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 Russian Laser Research

Dynamic Symmetries, Control, and Chaos with Moving Atoms in High-Quality Cavities

Sergey V. Prants

Published May 1, 2015• 2 citations
Publisher
DOI
10.1007/s10946-015-9494-z

Related papers

Dynamical chaos in the interaction of moving atoms with a cavity field

Sergey V. Prants, Leonid E. Kon’kov

Physics Letters A•Jan 1, 1997•29 citations

Hamiltonian chaos in the interaction of moving two-level atoms with cavity vacuum

Sergey V. Prants, Leonid E. Kon’kov

Chaos Solitons & Fractals•May 1, 2000•2 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

Atoms in Cavities and Traps

HERBERT WALTHER

Advances in atomic, molecular, and optical physics•Jan 1, 1994•30 citations

Transition to dynamic chaos in the interaction of a two-level atom in a cavity with its own radiation field

Sergei V Prants, Leonid E. Kon’kov

An analytic symmetry approach is proposed and applied to nonlinear Hamiltonian dynamics of the self-consistent interaction of a two-level atom in a high-Q cavity with its own radiation field. A numerical investigation is reported of a transition from quasiperiodic to deterministically chaotic oscillations in a system of this kind which has classical and quantum degrees of freedom. This occurs when the control parameter Ω, which is the constant of the atom—field interaction, is increased. The largest Lyapunov exponent (which is a measure of the degree of chaos of a system) is used to demonstrate an alternation of the order—chaos transitions with increase in Ω. The power spectra and the phase portraits obtained for different ranges of Ω confirm the predicted path of the appearance of dynamic chaos in the fundamental model of quantum electronics.

Quantum Electronics•Jan 31, 1996•2 citations

Homoclinic chaos in vacuum Rabi oscillations of moving two-level atoms

Sergei V Prants, Leonid E. Kon’kov

We study analytically and numerically vacuum Rabi oscillations of N identical two-level atoms moving through a single-mode lossless cavity. Equations of motion which take into account the atomic quantum correlations are obtained for the quantum mechanical expectation values in the strong-coupling, rotating-wave, pointlike, and Raman-Nath approximations. It is shown that moving atoms may demonstrate an unusual type of spontaneous emission, the chaotic vacuum Rabi oscillations. This manifestation of quantum dynamical chaos in the matter-vacuum interaction is caused by a spatial inhomogeneity of the cavity mode that modulates the vacuum Rabi frequency of moving atoms. For small values of the depth of this modulation we use the Melnikov method and show analytically the presence of homoclinic chaos in this interaction. Transition to global chaos and global phase space stochasticity under conditions of the strong modulation are studied numerically by computing the maximal Lyapunov exponent lambda of the atom-field dynamical system as a function of the number and velocity of atoms and detuning. We find a curious structure of the lambda(N) dependence reflecting an intermittent route to global chaos. The strength of chaos depends strongly on the initial state preparation of atoms just before injecting into a cavity. It is shown that initially fully inverted atoms, which are in a superfluorescent Dicke state, demonstrate much stronger chaos (under other equal conditions) than the atoms prepared initially in a superradiant state with macroscopic polarization. A maser operating with two-level Rydberg atoms to be injected into a high-Q superconducting microwave cavity seems to be a realistic device for observing some manifestations of the chaotic vacuum Rabi oscillations.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Apr 1, 2000•13 citations
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.
An analytic symmetry approach is proposed and applied to nonlinear Hamiltonian dynamics of the self-consistent interaction of a two-level atom in a high-Q cavity with its own radiation field. A numerical investigation is reported of a transition from quasiperiodic to deterministically chaotic oscillations in a system of this kind which has classical and quantum degrees of freedom. This occurs when the control parameter Ω, which is the constant of the atom—field interaction, is increased. The largest Lyapunov exponent (which is a measure of the degree of chaos of a system) is used to demonstrate an alternation of the order—chaos transitions with increase in Ω. The power spectra and the phase portraits obtained for different ranges of Ω confirm the predicted path of the appearance of dynamic chaos in the fundamental model of quantum electronics.
We study analytically and numerically vacuum Rabi oscillations of N identical two-level atoms moving through a single-mode lossless cavity. Equations of motion which take into account the atomic quantum correlations are obtained for the quantum mechanical expectation values in the strong-coupling, rotating-wave, pointlike, and Raman-Nath approximations. It is shown that moving atoms may demonstrate an unusual type of spontaneous emission, the chaotic vacuum Rabi oscillations. This manifestation of quantum dynamical chaos in the matter-vacuum interaction is caused by a spatial inhomogeneity of the cavity mode that modulates the vacuum Rabi frequency of moving atoms. For small values of the depth of this modulation we use the Melnikov method and show analytically the presence of homoclinic chaos in this interaction. Transition to global chaos and global phase space stochasticity under conditions of the strong modulation are studied numerically by computing the maximal Lyapunov exponent lambda of the atom-field dynamical system as a function of the number and velocity of atoms and detuning. We find a curious structure of the lambda(N) dependence reflecting an intermittent route to global chaos. The strength of chaos depends strongly on the initial state preparation of atoms just before injecting into a cavity. It is shown that initially fully inverted atoms, which are in a superfluorescent Dicke state, demonstrate much stronger chaos (under other equal conditions) than the atoms prepared initially in a superradiant state with macroscopic polarization. A maser operating with two-level Rydberg atoms to be injected into a high-Q superconducting microwave cavity seems to be a realistic device for observing some manifestations of the chaotic vacuum Rabi oscillations.