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

Soviet Physics Uspekhi

Quantum chaos in interactions of multilevel quantum systems with a coherent radiation field

G. P. Berman, A. R. Kolovskii

Published Apr 30, 1992• 26 citations
Publisher

Abstract

Studies on the dynamics of multilevel quantum systems in a coherent radiation field are reviewed. Major attention is paid to phenomena of quantum nonlinear resonance and the interaction of two quantum nonlinear resonances, and also to the analysis of the real physical systems where these phenomena are realized.
DOI
10.1070/pu1992v035n04abeh002228

Related papers

Coherent interaction of radiation pulses with resonant multilevel media (review)

Leonid A Bol'shov, Vladimir V. Likhanskii

A review is given of recent theoretical investigations on coherent propagation and nonlinear interaction of multifrequency ultrashort radiation pulses in resonantly absorbing media. An analysis is made of frequency conversion by parametric interaction and stimulated Raman scattering of laser pulses in resonant three-level media. New ways of controlling the parameters of coherent pulses and the use of multifrequency pulses in the spectroscopy of multilevel media are discussed. The experimental capabilities of the investigated effects are considered.

Soviet Journal of Quantum Electronics•Jul 31, 1985•20 citations

Quantum systems in regular and stochastic fields. Creation and destruction of the coherence

Alexander V. Gorokhov

The problem of the coherent state generation with definite parameters for multilevel quantum systems is investigated. The interaction with external environment and stochastic fields can destroy the coherence. The competition of these processes is considered on the basis of the Fokker-Planck equations approach, derived from the master equation for the density matrix of the system. Examples of the coherent states dynamics for two-level atoms in an external stochastic field in a nonideal resonator are considered. Average over the realizations of stochastic fields is performed for the case of the white Gaussian noise and the Kubo-Anderson process. Explicit formulas for probability and shape of radiation line are obtained.

Physics of Particles and Nuclei Letters•Mar 1, 2007•0 citations

Quantum Chaos in Two-Level Systems Interacting with Resonant Radiation Field

Quantum systems of Two-level atoms and radiation which corresponds to semiclassical systems where chaos occurs, are investigated, by using distribution functions obtained fron quantum master equations and its numerical analisis.

•Jan 1, 1988•0 citations

Quantum chaos in interactions of multilevel quantum systems with a coherent radiation field

G. P. Berman, A. R. Kolovskii

Квантовый хаос при взаимодействии многоуровневых квантовых систем с полем когерентного излучения, Берман Г.П., Коловский А.Р.

Uspekhi Fizicheskih Nauk•Jan 1, 1992•8 citations

Quantum chaos of atoms in a resonator driven by an external resonant field

G. P. Berman, Evgeny N. Bulgakov, Darryl D. Holm

A system of N two-level atoms in a resonator is considered interacting with a resonant eigenmode field and with an external coherent field, with a frequency slightly different from the frequency of the atomic transition. A model Hamiltonian is constructed for describing the slow quantum dynamics of the system, and a set of closed c-number equations for time-dependent quantum expectation values is derived in the boson and spin coherent states. In the region of parameters for developed chaos in the semiclassical limit (when the radiation field is considered classically) we show that the semiclassical approximation is violated by quantum effects at the time scale ${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\Elzxh}}}$\ensuremath{\sim}lnN. We also show that quantum correlations grow exponentially during the time interval 0${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\Elzxh}}}$. An additional averaging over the initial density matrix is considered. The connection of our model with the Dicke model [Phys. Rev. 93, 99 (1956)] is demonstrated, and the possiblity of measuring the quantum chaos effects considered in this paper is discussed.

Physical Review A•Jun 1, 1994•6 citations

Quantum chaos of atoms in a resonant cavity

G. P. Berman, Evgeny N. Bulgakov, G. M. Zaslavsky

A system of atoms interacting with a radiation field in a resonant cavity is studied under conditions when the dynamics in the classical limit is stochastic. This situation is called quantum chaos. Equations of motion are obtained for the quantum-mechanical expectation values which take into account the quantum correlation functions. It is shown that in a situation corresponding to quantum chaos, the quantum corrections grow exponentially, making the evolution of the system essentially quantal after a certain time tau( variant Planck's over 2pi ) has elapsed. Analytical and numerical analysis show that in this regime the time tau( variant Planck's over 2pi ) obeys the logarithmic law tau( variant Planck's over 2pi ) approximately ln N (N is the number of atoms), and not the law tau( variant Planck's over 2pi ) approximately N(alpha) (alpha is a certain constant of order unity), as would be the case in the absence of chaos.

Chaos An Interdisciplinary Journal of Nonlinear Science•Apr 1, 1992•11 citations
A review is given of recent theoretical investigations on coherent propagation and nonlinear interaction of multifrequency ultrashort radiation pulses in resonantly absorbing media. An analysis is made of frequency conversion by parametric interaction and stimulated Raman scattering of laser pulses in resonant three-level media. New ways of controlling the parameters of coherent pulses and the use of multifrequency pulses in the spectroscopy of multilevel media are discussed. The experimental capabilities of the investigated effects are considered.
The problem of the coherent state generation with definite parameters for multilevel quantum systems is investigated. The interaction with external environment and stochastic fields can destroy the coherence. The competition of these processes is considered on the basis of the Fokker-Planck equations approach, derived from the master equation for the density matrix of the system. Examples of the coherent states dynamics for two-level atoms in an external stochastic field in a nonideal resonator are considered. Average over the realizations of stochastic fields is performed for the case of the white Gaussian noise and the Kubo-Anderson process. Explicit formulas for probability and shape of radiation line are obtained.
A system of N two-level atoms in a resonator is considered interacting with a resonant eigenmode field and with an external coherent field, with a frequency slightly different from the frequency of the atomic transition. A model Hamiltonian is constructed for describing the slow quantum dynamics of the system, and a set of closed c-number equations for time-dependent quantum expectation values is derived in the boson and spin coherent states. In the region of parameters for developed chaos in the semiclassical limit (when the radiation field is considered classically) we show that the semiclassical approximation is violated by quantum effects at the time scale ${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\Elzxh}}}$\ensuremath{\sim}lnN. We also show that quantum correlations grow exponentially during the time interval 0${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\Elzxh}}}$. An additional averaging over the initial density matrix is considered. The connection of our model with the Dicke model [Phys. Rev. 93, 99 (1956)] is demonstrated, and the possiblity of measuring the quantum chaos effects considered in this paper is discussed.
A system of atoms interacting with a radiation field in a resonant cavity is studied under conditions when the dynamics in the classical limit is stochastic. This situation is called quantum chaos. Equations of motion are obtained for the quantum-mechanical expectation values which take into account the quantum correlation functions. It is shown that in a situation corresponding to quantum chaos, the quantum corrections grow exponentially, making the evolution of the system essentially quantal after a certain time tau( variant Planck's over 2pi ) has elapsed. Analytical and numerical analysis show that in this regime the time tau( variant Planck's over 2pi ) obeys the logarithmic law tau( variant Planck's over 2pi ) approximately ln N (N is the number of atoms), and not the law tau( variant Planck's over 2pi ) approximately N(alpha) (alpha is a certain constant of order unity), as would be the case in the absence of chaos.