gaussian-Klauder state provides a general means of construction for Husimi-Wigner distributions and can be used to show the quantum and classical correspondence. We conflrmed that the uncertainty product in Gaussian-Klauder state is the same as the minimum uncertainty product in number state. This property of the generalized coherent state is well agree with that of the well known Glauber coherent state.

PIERS Online•Dec 25, 2009•4 citations

Dynamics of Nonclassicality of Time- and Conductivity-Dependent Squeezed States and Excited Even/Odd Coherent States

Roohollah Daneshmand, Mohammad Kazem Tavassoly

Abstract Recently, the quantum description of electromagnetic waves in conducting media has been performed. It has been demonstrated that in particular case, the Hamiltonian of the corresponding field can be expressed by Caldirola–Kanai Hamiltonian. In this paper, using the associated annihilation and creation operators of the above-mentioned quantized field, the time- and conductivity-dependent squeezed vacuum and one-photon squeezed states as well as their superpositions, and also the time- and conductivity-dependent excited even and odd coherent states are produced. Also, using a few well-known nonclassicality criteria, the time evolution of nonclassicality features of the above classes of obtained states, in addition to the influence of medium conductivity on them are demonstrated, numerically. It has been shown that the nonclassicality indicators may be adjusted by tuning the conductivity of media.

Communications in Theoretical Physics•Mar 1, 2017•5 citations

Quantum Light and Coherent States in Conducting Media

I. A. Pedrosa

We present a simple description of classical and quantum light propagating through homogeneous conducting linear media. With the choice of Coulomb gauge, we demonstrate that this description can be performed in terms of a damped harmonic oscillator which is governed by the Caldirola-Kanai Hamiltonian. By using the dynamical invariant method and the Fock states representation we solve the time-dependent Schrödinger equation associated with this Hamiltonian and write its solutions in terms of a special solution of the Milne-Pinney equation. We also construct coherent states for the quantized light and show that they are equivalent to the well-known squeezed states. Finally, we evaluate some important properties of the quantized light such as expectation values of the amplitude and momentum of each mode, their variances and the respective uncertainty principle.

Journal of Applied Mathematics and Physics•Jan 1, 2020•1 citation
Integrals of motion and statistical properties of quantized electromagnetic field (e.-m. field) in time-dependent linear dielectric and conductive media are considered, using Choi-Yeon quantization, based on Caldirola-Kanai type Hamiltonian. Eigenstates of quadratic and linear invariants are constructed, the solutions being expressed in terms of a complex parametric function that obeys classical oscillator equation with time-varying frequency. The time evolutions of initial Glauber coherent states and Fock states are considered. The medium conductivity and the time-dependent electric permeability are shown to generate squeezing and non-vanishing covariances. In the time-evolved coherent and squeezed states all the second statistical moments of the electric and magnetic field components are calculated and shown to mminimize the Robertson-Schrödinger uncertainty relation.
Dynamical invariants and statistical properties of the quantized electromagnetic field in nonstationary linear media (dielectric and/or conductive) are considered in the framework of Choi‐Yeon quantization scheme. It is shown that in the eigenstates of linear dynamical invariant the Robertson‐Schrödinger uncertainty relation is minimized, both for the photon annihilation operator quadratures and for the electric and magnetic field components. The time evolution of initial Glauber coherent states and Fock (photon number) states is considered. On an initial coherent state the medium conductivity and the time‐dependent electric permeability both are shown to act as squeezing and correlating factors.
Dynamical invariants and statistical properties of the quantized electromagnetic field in nonstationary linear media (dielectric and/or conductive) are considered in the framework of Choi‐Yeon quantization scheme. It is shown that in the eigenstates of linear dynamical invariant the Robertson‐Schrödinger uncertainty relation is minimized, both for the photon annihilation operator quadratures and for the electric and magnetic field components. The time evolution of initial Glauber coherent states and Fock (photon number) states is considered. On an initial coherent state the medium conductivity and the time‐dependent electric permeability both are shown to act as squeezing and correlating factors.
In this work we investigate the quantization of electromagnetic waves propagating through homogeneous conducting linear media with no charge density. We use Coulomb's gauge to reduce the problem to that of a time-dependent harmonic oscillator, which is described by the Caldirola–Kanai Hamiltonian. Furthermore, we obtain the corresponding exact wave functions with the help of quadratic invariants and of the dynamic invariant method. These wave functions are written in terms of a particular solution of the Milne–Pinney equation. We also construct coherent and squeezed states for the quantized electromagnetic waves and evaluate the quantum fluctuations in coordinates and momentum as well as the uncertainty product for each mode of the electromagnetic field.
If the parameters of the materials, such as electric permittivity, magnetic perme- ability, and conductivity, vary explicitly with time, the corresponding Hamiltonian is a time- dependent form and such materials are classifled as the time-varying media of light. The quan- tization of electromagnetic flelds in time-varying linear media is well described by means of the invariant operator theory of Lewis-Riesenfeld. The Coulomb gauge is chosen in the development of theory, which allows us to evaluate quantized electric and magnetic flelds by expanding only the vector potential in charge free space, since the scalar potential in this situation vanishes. The generalized coherent state, i.e., Gaussian-Klauder state, of electromagnetic flelds conflned inside a cavity fllled with a nontrivial conductive medium is investigated. The Gaussian-Klauder state provides a general means of construction for Husimi-Wigner distributions and can be used to show the quantum and classical correspondence. We conflrmed that the uncertainty product in Gaussian-Klauder state is the same as the minimum uncertainty product in number state. This property of the generalized coherent state is well agree with that of the well known Glauber coherent state.
Abstract Recently, the quantum description of electromagnetic waves in conducting media has been performed. It has been demonstrated that in particular case, the Hamiltonian of the corresponding field can be expressed by Caldirola–Kanai Hamiltonian. In this paper, using the associated annihilation and creation operators of the above-mentioned quantized field, the time- and conductivity-dependent squeezed vacuum and one-photon squeezed states as well as their superpositions, and also the time- and conductivity-dependent excited even and odd coherent states are produced. Also, using a few well-known nonclassicality criteria, the time evolution of nonclassicality features of the above classes of obtained states, in addition to the influence of medium conductivity on them are demonstrated, numerically. It has been shown that the nonclassicality indicators may be adjusted by tuning the conductivity of media.
We present a simple description of classical and quantum light propagating through homogeneous conducting linear media. With the choice of Coulomb gauge, we demonstrate that this description can be performed in terms of a damped harmonic oscillator which is governed by the Caldirola-Kanai Hamiltonian. By using the dynamical invariant method and the Fock states representation we solve the time-dependent Schrödinger equation associated with this Hamiltonian and write its solutions in terms of a special solution of the Milne-Pinney equation. We also construct coherent states for the quantized light and show that they are equivalent to the well-known squeezed states. Finally, we evaluate some important properties of the quantized light such as expectation values of the amplitude and momentum of each mode, their variances and the respective uncertainty principle.