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

Canadian Journal of Physics

Application of a diagram technique to the problem of resonance fluorescence from strongly driven two level atoms

Haider R. Zaidi

Published Jun 1, 1981• 8 citations
Publisher

Abstract

A Green's function formulation, valid for thermal as well as nonthermal equilibrium, is developed for the resonance fluorescence from strongly driven two level atoms. Translational motion and the Doppler broadening are also taken into account (collisions are considered in a second paper). The Feynman diagram technique is used to calculate the contribution of the physically important processes. The formulation is not based on the Markovian approximation or the quantum regression theorem. It takes full account of the dynamic Stark splitting and the saturation, and leads to a generalization of the "dressed atom" approach. Our "generalized dressed atom" (GDA) approach is valid for arbitrary values of the detuning and the pump field strength. The lowest order diagrams in the GDA picture give results equivalent to the existing theories. Some higher order diagrams are also considered. Although the resulting corrections are small, the physical processes involved are of some interest. These corrections include nonMarkovian effects.

DOI
10.1139/p81-096

Related papers

Theory of resonance fluorescence from a gas of identical two level atoms

Haider R. Zaidi

A Green's function formulation of the problem of resonance fluorescence from a system of identical two level atoms is presented. The general formulation is suitable for the investigation of a variety of nonlinear phenomena, e.g., propagation of electromagnetic waves inside the medium, fluorescence from a finite medium, optical bistability, atomic correlations, and additional side bands. Translational motion, collisions, Coulomb dipole–dipole interaction, excitation transfer, and local field corrections are also included in the basic equations. The effect of atom–atom correlations in the relaxation mechanism (radiative or collisional) is also taken into account. Finally, the results are also presented in the "generalized dressed atom" (GDA) representation. Applications of the general theory will be given in a future paper.

Canadian Journal of Physics•Feb 1, 1983•2 citations

Effects of detuning and fluctuations on fluorescence radiation from a strongly driven three-level atom: Some analytical results

S. V. Lawande, Richard D’Souza, Ravinder Rupchand Puri

We generalize our earlier formalism to treat the effects of both the finite-bandwidth excitations and finite arbitrary detunings, on the fluorescent spectra and second-order intensity correlation functions in optical double resonance. It is assumed that the bandwidth arises from the phase and/or amplitude fluctuations in the fields driving a three-level atom in cascade configuration. Under the conditions that one or both of these fields are intense, secular approximation and the theory of multiplicative stochastic processes are invoked to derive a Markovian master equation for the atomic-density operator averaged over both phase and amplitude. The quantum regression theorem is used to derive analytical expressions for the fluorescent spectra and the second-order intensity correlation functions which explicitly display the effects due to detunings and fluctuations.

Physical Review A•Oct 1, 1987•9 citations

Green's function equations of motion for driven two-level atoms

Haider R. Zaidi

Using a diagram technique, equations of motion for N coherently driven two-level atoms are obtained from Green's functions. The longitudinal (Coulomb) dipole–dipole interaction is neglected. Three approximations (Born approximation, extended Born approximation, and screened interaction approximation) are considered. The existing theories are shown to be equivalent to the extended Born approximation. For a small sample, the equations of motion exhibit S conservation in this case. The screened interaction model predicts a different behaviour; in particular, S-breaking terms appear in the equations of motion for a small sample.

Canadian Journal of Physics•Mar 1, 1985•1 citation

Analysis of strong light-matter interaction using a dressed propagator approach

James G. Fujimoto, Ting K. Yee

A diagrammatic density matrix technique is developed and applied to study nonlinear optical processes involving responses from weak probe fields interacting with a system under strong excitation. These diagrams consist of lowest-order double-Feynman diagrams which represent the density matrix perturbation terms describing the system response to the weak probe fields1,2 combined with dressed propagators which represent the density matrix elements of the system under strong excitation. The dressed propagators are described by a set of linear equations which, in most cases, may be derived in inspection. The methodology is similar to the bare-atom approach.2 The advantages of using this diagrammatic technique are that (1) it allows one to select and express analytically the dominant and appropriate density matrix elements (diagrams and dressed propagators); (2) analytical expressions may be constructed directly from the diagrams and thus lengthy calculations needed to obtain closed-form solutions are greatly reduced; (3) it provides a physical interpretation for the density matrix solutions and nonlinear optical processes; and (4) it may be generalized to more complicated, multilevel systems. We demonstrate the application of this technique to describe gain saturation, Stark splitting, and Raman scattering.

Annual Meeting Optical Society of America•Jan 1, 1985•0 citations

Theory of resonant light scattering from two level atoms in the presence of collisions

Haider R. Zaidi

A theory of resonant light scattering from two level atoms in a gas is developed for an arbitrarily strong pump field. The Doppler effect and two body foreign gas collisions are considered. Elastic, inelastic (upward and downward), and the velocity changing collisions are retained in the general formulation. The impact approximation is not made, and the expressions for all (field dependent) collision rates are generated internally. Particular attention is paid to the lower state interaction, and a more complete parameterization of the theory is achieved. The general theory is non-Markovian and the quantum regression theorem is not used; it reduces to existing theories in special cases. It is shown that the coherent scattering is not a general property of the system if the lower state interaction is present; the "coherent" component acquires a small, but nonzero, width in the strong field region. This width could provide information about some new collision parameters.

Canadian Journal of Physics•Jun 1, 1981•12 citations

Non-Markovian dephasing of two-level resonance fluorescence in a strong radiation field

Zhifang Deng, Shaul Mukamel

A non-Markovian microscopic theory for the spontaneous emission spectrum of a two-level atom driven by a strong laser field and undergoing dephasing via the interaction with a thermal bath is developed. The present theory is valid for an arbitrary correlation time scale of the bath relative to the linewidth and interpolates from the Markovian to the static limits. Model calculations using the stochastic line-shape function of Kubo show how the characteristic triplet spectrum is modified by the interaction with the bath. The present results generalize our previous studies of resonance Raman scattering in a three-level system in a strong radiation field.

Physical Review A•Apr 1, 1984•9 citations
A Green's function formulation, valid for thermal as well as nonthermal equilibrium, is developed for the resonance fluorescence from strongly driven two level atoms. Translational motion and the Doppler broadening are also taken into account (collisions are considered in a second paper). The Feynman diagram technique is used to calculate the contribution of the physically important processes. The formulation is not based on the Markovian approximation or the quantum regression theorem. It takes full account of the dynamic Stark splitting and the saturation, and leads to a generalization of the "dressed atom" approach. Our "generalized dressed atom" (GDA) approach is valid for arbitrary values of the detuning and the pump field strength. The lowest order diagrams in the GDA picture give results equivalent to the existing theories. Some higher order diagrams are also considered. Although the resulting corrections are small, the physical processes involved are of some interest. These corrections include nonMarkovian effects.
A Green's function formulation of the problem of resonance fluorescence from a system of identical two level atoms is presented. The general formulation is suitable for the investigation of a variety of nonlinear phenomena, e.g., propagation of electromagnetic waves inside the medium, fluorescence from a finite medium, optical bistability, atomic correlations, and additional side bands. Translational motion, collisions, Coulomb dipole–dipole interaction, excitation transfer, and local field corrections are also included in the basic equations. The effect of atom–atom correlations in the relaxation mechanism (radiative or collisional) is also taken into account. Finally, the results are also presented in the "generalized dressed atom" (GDA) representation. Applications of the general theory will be given in a future paper.
We generalize our earlier formalism to treat the effects of both the finite-bandwidth excitations and finite arbitrary detunings, on the fluorescent spectra and second-order intensity correlation functions in optical double resonance. It is assumed that the bandwidth arises from the phase and/or amplitude fluctuations in the fields driving a three-level atom in cascade configuration. Under the conditions that one or both of these fields are intense, secular approximation and the theory of multiplicative stochastic processes are invoked to derive a Markovian master equation for the atomic-density operator averaged over both phase and amplitude. The quantum regression theorem is used to derive analytical expressions for the fluorescent spectra and the second-order intensity correlation functions which explicitly display the effects due to detunings and fluctuations.
Using a diagram technique, equations of motion for N coherently driven two-level atoms are obtained from Green's functions. The longitudinal (Coulomb) dipole–dipole interaction is neglected. Three approximations (Born approximation, extended Born approximation, and screened interaction approximation) are considered. The existing theories are shown to be equivalent to the extended Born approximation. For a small sample, the equations of motion exhibit S conservation in this case. The screened interaction model predicts a different behaviour; in particular, S-breaking terms appear in the equations of motion for a small sample.
A diagrammatic density matrix technique is developed and applied to study nonlinear optical processes involving responses from weak probe fields interacting with a system under strong excitation. These diagrams consist of lowest-order double-Feynman diagrams which represent the density matrix perturbation terms describing the system response to the weak probe fields1,2 combined with dressed propagators which represent the density matrix elements of the system under strong excitation. The dressed propagators are described by a set of linear equations which, in most cases, may be derived in inspection. The methodology is similar to the bare-atom approach.2 The advantages of using this diagrammatic technique are that (1) it allows one to select and express analytically the dominant and appropriate density matrix elements (diagrams and dressed propagators); (2) analytical expressions may be constructed directly from the diagrams and thus lengthy calculations needed to obtain closed-form solutions are greatly reduced; (3) it provides a physical interpretation for the density matrix solutions and nonlinear optical processes; and (4) it may be generalized to more complicated, multilevel systems. We demonstrate the application of this technique to describe gain saturation, Stark splitting, and Raman scattering.
A theory of resonant light scattering from two level atoms in a gas is developed for an arbitrarily strong pump field. The Doppler effect and two body foreign gas collisions are considered. Elastic, inelastic (upward and downward), and the velocity changing collisions are retained in the general formulation. The impact approximation is not made, and the expressions for all (field dependent) collision rates are generated internally. Particular attention is paid to the lower state interaction, and a more complete parameterization of the theory is achieved. The general theory is non-Markovian and the quantum regression theorem is not used; it reduces to existing theories in special cases. It is shown that the coherent scattering is not a general property of the system if the lower state interaction is present; the "coherent" component acquires a small, but nonzero, width in the strong field region. This width could provide information about some new collision parameters.
A non-Markovian microscopic theory for the spontaneous emission spectrum of a two-level atom driven by a strong laser field and undergoing dephasing via the interaction with a thermal bath is developed. The present theory is valid for an arbitrary correlation time scale of the bath relative to the linewidth and interpolates from the Markovian to the static limits. Model calculations using the stochastic line-shape function of Kubo show how the characteristic triplet spectrum is modified by the interaction with the bath. The present results generalize our previous studies of resonance Raman scattering in a three-level system in a strong radiation field.