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 Letters

Chaotic Rabi oscillations under quasiperiodic perturbation

Yves Pomeau A, Bernadette Dorizzi, Basil Grammaticos

Published Feb 17, 1986• 80 citations
Publisher

Abstract

We have found quantum chaos in a system consisting of two levels coupled through a time-dependent perturbation, when this perturbation is quasiperiodic with two incommensurate frequencies. This contrasts with the case of a monochromatic perturbation where the oscillations of the physical observables are nonchaotic, because of the Floquet theorem. The existence of chaos is confirmed by the observation of rapidly decreasing autocorrelation functions, and by a continuous Fourier spectrum for time-dependent fluctuations of physical observables.

DOI
10.1103/physrevlett.56.681

Related papers

Generalized Rabi oscillations in a three-level metastable system under periodic and quasiperiodic perturbations

Satrajit Adhikari, D. N. Nath, S. P. Bhattacharyya

The quantum dynamics of prototypical three-level metastable system under external perturbations, both time-independent and time-dependent, are studied numerically as well as analytically. The regular Rabi oscillations generated in the system under a monochromatic perturbation are shown to develop additional features when the system has a metastable state. The autocorrelation function of ψ(t) reveals nondecaying, almost quasiperiodic, behavior in such systems. The Rabi oscillations turn more complex when a bichromatic perturbation with two incommensurate frequencies is allowed to interact with the three-level system, irrespective of the presence or absence of a metastable state. A rapid decay in the autocorrelation function of the wavefunction [ψ(t)] is observed in such cases. © 1996 Wiley & Sons, Inc.

International Journal of Quantum Chemistry•Jan 1, 1996•1 citation

Quasiperiodically kicked quantum systems

Peter W. Milonni, Jay R. Ackerhalt, M. E. Goggin

We consider a two-state system kicked quasiperiodically by an external force. When the two kicking frequencies assumed for the force are incommensurate, there can be quantum chaos in the sense that (a) the autocorrelation function of the state vector decays, (b) the power spectrum of the state vector is broadband, and (c) the motion on the Bloch sphere is ergodic. The time evolution of the state vector is nevertheless dynamically stable in the sense that memory of the initial state is retained. We also consider briefly the kicked quantum rotator and find, in agreement with Shepelyansky [Physica 8D, 208 (1983)], that the quantum localization effect is greatly weakened by the presence of two incommensurate driving frequencies.

Physical Review A•Feb 1, 1987•32 citations

Quasiperiodic and chaotic motions in intense field multiphoton processes

Shih‐I Chu

The question of the behavior of quantum systems in time-dependent fields whose classical counterparts exhibit chaotic behavior is addressed. For any nondissipative bounded quantum system under the influence of polychromatic (i.e., quasiperiodic) fields, it is proved by means of the many-mode Floquet theory1 that the autocorrelation function will recur infinitely often in the course of time, indicating no strict quantum stochasticity is possible.2 In particular, for an N-level quantum system undergoing multiphoton transitions, its dynamic behavior is described by the quasiperiodic motion of an (N2 – 1)-dimensional coherence vector S in accord with the SU(N) dynamic symmetries. On the other hand, for any dissipative quantum system, SU(N) symmetries are broken, and chaotic behavior is observed as the coherence vector Sevolves from an initially (N2 – 1)-dimensional space to a lower-dimensional space. The recurrence and chaotic phenomena are illustrated for two- and three-level quantum systems driven by intense bichromatic laser fields.2

International Laser Science Conference•Jan 1, 1986•0 citations

Quasiperiodic and chaotic motions in intense field multiphoton processes

Shih‐I Chu

The question of the behavior of quantum systems in time‐dependent fields whose classical counterparts exhibit chaotic behavior is addressed. For any nondissipative bounded quantum system under the influence of polychromatic (i.e., quasiperiodic) fields, it is proved by means of the many‐mode Floquet theory that the auto‐correlation function will recur infinitely often in the course of time, indicating no strict quantum stochasticity is possible. In particular, for an N‐level quantum system undergoing multiphoton transitions, its dynamic behavior is described by the quasiperiodic motion of an (N2–1)‐dimensional coherence vector S↘ in accord with the SU(N) dynamic symmetries. On the other hand, for any dissipative quantum system, SU(N) symmetries are broken, and non‐quasiperiodic behavior is observed as the coherence vector S↘ evolves from an initially (N2–1)‐dimensional space to a lower‐dimensional space. The dynamical behaviors are illustrated for two‐ and three‐level quantum systems driven by intense bichromatic laser fields.

AIP conference proceedings•Jan 1, 1987•1 citation

Chaotic vacuum Rabi oscillations with moving two-level atoms in cavity QED: a new kind of reversible spontaneous emission

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

We study nonlinear dynamics in the fundamental cavity QED system, consisting of a point-like collection of two-level atoms moving through a single-mode cavity, with a spatially inhomogenous field. In the semiclassical, strong-coupling and rotating-wave approximations, the model is shown to be integrable with atoms moving at exact resonance through a cavity with an arbitrary spatial profile of the mode along the propagation axis. The general exact semiclassical solution is derived in an explicit form, in terms of Jacobian elliptic functions. Numerical simulation confirms that perturbations, which are produced by a modulation of the coupling between moving atoms and a cavity mode, provide, our of resonance, a mechanism responsible for Hamiltonian chaos. Taking into account the interatomic quantum correlations, we go beyond the semiclassical model and derive a dynamical system, which is able to describe vacuum Rabi oscillation with moving atoms. At resonance, this system is again shown to be integrable with a general semiquantum solution found. Out of resonance, it can demonstrate chaotic vacuum Rabi oscillations, which may be considered as a new kind of reversible spontaneous emission.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Feb 25, 1999•0 citations

Revival of Order in the Chaotic Dynamics with Position and Time Dependent Perturbed System

Lylyane S. Yonya Tchapda, Martin Tchoffo, M. Vubangsi +2 more

Studying quantum properties of a system has been quite popular in quantum mechanics. One of the most important systems that are very crucial to the framework of quantum mechanics is the system of harmonic oscillator a system whose classical evolution is known to exhibit peculiar chaotic dynamics. We are motivated to investigate the behavior of quantum properties for a system with position and time dependent perturbed. Starting with Hamiltonian, we determined the equation of motion and obtained the wave function. The energy of the whole system using the operator ordering method was found. We show that the quantum mechanical picture alludes to a chaotic dynamics as expected. This is evidenced through the appearance of energy level crossings. An additional signature to this chaotic dynamics is observed in the transition of Eigen values from real to imaginary. We also show numerically that one can give the behavior of the system is Poincare section. By so doing we confirmed that increasing and decreasing the perturbation amplitude of the system becomes chaotic.

Journal of Applied Mathematics and Physics•Jan 1, 2020•0 citations
We have found quantum chaos in a system consisting of two levels coupled through a time-dependent perturbation, when this perturbation is quasiperiodic with two incommensurate frequencies. This contrasts with the case of a monochromatic perturbation where the oscillations of the physical observables are nonchaotic, because of the Floquet theorem. The existence of chaos is confirmed by the observation of rapidly decreasing autocorrelation functions, and by a continuous Fourier spectrum for time-dependent fluctuations of physical observables.
The quantum dynamics of prototypical three-level metastable system under external perturbations, both time-independent and time-dependent, are studied numerically as well as analytically. The regular Rabi oscillations generated in the system under a monochromatic perturbation are shown to develop additional features when the system has a metastable state. The autocorrelation function of ψ(t) reveals nondecaying, almost quasiperiodic, behavior in such systems. The Rabi oscillations turn more complex when a bichromatic perturbation with two incommensurate frequencies is allowed to interact with the three-level system, irrespective of the presence or absence of a metastable state. A rapid decay in the autocorrelation function of the wavefunction [ψ(t)] is observed in such cases. © 1996 Wiley & Sons, Inc.
We consider a two-state system kicked quasiperiodically by an external force. When the two kicking frequencies assumed for the force are incommensurate, there can be quantum chaos in the sense that (a) the autocorrelation function of the state vector decays, (b) the power spectrum of the state vector is broadband, and (c) the motion on the Bloch sphere is ergodic. The time evolution of the state vector is nevertheless dynamically stable in the sense that memory of the initial state is retained. We also consider briefly the kicked quantum rotator and find, in agreement with Shepelyansky [Physica 8D, 208 (1983)], that the quantum localization effect is greatly weakened by the presence of two incommensurate driving frequencies.
The question of the behavior of quantum systems in time-dependent fields whose classical counterparts exhibit chaotic behavior is addressed. For any nondissipative bounded quantum system under the influence of polychromatic (i.e., quasiperiodic) fields, it is proved by means of the many-mode Floquet theory1 that the autocorrelation function will recur infinitely often in the course of time, indicating no strict quantum stochasticity is possible.2 In particular, for an N-level quantum system undergoing multiphoton transitions, its dynamic behavior is described by the quasiperiodic motion of an (N2 – 1)-dimensional coherence vector S in accord with the SU(N) dynamic symmetries. On the other hand, for any dissipative quantum system, SU(N) symmetries are broken, and chaotic behavior is observed as the coherence vector Sevolves from an initially (N2 – 1)-dimensional space to a lower-dimensional space. The recurrence and chaotic phenomena are illustrated for two- and three-level quantum systems driven by intense bichromatic laser fields.2
The question of the behavior of quantum systems in time‐dependent fields whose classical counterparts exhibit chaotic behavior is addressed. For any nondissipative bounded quantum system under the influence of polychromatic (i.e., quasiperiodic) fields, it is proved by means of the many‐mode Floquet theory that the auto‐correlation function will recur infinitely often in the course of time, indicating no strict quantum stochasticity is possible. In particular, for an N‐level quantum system undergoing multiphoton transitions, its dynamic behavior is described by the quasiperiodic motion of an (N2–1)‐dimensional coherence vector S↘ in accord with the SU(N) dynamic symmetries. On the other hand, for any dissipative quantum system, SU(N) symmetries are broken, and non‐quasiperiodic behavior is observed as the coherence vector S↘ evolves from an initially (N2–1)‐dimensional space to a lower‐dimensional space. The dynamical behaviors are illustrated for two‐ and three‐level quantum systems driven by intense bichromatic laser fields.
We study nonlinear dynamics in the fundamental cavity QED system, consisting of a point-like collection of two-level atoms moving through a single-mode cavity, with a spatially inhomogenous field. In the semiclassical, strong-coupling and rotating-wave approximations, the model is shown to be integrable with atoms moving at exact resonance through a cavity with an arbitrary spatial profile of the mode along the propagation axis. The general exact semiclassical solution is derived in an explicit form, in terms of Jacobian elliptic functions. Numerical simulation confirms that perturbations, which are produced by a modulation of the coupling between moving atoms and a cavity mode, provide, our of resonance, a mechanism responsible for Hamiltonian chaos. Taking into account the interatomic quantum correlations, we go beyond the semiclassical model and derive a dynamical system, which is able to describe vacuum Rabi oscillation with moving atoms. At resonance, this system is again shown to be integrable with a general semiquantum solution found. Out of resonance, it can demonstrate chaotic vacuum Rabi oscillations, which may be considered as a new kind of reversible spontaneous emission.
Studying quantum properties of a system has been quite popular in quantum mechanics. One of the most important systems that are very crucial to the framework of quantum mechanics is the system of harmonic oscillator a system whose classical evolution is known to exhibit peculiar chaotic dynamics. We are motivated to investigate the behavior of quantum properties for a system with position and time dependent perturbed. Starting with Hamiltonian, we determined the equation of motion and obtained the wave function. The energy of the whole system using the operator ordering method was found. We show that the quantum mechanical picture alludes to a chaotic dynamics as expected. This is evidenced through the appearance of energy level crossings. An additional signature to this chaotic dynamics is observed in the transition of Eigen values from real to imaginary. We also show numerically that one can give the behavior of the system is Poincare section. By so doing we confirmed that increasing and decreasing the perturbation amplitude of the system becomes chaotic.