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

Physical Review A

Effects of quantum noise on a two-level system in a single-mode cavity

Linda L. Vahala

Published Aug 1, 1990• 1 citation
Publisher

Abstract

The effects of quantum noise on a two-level system in the bad-cavity regime are considered perturbatively in the form of closure at the pair-correlation level. It is found that pair-correlation effects can reduce the level of semiclassical chaos. However, under the rotating-wave approximation (RWA), quantum noise can lead to chaos if there is an initial population inversion, while the full RWA Hamiltonian system remains integrable.

DOI
10.1103/physreva.42.1813

Related papers

Chaos in the Semiclassical N -Atom Jaynes-Cummings Model: Failure of the Rotating-Wave Approximation

Peter W. Milonni, Jay R. Ackerhalt, H. W. Galbraith

The problem of a collection of two-level atoms interacting with a single-mode classical electromagnetic field is considered. It is found that the model with an initial population inversion exhibits chaotic behavior that becomes stronger for higher atomic number density. The chaos is characterized by Fourier analysis and the maximal Lyapunov exponent. In the rotating-wave approximation, however, there is no prediction of chaos.

Physical Review Letters•Mar 28, 1983•214 citations

Quantum effects versus the semiclassical approximation

Luca Bonci, Paolo Grigolini A

We study a two-level quantum system interacting through a coupling strength g with a single-mode radiation field. We show that the rotating-wave-approximation (RWA) Hamiltonian produces quantum-mechanical effects more persistent than those generated by the full Hamiltonian. Within the full Hamiltonian the semiclassical prediction is recovered upon increase of the radiation field intensity, whereas with the RWA Hamiltonian no reconciliation with the predictions of the semiclassical approximation is realized by fields of any intensity, if the interaction strength g is kept unchanged.

Physical Review A•Oct 1, 1992•5 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

Control and chaos of atomic Rabi oscillations in a cavity

Igor Leonidovich Kirilyuk, Sergey V. Prants

The semiclassical dynamics of an ensemble of two-level atoms interacting with a single-mode cavity field is investigated. Without any dissipation, the respective dynamical system is shown to be integrable with atoms at rest inside a cavity. A new coherent effect of population trapping is shown to occur in the integrable system under specific initial conditions. The effect of dissipation on the trapping is treated numerically. It is shown analytically that homoclinic Hamiltonian chaos may arise when atoms move through a cavity.

International Conference on Control of Oscillations and Chaos (COC)•Nov 7, 2002•3 citations

A mechanism of emergence of Hamiltonian chaos in a basic quantum-optical model

Igor Leonidovich Kirilyuk, Sergey V. Prants

A mechanism of emergence of Hamiltonian chaos is considered for the model describing the interaction between two-level atoms and their own radiation field in an ideal single-mode cavity. The analysis of the semiclassical Maxwell-Bloch equations shows that the Hamiltonian terms that are neglected in the rotating-wave approximation (RWA) give rise to the formation of a stochastic layer near the RWA-system separatrix. The Mel’nikov method is used to prove that the splitting of the separatrix takes place for arbitrarily small vacuum Rabi frequencies Ω N . The computation of Poincare sections shows that the stochastic layer, which is exponentially narrow for small Ω N , expands with increasing Ω N , and at Ω N ≃ 1, the system exhibits global chaos that manifests itself in irregular oscillation of the atomic population inversion and the broadening of the power spectrum. Promising candidates for observing manifestations of dynamic chaos in this basic quantum-optical system are Rydberg atoms placed in a high-Q superconducting microwave cavity.

Optics and Spectroscopy•Dec 1, 2000•2 citations

Quantum dynamics of a f-deformed cavity-field beyond the rotating wave approximation

Mohsen Daeimohammad

The aim of this study is to investigate dynamical properties of a two-mode f-deformed cavity- field ‎coupled to an effective two-level atom with and without the rotating wave approximation. The first ‎section discusses the theoretical model of the interaction between a two-mode cavity-field and an ‎effective two-level atom within the framework of an f-DJCM without the rotating wave ‎approximation. After that, we obtain the reduced density matrix of the cavity-field with and without ‎the rotating-wave approximation. Then, we have investigated the effect of the counter-rotating ‎terms on temporal evolution of various non-classical properties of the cavity-field, i.e., photon-‎counting statistics, the cross correlation between the modes of the field, and the quantum ‎fluctuations of the quadrature components. Particularly, we compare the numerical result for three ‎different values of the deformation parameter q (q=1, q=1.1, q=0.9) with and without applying the rotating ‎wave approximation. By using of the numerical method, we concluded that even under the ‎condition in which the RWA is considered to be valid, there are the significant effects of virtual-‎photon field on the photon-counting statistics, the cross correlation between the modes of the ‎field, and the quantum fluctuations of the quadrature components‎.

Iranian Journal of Physics Research•May 1, 2021•0 citations
The effects of quantum noise on a two-level system in the bad-cavity regime are considered perturbatively in the form of closure at the pair-correlation level. It is found that pair-correlation effects can reduce the level of semiclassical chaos. However, under the rotating-wave approximation (RWA), quantum noise can lead to chaos if there is an initial population inversion, while the full RWA Hamiltonian system remains integrable.
We study a two-level quantum system interacting through a coupling strength g with a single-mode radiation field. We show that the rotating-wave-approximation (RWA) Hamiltonian produces quantum-mechanical effects more persistent than those generated by the full Hamiltonian. Within the full Hamiltonian the semiclassical prediction is recovered upon increase of the radiation field intensity, whereas with the RWA Hamiltonian no reconciliation with the predictions of the semiclassical approximation is realized by fields of any intensity, if the interaction strength g is kept unchanged.
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 semiclassical dynamics of an ensemble of two-level atoms interacting with a single-mode cavity field is investigated. Without any dissipation, the respective dynamical system is shown to be integrable with atoms at rest inside a cavity. A new coherent effect of population trapping is shown to occur in the integrable system under specific initial conditions. The effect of dissipation on the trapping is treated numerically. It is shown analytically that homoclinic Hamiltonian chaos may arise when atoms move through a cavity.
A mechanism of emergence of Hamiltonian chaos is considered for the model describing the interaction between two-level atoms and their own radiation field in an ideal single-mode cavity. The analysis of the semiclassical Maxwell-Bloch equations shows that the Hamiltonian terms that are neglected in the rotating-wave approximation (RWA) give rise to the formation of a stochastic layer near the RWA-system separatrix. The Mel’nikov method is used to prove that the splitting of the separatrix takes place for arbitrarily small vacuum Rabi frequencies Ω N . The computation of Poincare sections shows that the stochastic layer, which is exponentially narrow for small Ω N , expands with increasing Ω N , and at Ω N ≃ 1, the system exhibits global chaos that manifests itself in irregular oscillation of the atomic population inversion and the broadening of the power spectrum. Promising candidates for observing manifestations of dynamic chaos in this basic quantum-optical system are Rydberg atoms placed in a high-Q superconducting microwave cavity.
The aim of this study is to investigate dynamical properties of a two-mode f-deformed cavity- field ‎coupled to an effective two-level atom with and without the rotating wave approximation. The first ‎section discusses the theoretical model of the interaction between a two-mode cavity-field and an ‎effective two-level atom within the framework of an f-DJCM without the rotating wave ‎approximation. After that, we obtain the reduced density matrix of the cavity-field with and without ‎the rotating-wave approximation. Then, we have investigated the effect of the counter-rotating ‎terms on temporal evolution of various non-classical properties of the cavity-field, i.e., photon-‎counting statistics, the cross correlation between the modes of the field, and the quantum ‎fluctuations of the quadrature components. Particularly, we compare the numerical result for three ‎different values of the deformation parameter q (q=1, q=1.1, q=0.9) with and without applying the rotating ‎wave approximation. By using of the numerical method, we concluded that even under the ‎condition in which the RWA is considered to be valid, there are the significant effects of virtual-‎photon field on the photon-counting statistics, the cross correlation between the modes of the ‎field, and the quantum fluctuations of the quadrature components‎.