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

physica status solidi (b)

Nonlinear Polarisation of an Impurity Crystal

Evgenii Dmitrievich Trifonov, A. S. Troshin

Published Jan 1, 1968• 0 citations
Publisher

Abstract

Abstract The polarization in a crystal containing impurities which is caused by the interaction with an electromagnetic field is given in terms of the Fourier transforms of the first‐order emission and absorption spectra due to the impurities. The results are obtained by means of the time‐dependent perturbation theory using the diagram technique. It is also shown that electron density matrix of the impurities satisfies the equations with two relaxation constants γ and Γ if the first‐order spectra are supposed to be of Lorentzian type.

DOI
10.1002/pssb.19680260215

Related papers

Interaction of Crystal Impurity Centres with a Coherent Electromagnetic Field

Pavel A Apanasevich, Vladimir I. Kruglov, Igor E. Tralle

Abstract By the projection operator technique the non‐Markovian kinetic equation for the density matrix of a crystal impurity centre in an external electromagnetic field is derived, taking into account the electron–phonon interaction. The analytical solutions of this equation are obtained for the external field as an ultrashort pulse and in the case of a monochromatic wave.

physica status solidi (b)•Oct 1, 1986•2 citations

Absorption spectra of a donor impurity in a quantum ring

Wenfang Xie

Abstract The linear and the third‐order nonlinear optical absorption spectra of a donor impurity confined by a quantum ring are studied using the matrix diagonalization method within the effective‐mass approximation. The linear and the third‐order nonlinear optical absorption coefficients between the ground (L = 0) and the first excited state (L = 1) have been examined based on the computed energies and wavefunctions. The results are presented as a function of the incident photon energy for the different values of the confinement strength, the incident optical density and the ring radius. We found the confinement strength, the incident optical density and the ring radius have a great effect on the linear, the third‐order nonlinear and total absorption spectra. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

physica status solidi (b)•Mar 5, 2009•46 citations

Some features of the optical manifestation of relaxation

Pavel A Apanasevich, Alexander P. Nizovtsev

It is shown that, in general, the interaction between relaxing quantum systems and radiation is described by non-Markov transport equations for the density matrix ρ p and the relaxation matrix depends on the properties of the radiation. The usual Markov-type equations for ρ p are obtained from these equations if γτ c ≪1 and (∊ 2 +4 V 2 ) 1/2 τ c ≪1 (γ is the width of the investigated transition in a quantum system, rc is the correlation time of the perturbations causing relaxation, e is the frequency detuning, and V is the energy of the interaction between the system and the radiation field). When the second inequality is disobeyed, the relaxation process deviates strongly from the Markov type. In the case of small values of V , this results in a non-Lorentzian profile of the absorption lines characterized by a steep descent in the wings. In the range of high values of V , when 2 V τ c 1, the whole relaxation process becomes greatly modified: the dependence of the relaxation coefficients on V becomes strong and a coupling appears between the relaxations of the diagonal and the nondiagonal elements of the density matrix. This is manifested, in particular, in the saturation effect: the term describing saturation in the expression for the polarizability changes considerably and the expression for the line width loses the component due to the adiabatic (elastic) perturbation.

Soviet Journal of Quantum Electronics•Aug 31, 1975•2 citations

Time-dependent Perturbations and Semi-classical Treatment of Interaction of Field with Matter

A. C. Sharma

How to deal with time-dependent potentials, what kinds of physical problems having time-dependent potentials can be solved exactly and which are to be solved with the use of perturbation theory, what are different possible forms of time-dependent perturbating fields, and semi-classical treatment of the interaction of fields with matter are the subject matters of this chapter. First order perturbation theory, computation of transition probability, transition rates and Fermi's Golden Rule for harmonic and constant perturbations, absorption, stimulated emission and dipole approximation when electromagnetic fields interact with matter, spontaneous emission and Einstein coefficients, and dipole selection rules are other topics which are dealt with in detail in the chapter. Discussions with properly justified mathematical treatment on time-dependent potentials and on the exactly solvable time-dependent two-state systems are the special foci of this chapter.

CRC Press eBooks•Jun 18, 2021•0 citations

Optical bistability and lasing of crystals containing impurities in the case of an adiabatic electron–phonon interaction

A. P. Saǐko, V. S. Kuz’min

A theoretical study is made of the threshold conditions for the observation of optical bistability and stimulated emission of zero-phonon lines of crystals containing impurities. A reduction in the electron–photon interaction constant ensures that nonlinear absorption due to a purely electronic transition is attained in a lower saturating field and the lasing threshold rises exponentially as the reciprocal of the Debye–Waller factor. It is shown that there are critical temperatures for the appearance of these effects. Experimental studies of the threshold conditions for lasing and optical bistability make it possible to determine directly the Debye–Waller factor at different temperatures of a crystal.

Soviet Journal of Quantum Electronics•Jun 30, 1988•0 citations

Quantum theory of the resonance interaction of an intense monochromatic electromagnetic wave with arbitrary polarization composition

A. A. Panteleev

A theory describing the absorption and emission spectra of an atomic transition in the field of an intense monochromatic wave with arbitrary polarization composition is developed. The theory includes a quantum description of forward-directed four-wave interaction processes. Expressions are obtained for describing the absorption and emission spectra in transitions adjacent to the working transition. The description developed includes the perturbation of the atomic subsystem by a constant magnetic field. The spectral characteristics, polarization composition, and angular distribution of the resonance fluorescence are investigated. The nonlinear Faraday effect and the properties of resonance fluorescence are investigated for the transition J =1→ J =0.

Journal of Experimental and Theoretical Physics•Feb 1, 1997•0 citations
Abstract The polarization in a crystal containing impurities which is caused by the interaction with an electromagnetic field is given in terms of the Fourier transforms of the first‐order emission and absorption spectra due to the impurities. The results are obtained by means of the time‐dependent perturbation theory using the diagram technique. It is also shown that electron density matrix of the impurities satisfies the equations with two relaxation constants γ and Γ if the first‐order spectra are supposed to be of Lorentzian type.
Abstract The linear and the third‐order nonlinear optical absorption spectra of a donor impurity confined by a quantum ring are studied using the matrix diagonalization method within the effective‐mass approximation. The linear and the third‐order nonlinear optical absorption coefficients between the ground (L = 0) and the first excited state (L = 1) have been examined based on the computed energies and wavefunctions. The results are presented as a function of the incident photon energy for the different values of the confinement strength, the incident optical density and the ring radius. We found the confinement strength, the incident optical density and the ring radius have a great effect on the linear, the third‐order nonlinear and total absorption spectra. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
It is shown that, in general, the interaction between relaxing quantum systems and radiation is described by non-Markov transport equations for the density matrix ρ p and the relaxation matrix depends on the properties of the radiation. The usual Markov-type equations for ρ p are obtained from these equations if γτ c ≪1 and (∊ 2 +4 V 2 ) 1/2 τ c ≪1 (γ is the width of the investigated transition in a quantum system, rc is the correlation time of the perturbations causing relaxation, e is the frequency detuning, and V is the energy of the interaction between the system and the radiation field). When the second inequality is disobeyed, the relaxation process deviates strongly from the Markov type. In the case of small values of V , this results in a non-Lorentzian profile of the absorption lines characterized by a steep descent in the wings. In the range of high values of V , when 2 V τ c 1, the whole relaxation process becomes greatly modified: the dependence of the relaxation coefficients on V becomes strong and a coupling appears between the relaxations of the diagonal and the nondiagonal elements of the density matrix. This is manifested, in particular, in the saturation effect: the term describing saturation in the expression for the polarizability changes considerably and the expression for the line width loses the component due to the adiabatic (elastic) perturbation.
How to deal with time-dependent potentials, what kinds of physical problems having time-dependent potentials can be solved exactly and which are to be solved with the use of perturbation theory, what are different possible forms of time-dependent perturbating fields, and semi-classical treatment of the interaction of fields with matter are the subject matters of this chapter. First order perturbation theory, computation of transition probability, transition rates and Fermi's Golden Rule for harmonic and constant perturbations, absorption, stimulated emission and dipole approximation when electromagnetic fields interact with matter, spontaneous emission and Einstein coefficients, and dipole selection rules are other topics which are dealt with in detail in the chapter. Discussions with properly justified mathematical treatment on time-dependent potentials and on the exactly solvable time-dependent two-state systems are the special foci of this chapter.
A theoretical study is made of the threshold conditions for the observation of optical bistability and stimulated emission of zero-phonon lines of crystals containing impurities. A reduction in the electron–photon interaction constant ensures that nonlinear absorption due to a purely electronic transition is attained in a lower saturating field and the lasing threshold rises exponentially as the reciprocal of the Debye–Waller factor. It is shown that there are critical temperatures for the appearance of these effects. Experimental studies of the threshold conditions for lasing and optical bistability make it possible to determine directly the Debye–Waller factor at different temperatures of a crystal.
A theory describing the absorption and emission spectra of an atomic transition in the field of an intense monochromatic wave with arbitrary polarization composition is developed. The theory includes a quantum description of forward-directed four-wave interaction processes. Expressions are obtained for describing the absorption and emission spectra in transitions adjacent to the working transition. The description developed includes the perturbation of the atomic subsystem by a constant magnetic field. The spectral characteristics, polarization composition, and angular distribution of the resonance fluorescence are investigated. The nonlinear Faraday effect and the properties of resonance fluorescence are investigated for the transition J =1→ J =0.