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

arXiv:quant-ph/0405122

A semiclassical derivation of Einstein's rate equations for light-matter interaction

Germán J. de Valcárcel, Eugenio Roldán

Published May 21, 2004• 0 citations
arXivHTMLPDF

Abstract

Einstein's rate equations are derived from the semiclassical Bloch equations describing the interaction of a classical broadband light field with a two--level system.
DOI
10.48550/arxiv.quant-ph/0405122

Related papers

Fundamentals and applications

J. Weiner, Ping-Tong Ho

Preface.PART I: LIGHT-MATTER INTERACTION: FUNDAMENTALS.Absorption and Emission of Radiation.Semiclassical Treatment of Absorption and Emission.The Optical Bloch Equations.Optical Bloch Equations of a Two-Level Atom.Quantized Fields and Dressed States.Forces from Atom-Light Interaction.The Laser.Elements of Optics.Index.

Wiley eBooks•Jan 1, 2003•1,997 citations

The interaction of atoms with radiation

Christopher J. Foot

Abstract To describe the interaction of a two-level atom with radiation we shall use a semiclassical treatment, i.e. the radiation is treated as a classical electric field but we use quantum mechanics to treat the atom. From the theory of the interaction with radiation, we will be able to find the conditions for which the equations reduce to a set of rate equations that describe the populations of the atomic energy levels (with a steady-state solution). In particular, for an atom illuminated by broad band radiation, this approach allows us to make a connection with Einstein’s treatment of radiation that was presented in Chapter 1; we shall find the Einstein B coefficient in terms of the matrix element for the transition.

•Nov 25, 2004•1 citation

A semiclassical optics derivation of Einstein’s rate equations

Robert Höppner, Eugenio Roldán, Germán J. de Valcárcel

We provide a semiclassical optics derivation of Einstein’s rate equations (ERE) for a two-level system illuminated by a broadband light field, setting a limit on their validity that depends on the spectral properties of the light field. Starting from the optical Bloch equations for individual atoms, the ensemble averaged atomic inversion is shown to follow ERE under two concurrent hypotheses: (i) the decorrelation of the inversion at a given time from the field at later times and (ii) a Markov approximation owing to the short correlation time of the light field. When the latter hypothesis is relaxed, we find effective Bloch equations for the ensemble average in which the atomic polarization decay rate is increased by an amount equal to the width of the light spectrum, which allows its adiabatic elimination for a large enough spectral width. The use of a phase-diffusion model of light allows us to check our results and hypotheses using numerical simulations of the corresponding stochastic differential equations. We take into account both light bandwidth and atomic linewidth, which allows us to discuss the differences existing between rate equations in the limits of large light bandwidth or large atomic linewidth. Only in the former case does one obtain ERE with the correct expression for Einstein’s B coefficient.

arXiv:1105.4120•American Journal of Physics•Sep 18, 2012•9 citations

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

Derivation of Einstein's postulate regarding the energy of light quanta from a more elementary postulate and special relativity

Martin Lessen

Foundations of Physics•Sep 1, 1974•0 citations

Laser gain and some of its consequences

Warren Nagourney

The laser gain equation is derived in two ways. First, the optical Bloch equations are derived, based upon a semiclassical treatment of a two-level atomic system and a radiation field. As a visualization aid, there follows a discussion of the formally identical classical Bloch equations, which describe the behavior of a magnetic moment in a combined static and rotating magnetic field. It is shown that laser gain is proportional to the imaginary part of the linear susceptibility, which is obtained from the semiclassical treatment. The second viewpoint uses a slightly modified form of Einstein’s A and B coefficients adapted to describing interactions between atoms and monochromatic fields. Various damping and broadening mechanisms are introduced in a reasonable but non-rigorous fashion, and the crucial distinction between homogeneous and inhomogeneous broadening is introduced.

Oxford University Press eBooks•May 8, 2014•0 citations
Abstract To describe the interaction of a two-level atom with radiation we shall use a semiclassical treatment, i.e. the radiation is treated as a classical electric field but we use quantum mechanics to treat the atom. From the theory of the interaction with radiation, we will be able to find the conditions for which the equations reduce to a set of rate equations that describe the populations of the atomic energy levels (with a steady-state solution). In particular, for an atom illuminated by broad band radiation, this approach allows us to make a connection with Einstein’s treatment of radiation that was presented in Chapter 1; we shall find the Einstein B coefficient in terms of the matrix element for the transition.
We provide a semiclassical optics derivation of Einstein’s rate equations (ERE) for a two-level system illuminated by a broadband light field, setting a limit on their validity that depends on the spectral properties of the light field. Starting from the optical Bloch equations for individual atoms, the ensemble averaged atomic inversion is shown to follow ERE under two concurrent hypotheses: (i) the decorrelation of the inversion at a given time from the field at later times and (ii) a Markov approximation owing to the short correlation time of the light field. When the latter hypothesis is relaxed, we find effective Bloch equations for the ensemble average in which the atomic polarization decay rate is increased by an amount equal to the width of the light spectrum, which allows its adiabatic elimination for a large enough spectral width. The use of a phase-diffusion model of light allows us to check our results and hypotheses using numerical simulations of the corresponding stochastic differential equations. We take into account both light bandwidth and atomic linewidth, which allows us to discuss the differences existing between rate equations in the limits of large light bandwidth or large atomic linewidth. Only in the former case does one obtain ERE with the correct expression for Einstein’s B coefficient.
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
The laser gain equation is derived in two ways. First, the optical Bloch equations are derived, based upon a semiclassical treatment of a two-level atomic system and a radiation field. As a visualization aid, there follows a discussion of the formally identical classical Bloch equations, which describe the behavior of a magnetic moment in a combined static and rotating magnetic field. It is shown that laser gain is proportional to the imaginary part of the linear susceptibility, which is obtained from the semiclassical treatment. The second viewpoint uses a slightly modified form of Einstein’s A and B coefficients adapted to describing interactions between atoms and monochromatic fields. Various damping and broadening mechanisms are introduced in a reasonable but non-rigorous fashion, and the crucial distinction between homogeneous and inhomogeneous broadening is introduced.