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

Europhysics Letters (EPL)

Dynamics of a Two-Level System in a Classical Field–A Description in Different Observation Levels

E. Heiner, Lutz Steinbeck

Published Jun 15, 1992• 0 citations
Publisher

Abstract

Effects of contraction in the description of a two-level quantum system coupled to a classical electromagnetic field are studied. Different observation levels are introduced and the corresponding nonlinear equations of motion are obtained. The solutions are discussed with respect to stability, constants of motion and evolution of relevant entropies.

DOI
10.1209/0295-5075/19/4/002

Related papers

Light-Matter Interactions: A Coupled Oscillator Description

Martin Frimmer, Lukáš Novotný

The semiclassical theory of light-matter interactions describes the interaction between a classical electromagnetic field with a quantum mechanical two-level system.We show that the quantum mechanical two-level system can be modeled by a system of two coupled classical harmonic oscillators whose eigenstates are split in frequency according to the coupling strength and play the roles of the two levels of the quantum mechanical two-level system. The effect of the light field on the mechanical system is modeled as a modulation of the spring constants of the individual oscillators. Using this fully classical model, we derive the Bloch equations for a two-level system and discuss the mechanical analogues of Rabi oscillations and coherent control experiments

arXiv:1604.04367•Apr 15, 2016•0 citations

Exact dynamics of a class of two-level and three-level atoms interacting with quantized field

Ravinder Rupchand Puri

An unified approach to the dynamics of a class encompassing several widely encountered models of a two-level and of a three-level atom interacting with a quantized electromagnetic field is developed. The approach is based on separating the dependence of the dynamics on the field and the atomic operators by expressing the unitary evolution operator in the basis of the atomic operators. The evolution operator then resembles the one for the atoms in an externally applied classical field. The exactly solvable examples of the deterministic, as well as fluctuating, time-dependence of the atom-field coupling are discussed. The issue of an effective two-level description for a three-level system is also analysed. The proposed method not only provides an unified approach to the models belonging to the class considered but is found to uncover several new results even for simple widely studied models.

Journal of Modern Optics•Aug 1, 1999•8 citations

Excitation of Atomic Systems by Nonclassical Electromagnetic Fields

К. В. Запьянцев, Olga V. Tikhonova

Abstract Interaction between atomic systems and nonclassical electromagnetic fields is considered using the example of a two-level system. The dynamics of such characteristics as the population of atomic levels, the entanglement of field and atomic subsystems, and the distribution of the number of photons for an active field are investigated.

Bulletin of the Russian Academy of Sciences Physics•Nov 1, 2018•2 citations

Squeezing in four-mode Kerr nonlinear coupler via phase space representation

Rafael Julius, Abdel-Baset M.A. Ibrahim, Mohd Salleh Mohd Deni +1 more

Quantum statistical properties of interacting optical fields in Kerr nonlinear coupler can be regarded as one of the most fundamental problems in quantum optics. As the analytical solution to these systems is not always possible, a semi-analytic or direct numerical solution has to be employed to obtain more complete description of their evolution. This paper investigates the quantum properties of a four-mode coupler composed of two Kerr nonlinear waveguides via phase-space representation. In this system, the electromagnetic field is described by its Hamiltonian and the time evolution of the system is described by Von-Neumann equation. Following the standard techniques, the master equation for the density matrix of the system is obtained and converted to the corresponding classical Fokker-Planck equation using both positive-P and Wigner representations. The corresponding set of Langevin Stochastic equations are then obtained from the Fokker-Planck equation using Ito rules. Finally, the system is integrated numerically and averaged over many trajectories to get the relevant information. The dynamics of the mean fields, the effects of self-action nonlinearity, cross-action coupling and initial energy of the coherent light on the evolution of the field quadrature variances are investigated. Further, the influences of multimode interaction on the dynamics of the squeezed states are discussed. We show that the system can produce squeezed states in both quadrature variances for all calculated parameters. In addition, the multimode interaction extends the range of squeezing at the expense of its amplitude.

AIP conference proceedings•Jan 1, 2013•2 citations

QUANTUM DYNAMICS OF TWO-LEVEL ATOMS INTERACTING WITH AN ELECTROMAGNETIC FIELD

Nikolay N. Bogolubov, M. Yu. Rasulova, I. A. TISHABOEV

We consider the dynamics of a system consisting of N two-level atoms interacting with a multi-mode cavity field. For the given system, the generalized kinetic equation (GKE) is obtained and conditions are given under which its solution is reduced to solution of a linear equation, and of the one-dimensional nonlinear Schrödinger equation, respectively.

International Journal of Modern Physics B•Feb 13, 2014•1 citation

Dynamical evolution of a five-level atom interacting with an intensity-dependent coupling regime influenced by a nonlinear Kerr-like medium

N. H. Abdel-Wahab, S. M. Zangi, Tamer A. Seoudy +1 more

We present an analytical solution for a quantum system characterized by a double $$\Lambda$$ five-level atom interacting with an intensity-dependent coupling regime, influenced by a nonlinear Kerr-like medium. We also derive the constants of motion through Heisenberg’s equations. Furthermore, the dynamical evolution of the entanglement and quantum coherence between the atom and the field is discussed using linear entropy and $$l_{1}$$ -norm of coherence. Through a comprehensive examination of the quantum system, it is observed that both the detuning and the Kerr-like parameters exert a significant impact on the degree of entanglement and coherence. However, the impacts of detuning and the Kerr effect become less pronounced when the photon multiplicity is high. In addition, we conduct a comparison between the five-level atomic system and a four-level system, revealing that the number of energy levels has a profound impact on the behavior of entanglement and coherence. These findings highlight the importance of atomic structure and photon multiplicity in controlling and optimizing quantum processes, particularly in applications involving quantum communication and information processing.

Scientific Reports•Oct 24, 2024•6 citations
Effects of contraction in the description of a two-level quantum system coupled to a classical electromagnetic field are studied. Different observation levels are introduced and the corresponding nonlinear equations of motion are obtained. The solutions are discussed with respect to stability, constants of motion and evolution of relevant entropies.
The semiclassical theory of light-matter interactions describes the interaction between a classical electromagnetic field with a quantum mechanical two-level system.We show that the quantum mechanical two-level system can be modeled by a system of two coupled classical harmonic oscillators whose eigenstates are split in frequency according to the coupling strength and play the roles of the two levels of the quantum mechanical two-level system. The effect of the light field on the mechanical system is modeled as a modulation of the spring constants of the individual oscillators. Using this fully classical model, we derive the Bloch equations for a two-level system and discuss the mechanical analogues of Rabi oscillations and coherent control experiments
An unified approach to the dynamics of a class encompassing several widely encountered models of a two-level and of a three-level atom interacting with a quantized electromagnetic field is developed. The approach is based on separating the dependence of the dynamics on the field and the atomic operators by expressing the unitary evolution operator in the basis of the atomic operators. The evolution operator then resembles the one for the atoms in an externally applied classical field. The exactly solvable examples of the deterministic, as well as fluctuating, time-dependence of the atom-field coupling are discussed. The issue of an effective two-level description for a three-level system is also analysed. The proposed method not only provides an unified approach to the models belonging to the class considered but is found to uncover several new results even for simple widely studied models.
Quantum statistical properties of interacting optical fields in Kerr nonlinear coupler can be regarded as one of the most fundamental problems in quantum optics. As the analytical solution to these systems is not always possible, a semi-analytic or direct numerical solution has to be employed to obtain more complete description of their evolution. This paper investigates the quantum properties of a four-mode coupler composed of two Kerr nonlinear waveguides via phase-space representation. In this system, the electromagnetic field is described by its Hamiltonian and the time evolution of the system is described by Von-Neumann equation. Following the standard techniques, the master equation for the density matrix of the system is obtained and converted to the corresponding classical Fokker-Planck equation using both positive-P and Wigner representations. The corresponding set of Langevin Stochastic equations are then obtained from the Fokker-Planck equation using Ito rules. Finally, the system is integrated numerically and averaged over many trajectories to get the relevant information. The dynamics of the mean fields, the effects of self-action nonlinearity, cross-action coupling and initial energy of the coherent light on the evolution of the field quadrature variances are investigated. Further, the influences of multimode interaction on the dynamics of the squeezed states are discussed. We show that the system can produce squeezed states in both quadrature variances for all calculated parameters. In addition, the multimode interaction extends the range of squeezing at the expense of its amplitude.
We present an analytical solution for a quantum system characterized by a double Λ\LambdaΛ five-level atom interacting with an intensity-dependent coupling regime, influenced by a nonlinear Kerr-like medium. We also derive the constants of motion through Heisenberg’s equations. Furthermore, the dynamical evolution of the entanglement and quantum coherence between the atom and the field is discussed using linear entropy and l1l_{1}l1​ -norm of coherence. Through a comprehensive examination of the quantum system, it is observed that both the detuning and the Kerr-like parameters exert a significant impact on the degree of entanglement and coherence. However, the impacts of detuning and the Kerr effect become less pronounced when the photon multiplicity is high. In addition, we conduct a comparison between the five-level atomic system and a four-level system, revealing that the number of energy levels has a profound impact on the behavior of entanglement and coherence. These findings highlight the importance of atomic structure and photon multiplicity in controlling and optimizing quantum processes, particularly in applications involving quantum communication and information processing.