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

Coherent pulse interaction with two-level system embedded in a dispersive medium

Alexander A. Zabolotskii

Published Jun 25, 2012• 7 citations
Publisher

Abstract

We present an integrable generalization of the Maxwell-Bloch equations describing electromagnetic-field interaction with a two-level system implemented in a dispersive host medium. Two physical onsets of the model are presented. The technique of the inverse scattering transform for the two sets of physical parameters is used to find soliton solutions. It is found that the model possesses both singular and nonsingular soliton solutions. The application of the results for a lossless nonlinear dispersion management of solitons is discussed.

DOI
10.1103/physreva.85.063833

Related papers

Self-induced transparency in a dispersive medium

Alexander A. Zabolotskii

The evolution of the electromagnetic field in a two-level medium occurring in a matrix with finite response time has been studied. An integrable variant of the Maxwell-Bloch equations with allowance for nonlinear dispersion is derived and solved using the inverse scattering problem. It is shown that the nonlinear dispersion caused by the finite response time of the matrix yields a new possibility of controlling soliton parameters. A particular case of the constructed model can be used to describe field pulses in the parameter domain that occurs between the regions of applicability of the quasi-monochromatic approximation and the approximation of unidirectional propagation of pulses with durations on the order of the oscillation period.

Journal of Experimental and Theoretical Physics•Jul 1, 2012•0 citations

Few-cycle solitons of an integrable generalization of the reduced Maxwell-Bloch equations

С. В. Сазонов, N. V. Ustinov

The physical generalization of the system of the reduced Maxwell-Bloch equations describing the nonlinear interaction of the laser pulses with the multilevel quantum medium is obtained without using the slowly varying envelope approximation. It is shown that this system is integrable in the frameworks of the inverse scattering transformation method. The soliton and breather solutions in the form of the unipolar and few-cycle pulses are constructed. Their distinctive features caused solely by the multilevel structure of the medium are discussed. It is revealed that the collision of the solitons can lead to an appearance of the large-amplitude short-living pulse, whose dynamics resembles that of rogue waves.

Physical Review A•Nov 6, 2019•16 citations

Envelope-Free Solitons in a Two-Level Medium Implanted into an Anisotropic Matrix

Alexander A. Zabolotskii

Abstract A model of evolution of field pulses in a medium of two-level atoms implanted into an anisotropic matrix is considered. It is shown that the system of reduced Maxwell–Bloch equations in the approximation of unidirectional propagation can be completely integrable. For a particular case of the model, soliton solutions describing the field pulse evolution are obtained. It is shown that by changing the anisotropy parameters of the external medium, pulse parameters can be controlled.

Journal of Experimental and Theoretical Physics•Nov 1, 2019•1 citation

Dissipative solitons of self-induced transparency

Guram T. Adamashvili, David J. Kaup, A. Knorr

A theory of dispersive soliton of the self-induced transparency in a medium consisting of atoms or semiconductor quantum dots of two types is considered. A two-component medium is modeled by a set of two-level atoms of two types embedded into a conductive host material. These types of atoms correspond to passive atoms (attenuator atoms) and active atoms (amplifier atoms) with inverse population of the energetic levels. The complete solution is given of the Maxwell--Bloch equations for ensembles of two-type atoms with different parameters and different initial conditions by inverse scattering transform. The solutions of the Maxwell--Bloch equations for many-component atomic systems by inverse scattering transform are also discussed. The influence of the difference between dipole moments of atoms, the longitudinal and transverse relaxation times, pumping, and conductivity on the soliton is taken into account by means of perturbation theory. The memory effects are described in terms of generalized non-Markovian optical Bloch equations. The condition of a balance between the energy supplied and lost is obtained.

Physical Review A•Nov 19, 2014•5 citations

Evolution of the unidirectional electromagnetic pulses in an anisotropic two-level medium

Alexander A. Zabolotskii

We find a general integrable system of reduced Maxwell-Bloch equations describing the interaction of a two-component electromagnetic field with the dipole transition of a two-level medium. The anisotropy of the anisotropic dipole momentum of the transition as a permanent dipole momentum is taken into account. A solution of the model is found for a particular case by using the inverse scattering transform. The method is based on a solution of the Riemann-Hilbert problem taking into account the symmetry properties of the corresponding fundamental solutions.

Physical Review E•Mar 5, 2008•8 citations

Coherent soliton propagation in a mixture of two-level atoms

F. C. Moreira, WANESSA RODRIGUES NASCIMENTO, Solange Bessa Cavalcanti +1 more

Exact soliton solutions of a coupled system of Maxwell-Bloch equations are obtained analytically within the inverse scattering transform scheme. The equations describe a light pulse coherently propagating through a mixed ensemble of two-level atoms characterized by two slightly different detuning parameters. The solution illustrates the information about the detailed atomic properties which are impressed on both phase and velocity of the pulse during propagation, with potential applications in high resolution spectroscopy.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 21, 2004•0 citations
We present an integrable generalization of the Maxwell-Bloch equations describing electromagnetic-field interaction with a two-level system implemented in a dispersive host medium. Two physical onsets of the model are presented. The technique of the inverse scattering transform for the two sets of physical parameters is used to find soliton solutions. It is found that the model possesses both singular and nonsingular soliton solutions. The application of the results for a lossless nonlinear dispersion management of solitons is discussed.
The evolution of the electromagnetic field in a two-level medium occurring in a matrix with finite response time has been studied. An integrable variant of the Maxwell-Bloch equations with allowance for nonlinear dispersion is derived and solved using the inverse scattering problem. It is shown that the nonlinear dispersion caused by the finite response time of the matrix yields a new possibility of controlling soliton parameters. A particular case of the constructed model can be used to describe field pulses in the parameter domain that occurs between the regions of applicability of the quasi-monochromatic approximation and the approximation of unidirectional propagation of pulses with durations on the order of the oscillation period.
The physical generalization of the system of the reduced Maxwell-Bloch equations describing the nonlinear interaction of the laser pulses with the multilevel quantum medium is obtained without using the slowly varying envelope approximation. It is shown that this system is integrable in the frameworks of the inverse scattering transformation method. The soliton and breather solutions in the form of the unipolar and few-cycle pulses are constructed. Their distinctive features caused solely by the multilevel structure of the medium are discussed. It is revealed that the collision of the solitons can lead to an appearance of the large-amplitude short-living pulse, whose dynamics resembles that of rogue waves.
A theory of dispersive soliton of the self-induced transparency in a medium consisting of atoms or semiconductor quantum dots of two types is considered. A two-component medium is modeled by a set of two-level atoms of two types embedded into a conductive host material. These types of atoms correspond to passive atoms (attenuator atoms) and active atoms (amplifier atoms) with inverse population of the energetic levels. The complete solution is given of the Maxwell--Bloch equations for ensembles of two-type atoms with different parameters and different initial conditions by inverse scattering transform. The solutions of the Maxwell--Bloch equations for many-component atomic systems by inverse scattering transform are also discussed. The influence of the difference between dipole moments of atoms, the longitudinal and transverse relaxation times, pumping, and conductivity on the soliton is taken into account by means of perturbation theory. The memory effects are described in terms of generalized non-Markovian optical Bloch equations. The condition of a balance between the energy supplied and lost is obtained.
We find a general integrable system of reduced Maxwell-Bloch equations describing the interaction of a two-component electromagnetic field with the dipole transition of a two-level medium. The anisotropy of the anisotropic dipole momentum of the transition as a permanent dipole momentum is taken into account. A solution of the model is found for a particular case by using the inverse scattering transform. The method is based on a solution of the Riemann-Hilbert problem taking into account the symmetry properties of the corresponding fundamental solutions.
Exact soliton solutions of a coupled system of Maxwell-Bloch equations are obtained analytically within the inverse scattering transform scheme. The equations describe a light pulse coherently propagating through a mixed ensemble of two-level atoms characterized by two slightly different detuning parameters. The solution illustrates the information about the detailed atomic properties which are impressed on both phase and velocity of the pulse during propagation, with potential applications in high resolution spectroscopy.