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

Journal of Modern Optics

Two-level atom and multichromatic waves in a lossless cavity

Y.B. Xie

Published Feb 1, 1997• 2 citations
Publisher

Abstract

In this paper, we shall examine a generalized version of the Jaynes-Cummings model in which a two-level atom moves in a lossless cavity and is coupled to multichromatic waves with general frequencies and coupling constants. We shall show that both the motion of the atom and the photon conversion between multichromatic waves are dynamically correlated. Using the semiclassical approximations introduced in a previous paper, we obtain the equations which describe the dynamics of this quantum system and discuss the solutions in several special cases. In particular, we point out that the motion of the atom may be controlled by the electromagnetic modes, and vice versa, that is the amplitudes and phases of the electromagnetic fields in the cavity may also be determined by the position of the atom.

DOI
10.1080/09500349708241876

Related papers

Photon Conversion among Multichromatic Waves in Two-level Atom Systems

Y.B. Xie

In this paper, we shall discuss a generalized version of the Jaynes-Cummings model in which a two-level atom is coupled to multichromatic waves with general frequencies and coupling constants. We shall show that this two-level atom system can be mapped into an effective model in which a quantum particle moves in a lattice whose sites specify the number of photons in the multichromatic waves. In general, when the number L of modes is greater than two, large energy exchanges among different monochromatic waves are possible (L = 2 is a special case; exchanges of a large number of photons are possible only for degenerate modes). Depending on the frequencies of the elecromagnetic modes, we can classify the two-level systems in two categories. In one case, the eigenfunctions of the quantum particle are extended and thus exchange of a large number of photons is possible. In the other case, the eigenfunctions of the quantum particle are localized and exchange of a large number of photons is greatly suppressed.

Journal of Modern Optics•Nov 1, 1995•6 citations

Semiclassical interaction of moving two-level atoms with a cavity field: From integrability to Hamiltonian chaos

Sergey V. Prants, Leonid E. Kon’kov, Igor Leonidovich Kirilyuk

The dynamics of an ensemble of two-level atoms moving through a single-mode lossless cavity is investigated in the semiclassical and rotating-wave approximations. The dynamical system for the expectation values of the atomic and field observables is considered as a perturbation to one of the following integrable versions: (i) a model with atoms moving through a spatially inhomogeneous resonant field, and (ii) a model with atoms interacting with a nonresonant eigenmode which is assumed to be homogeneous on the cavity size. We find the general exact solutions for both the models and show that they contain special solutions describing a coherent effect of population and radiation trapping. Using the Melnikov method, we prove analytically transverse intersections of stable and unstable manifolds of a hyperbolic fixed point under a small modulation of the vacuum Rabi frequency. These intersections are believed to provide the Smale horseshoe mechanism of Hamiltonian chaos. The analytical results are accompanied with direct computation of topographical maps of maximal Lyapunov exponents that give a representative image of regularity and chaos in the atom-field system in different ranges of its control parameters--the frequency detuning, the number, and the velocity of atoms.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jul 1, 1999•31 citations

Interaction of a moving two-level atom with a single-mode quantized cavity field

Bimalendu Deb, Surajit Sen

We consider a variant of the Jaynes-Cummings model (JCM) which describes the interaction of a moving two-level atom with a single-mode electromagnetic field. The coupling of the moving dipole with the magnetic field which leads to the Roentgen interaction is taken into account. A solution in the dressed state description is presented in the spirit of the JCM.

Physical Review A•Sep 1, 1997•13 citations

Photon spectra and statistics in generalized Jaynes-Cummings model with photon losses and atom motion

Alexander V. Gorokhov, Ilya E. Sinaiski

The Jaynes-Cummings model (JCM) of two-level atom interacting with the photon mode in ideal cavity plays an essential role in modern quantum optics. In previous papers 1,2 an exact form of density matrix of the JCM with fixed atom position and photons dissipation was found. Here, taking into account the classical motion of the atom through the cavity, it is considered a case of nonideal cavity with zero temperature. We have obtained an exact expression for density matrix and calculated photon spectra and spectra of the mean number of photons in a cavity and and time dependencies of some values relevant for the one-atom maser theory.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 3, 2006•0 citations

Nonlinear Jaynes–Cummings model for two interacting two-level atoms

O de los Santos-Sánchez, Carlos A. González-Gutiérrez, J. Récamier

Abstract In this work we examine a nonlinear version of the Jaynes–Cummings model for two identical two-level atoms allowing for Ising-like and dipole–dipole interplays between them. The model is said to be nonlinear in the sense that it can incorporate both a general intensity-dependent interaction between the atomic system and the cavity field and/or the presence of a nonlinear medium inside the cavity. As an example, we consider a particular type of atom-field coupling based upon the so-called Buck–Sukumar model and a lossless Kerr-like cavity. We describe the possible effects of such features on the evolution of some quantities of current interest, such as atomic excitation, purity, concurrence, the entropy of the field and the evolution of the latter in phase space.

arXiv:1607.03216•Journal of Physics B Atomic Molecular and Optical Physics•Aug 4, 2016•26 citations

Jaynes-Cummings model with quasiclassical fields: The effect of dissipation

Julio R. Gea-Banacloche

An approximate solution is given for the Jaynes-Cummings model with cavity losses, i.e., the problem of a two-level atom interacting with a single mode of the quantized radiation field, in the rotating-wave approximation, when the field is damped by a reservoir at zero temperature. The approximate solution is derived for initial coherent field states with moderately large numbers of photons. It is simpler in form than earlier results derived by other authors and, over the appropriate parameter range, substantially more accurate than some of them, as shown by direct numerical integration of the master equation. In particular, it is found that an earlier treatment of this problem based on a secular approximation is seriously flawed, in that the conditions for its validity are much more restrictive than was previously believed. Among the results derived it is shown that, just as for the lossless case, when the atom is initially prepared in one of the semiclassical eigenstates the evolution is very simple, with the field and the atomic dipole drifting together in phase. For moderate losses this leads, as in the lossless case, to a ``state preparation''; i.e., to a good approximation, the state of the atom at a specific time can be made independent of its initial state. The effect of losses on the recently discovered ``Schr\"odinger cat'' state of the field is also analyzed. It is found that, although the dissipation destroys the coherence of the macroscopic superposition very rapidly, preparation and observation of the ``cat'' should be possible with the cavity quality factors reported in recent micromaser experiments.

Physical Review A•Mar 1, 1993•64 citations
In this paper, we shall examine a generalized version of the Jaynes-Cummings model in which a two-level atom moves in a lossless cavity and is coupled to multichromatic waves with general frequencies and coupling constants. We shall show that both the motion of the atom and the photon conversion between multichromatic waves are dynamically correlated. Using the semiclassical approximations introduced in a previous paper, we obtain the equations which describe the dynamics of this quantum system and discuss the solutions in several special cases. In particular, we point out that the motion of the atom may be controlled by the electromagnetic modes, and vice versa, that is the amplitudes and phases of the electromagnetic fields in the cavity may also be determined by the position of the atom.
In this paper, we shall discuss a generalized version of the Jaynes-Cummings model in which a two-level atom is coupled to multichromatic waves with general frequencies and coupling constants. We shall show that this two-level atom system can be mapped into an effective model in which a quantum particle moves in a lattice whose sites specify the number of photons in the multichromatic waves. In general, when the number L of modes is greater than two, large energy exchanges among different monochromatic waves are possible (L = 2 is a special case; exchanges of a large number of photons are possible only for degenerate modes). Depending on the frequencies of the elecromagnetic modes, we can classify the two-level systems in two categories. In one case, the eigenfunctions of the quantum particle are extended and thus exchange of a large number of photons is possible. In the other case, the eigenfunctions of the quantum particle are localized and exchange of a large number of photons is greatly suppressed.
The dynamics of an ensemble of two-level atoms moving through a single-mode lossless cavity is investigated in the semiclassical and rotating-wave approximations. The dynamical system for the expectation values of the atomic and field observables is considered as a perturbation to one of the following integrable versions: (i) a model with atoms moving through a spatially inhomogeneous resonant field, and (ii) a model with atoms interacting with a nonresonant eigenmode which is assumed to be homogeneous on the cavity size. We find the general exact solutions for both the models and show that they contain special solutions describing a coherent effect of population and radiation trapping. Using the Melnikov method, we prove analytically transverse intersections of stable and unstable manifolds of a hyperbolic fixed point under a small modulation of the vacuum Rabi frequency. These intersections are believed to provide the Smale horseshoe mechanism of Hamiltonian chaos. The analytical results are accompanied with direct computation of topographical maps of maximal Lyapunov exponents that give a representative image of regularity and chaos in the atom-field system in different ranges of its control parameters--the frequency detuning, the number, and the velocity of atoms.
The Jaynes-Cummings model (JCM) of two-level atom interacting with the photon mode in ideal cavity plays an essential role in modern quantum optics. In previous papers 1,2 an exact form of density matrix of the JCM with fixed atom position and photons dissipation was found. Here, taking into account the classical motion of the atom through the cavity, it is considered a case of nonideal cavity with zero temperature. We have obtained an exact expression for density matrix and calculated photon spectra and spectra of the mean number of photons in a cavity and and time dependencies of some values relevant for the one-atom maser theory.
Abstract In this work we examine a nonlinear version of the Jaynes–Cummings model for two identical two-level atoms allowing for Ising-like and dipole–dipole interplays between them. The model is said to be nonlinear in the sense that it can incorporate both a general intensity-dependent interaction between the atomic system and the cavity field and/or the presence of a nonlinear medium inside the cavity. As an example, we consider a particular type of atom-field coupling based upon the so-called Buck–Sukumar model and a lossless Kerr-like cavity. We describe the possible effects of such features on the evolution of some quantities of current interest, such as atomic excitation, purity, concurrence, the entropy of the field and the evolution of the latter in phase space.
An approximate solution is given for the Jaynes-Cummings model with cavity losses, i.e., the problem of a two-level atom interacting with a single mode of the quantized radiation field, in the rotating-wave approximation, when the field is damped by a reservoir at zero temperature. The approximate solution is derived for initial coherent field states with moderately large numbers of photons. It is simpler in form than earlier results derived by other authors and, over the appropriate parameter range, substantially more accurate than some of them, as shown by direct numerical integration of the master equation. In particular, it is found that an earlier treatment of this problem based on a secular approximation is seriously flawed, in that the conditions for its validity are much more restrictive than was previously believed. Among the results derived it is shown that, just as for the lossless case, when the atom is initially prepared in one of the semiclassical eigenstates the evolution is very simple, with the field and the atomic dipole drifting together in phase. For moderate losses this leads, as in the lossless case, to a ``state preparation''; i.e., to a good approximation, the state of the atom at a specific time can be made independent of its initial state. The effect of losses on the recently discovered ``Schr\"odinger cat'' state of the field is also analyzed. It is found that, although the dissipation destroys the coherence of the macroscopic superposition very rapidly, preparation and observation of the ``cat'' should be possible with the cavity quality factors reported in recent micromaser experiments.