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

Journal of Physics B Atomic and Molecular Physics

Effects of broadening mechanisms on atomic resonance fluorescence

A Al-Hilfy, R. Loudon

Published Sep 4, 1982• 5 citations
Publisher

Abstract

Calculations are presented for the degrees of first- and second-order coherence and the spectral distribution of the light emitted in resonance fluorescence by a two-level atom driven by monochromatic incident light. The theory includes the effects of both homogeneous and inhomogeneous broadening, but is restricted to ranges of the parameters for which analytic solutions can be obtained. There is a further restriction to forward scattering in the case where the inhomogeneous broadening is caused by the Doppler effect. The results show marked differences between the effects of the homogeneous and inhomogeneous broadening mechanisms.

DOI
10.1088/0022-3700/15/17/016

Related papers

Effect of collisions on the resonance fluorescence spectrum

А. И. Пархоменко, Anatolii M. Shalagin

The effect of collisions on the resonance fluorescence spectrum of two-level atoms excited by monochromatic resonance radiation is studied. Analysis is performed for systems where the Doppler broadening is small compared to the collision frequency (high buffer gas pressures) and for the general case where collisions arbitrarily change the phase of the radiation-induced dipole moment (from completely interrupted to completely unaffected phase of the dipole moment). Both at a relatively low and at a high excitation radiation intensity, the resonance fluorescence spectrum is shown to depend on whether the two-level system is closed or open. This is especially true for the narrow unshifted Rayleigh scattering line. It is shown that, although the absorption line is homogeneously broadened, the resonance fluorescence spectrum exhibits a clearly pronounced anisotropy. In a direction close to the direction of propagation of the excitation radiation, the Rayleigh scattering line is maximally narrowed. Under certain conditions (that can easily be created in experiments), the width of this line is proportional to the diffusion coefficient of atoms interacting with the radiation.

Journal of Experimental and Theoretical Physics•May 1, 2008•1 citation

Optical fluorescence at the combinational frequency in coherently driven three-level systems

Chris O’Brien, Shaoyan Gao, Olga A. Kocharovskaya

We derive and compare the optical fluorescence spectra for all three transitions for three-level systems coherently coupled with two fields in a cascade or lambda configuration. It is shown that the total intensity of fluorescence at the combinational frequency (the sum or difference of the driving field frequencies in the ladder and lambda systems, respectively) may essentially exceed the fluorescence intensity at the driven transitions under the condition of two-photon resonance. The influence of additional homogeneous and inhomogeneous line broadening on the distribution of intensities between different fluorescence channels is studied. In particular, Doppler broadening is found to suppress fluorescence from the driven transitions but in some cases not from the combinational transition.

Journal of Modern Optics•Aug 9, 2011•0 citations

The forward scattering of resonance radiation, with special reference to double resonance and level-crossing experiments

Alan Corney, B P Kibble, George William Series

Abstract A theoretical and experimental study has been made of the intensity of forward scattered light in conditions of radio-frequency double resonance and level-crossing. The main conclusions are (i) that the magnetic resonance and level-crossing effects which are familiar in the laterally scattered light are to be found also in the forward scattered light, but (ii) that the resonance curves are Doppler-broadened, and the strength of the oscillatory field necessary to generate them is correspondingly increased, and (iii) that coherence narrowing is much more pronounced in forward than in lateral scattering. The differences derive from the coherence between the radiation from different atoms which is present in forward, but not in lateral scattering, and which is implicitly recognized in the classical theory of the propagation of light in polarizable media. The equations of electromagnetism form the basis of the present analysis. In the presence of the oscillatory magnetic field the polarization tensor is complex and time-dependent. The time dependence leads to the result that the number of eigenwaves necessary to describe propagated waves in the medium is four, as against the usual two. An arbitrary wave is resolved into a superposition of the four eigenwaves, all of which have different propagation constants. The analysis is very general, and is applicable to experiments with lasers. The components of the polarization tensor are derived by finding first the polarizability of individual atoms from a semi-classical theory of their interaction with light and magnetic fields. The macroscopic polarization, obtained by summing over individual atoms, is then given by folding the individual polarizabilities with the Doppler distribution of resonance frequencies. In the particular case studied in detail (the inter-combination resonance line, 2537 A, in mercury), the Doppler width is much greater than the radiation width, and the imaginary (absorptive) part of the polarizability is Gaussian. Expressions are derived in a ‘weak scattering’ approximation for the intensity of the forward scattered light. They are magnetic resonance functions which are found to be the Doppler-broadened equivalents of the familiar functions, based on Lorentzians, characteristic of scattering by a single atom. In the case of double resonance the forward scattered light is strongly modulated, as is the laterally scattered light. To investigate coherence narrowing, the zero-field level-crossing has been studied with the restriction of ‘weak scattering’ removed. The result is obtained that the width of levelcrossing curves is inversely proportional to the vapour density for magnetic fields such that the Zeeman splitting is small in relation to the Doppler width. This analytical result has been verified experimentally.

Proceedings of the Royal Society of London A Mathematical and Physical Sciences•Jul 5, 1966•87 citations

Resonance fluorescence in intense radiation felds

V. Sethu Raman

The spectral density of resonance fluorescence from a two-level atom in a monochromatic radiation field of arbitrary strength and detuning is calculated by solution of the wave equation. A basis set in which the strong coupling of the atom and the quantised incident field is diagonal is used, and the resulting infinite set of coupled equations is solved by truncating them to a set of N equations and finally proceeding to the N to infinity limit. The resulting spectral densities of the inelastically scattered field for various levels of intensity of the incident field and degree of detuning are found to be identical with those of Kimble and Mandel (1976, 1977) obtained by solution of the coupled equations of motion of the atom and the radiation field in the Heisenberg picture.

Journal of Physics A Mathematical and General•Jun 1, 1978•1 citation

The Effect of Collisions on the Resonance Fluorescence Spectrum of Three-Level Atoms with a V-Configuration of Levels

А. И. Пархоменко, Anatolii M. Shalagin

The effect of collisions on the resonance fluorescence spectrum of three-level atoms with a V-configuration of levels when excited by two monochromatic resonance fields has been theoretically investigated. The analysis has been carried out for the systems with a small Doppler broadening compared to the collision frequency (high buffer gas pressures) and for the general case of an arbitrary change (from complete failure to complete preservation) of the phase memory at any of the three transitions in the V-system. It has been shown that in the three-level V-type atoms excited by two monochromatic fields, the resonant fluorescence spectrum (the number of spectral lines and their widths) at one of the transitions strongly depends on the presence of resonant radiation at the adjacent transition. Under certain conditions, the line widths will be completely determined by the relaxation characteristics of the adjacent transition and, in particular, can be repeatedly narrowed with an increase in the radiation intensity at the adjacent transition. It has been shown that despite the homogeneous nature of the broadening of the absorption lines, the resonance fluorescence spectrum has a pronounced anisotropy with respect to the mutual orientation of the wave vectors of spontaneous and exciting radiation. It has been established that the line widths in the resonance fluorescence spectrum are proportional to the diffusion coefficient of the atoms interacting with radiation under certain conditions. This fact can serve as the basis for a spectroscopic method for measuring the transport frequencies of the collisions of the radiation-absorbing particles with the buffer ones. It has been shown that the effects of phase memory in the collisions lead to a strong qualitative and quantitative modification of the resonance fluorescence spectrum.

Optics and Spectroscopy•Dec 1, 2021•1 citation

Theoretical analysis of the resonance fluorescence correlation spectrum of three-level multi-mer 85Rb atomic system

Chao Zhao

In a vapor cell, [Formula: see text] is the average velocity of the moving atoms. When [Formula: see text], the in-homogeneous broadening of the atomic spectral lines is important when taking into account thermal Doppler broadening. We also discover that the narrowing mechanism for inter-atomic with different components has more influence on the Doppler line-shape. Thus, the spectral line broadening of two-level and three-level multi-mer [Formula: see text] atom is not only influenced by the in-homogeneous Doppler broadening, but also affected by the Dicke narrowing effect. The fluorescence spectrum affords a good possibility for a detailed study of Dicke narrowing effect and thermal Doppler broadening effect. We analyze the influence of multi-mer [Formula: see text] atomic system component on resonance fluorescence spectrum (RFS). Based on the quantum regression theorem, we develop a method and derive a general analytical expression for the two-dimensional (2D) fluorescence correlation spectrum of three-level [Formula: see text] atomic system.

Modern Physics Letters B•Oct 3, 2023•0 citations
Calculations are presented for the degrees of first- and second-order coherence and the spectral distribution of the light emitted in resonance fluorescence by a two-level atom driven by monochromatic incident light. The theory includes the effects of both homogeneous and inhomogeneous broadening, but is restricted to ranges of the parameters for which analytic solutions can be obtained. There is a further restriction to forward scattering in the case where the inhomogeneous broadening is caused by the Doppler effect. The results show marked differences between the effects of the homogeneous and inhomogeneous broadening mechanisms.
The effect of collisions on the resonance fluorescence spectrum of two-level atoms excited by monochromatic resonance radiation is studied. Analysis is performed for systems where the Doppler broadening is small compared to the collision frequency (high buffer gas pressures) and for the general case where collisions arbitrarily change the phase of the radiation-induced dipole moment (from completely interrupted to completely unaffected phase of the dipole moment). Both at a relatively low and at a high excitation radiation intensity, the resonance fluorescence spectrum is shown to depend on whether the two-level system is closed or open. This is especially true for the narrow unshifted Rayleigh scattering line. It is shown that, although the absorption line is homogeneously broadened, the resonance fluorescence spectrum exhibits a clearly pronounced anisotropy. In a direction close to the direction of propagation of the excitation radiation, the Rayleigh scattering line is maximally narrowed. Under certain conditions (that can easily be created in experiments), the width of this line is proportional to the diffusion coefficient of atoms interacting with the radiation.
We derive and compare the optical fluorescence spectra for all three transitions for three-level systems coherently coupled with two fields in a cascade or lambda configuration. It is shown that the total intensity of fluorescence at the combinational frequency (the sum or difference of the driving field frequencies in the ladder and lambda systems, respectively) may essentially exceed the fluorescence intensity at the driven transitions under the condition of two-photon resonance. The influence of additional homogeneous and inhomogeneous line broadening on the distribution of intensities between different fluorescence channels is studied. In particular, Doppler broadening is found to suppress fluorescence from the driven transitions but in some cases not from the combinational transition.
Abstract A theoretical and experimental study has been made of the intensity of forward scattered light in conditions of radio-frequency double resonance and level-crossing. The main conclusions are (i) that the magnetic resonance and level-crossing effects which are familiar in the laterally scattered light are to be found also in the forward scattered light, but (ii) that the resonance curves are Doppler-broadened, and the strength of the oscillatory field necessary to generate them is correspondingly increased, and (iii) that coherence narrowing is much more pronounced in forward than in lateral scattering. The differences derive from the coherence between the radiation from different atoms which is present in forward, but not in lateral scattering, and which is implicitly recognized in the classical theory of the propagation of light in polarizable media. The equations of electromagnetism form the basis of the present analysis. In the presence of the oscillatory magnetic field the polarization tensor is complex and time-dependent. The time dependence leads to the result that the number of eigenwaves necessary to describe propagated waves in the medium is four, as against the usual two. An arbitrary wave is resolved into a superposition of the four eigenwaves, all of which have different propagation constants. The analysis is very general, and is applicable to experiments with lasers. The components of the polarization tensor are derived by finding first the polarizability of individual atoms from a semi-classical theory of their interaction with light and magnetic fields. The macroscopic polarization, obtained by summing over individual atoms, is then given by folding the individual polarizabilities with the Doppler distribution of resonance frequencies. In the particular case studied in detail (the inter-combination resonance line, 2537 A, in mercury), the Doppler width is much greater than the radiation width, and the imaginary (absorptive) part of the polarizability is Gaussian. Expressions are derived in a ‘weak scattering’ approximation for the intensity of the forward scattered light. They are magnetic resonance functions which are found to be the Doppler-broadened equivalents of the familiar functions, based on Lorentzians, characteristic of scattering by a single atom. In the case of double resonance the forward scattered light is strongly modulated, as is the laterally scattered light. To investigate coherence narrowing, the zero-field level-crossing has been studied with the restriction of ‘weak scattering’ removed. The result is obtained that the width of levelcrossing curves is inversely proportional to the vapour density for magnetic fields such that the Zeeman splitting is small in relation to the Doppler width. This analytical result has been verified experimentally.
The spectral density of resonance fluorescence from a two-level atom in a monochromatic radiation field of arbitrary strength and detuning is calculated by solution of the wave equation. A basis set in which the strong coupling of the atom and the quantised incident field is diagonal is used, and the resulting infinite set of coupled equations is solved by truncating them to a set of N equations and finally proceeding to the N to infinity limit. The resulting spectral densities of the inelastically scattered field for various levels of intensity of the incident field and degree of detuning are found to be identical with those of Kimble and Mandel (1976, 1977) obtained by solution of the coupled equations of motion of the atom and the radiation field in the Heisenberg picture.
The effect of collisions on the resonance fluorescence spectrum of three-level atoms with a V-configuration of levels when excited by two monochromatic resonance fields has been theoretically investigated. The analysis has been carried out for the systems with a small Doppler broadening compared to the collision frequency (high buffer gas pressures) and for the general case of an arbitrary change (from complete failure to complete preservation) of the phase memory at any of the three transitions in the V-system. It has been shown that in the three-level V-type atoms excited by two monochromatic fields, the resonant fluorescence spectrum (the number of spectral lines and their widths) at one of the transitions strongly depends on the presence of resonant radiation at the adjacent transition. Under certain conditions, the line widths will be completely determined by the relaxation characteristics of the adjacent transition and, in particular, can be repeatedly narrowed with an increase in the radiation intensity at the adjacent transition. It has been shown that despite the homogeneous nature of the broadening of the absorption lines, the resonance fluorescence spectrum has a pronounced anisotropy with respect to the mutual orientation of the wave vectors of spontaneous and exciting radiation. It has been established that the line widths in the resonance fluorescence spectrum are proportional to the diffusion coefficient of the atoms interacting with radiation under certain conditions. This fact can serve as the basis for a spectroscopic method for measuring the transport frequencies of the collisions of the radiation-absorbing particles with the buffer ones. It has been shown that the effects of phase memory in the collisions lead to a strong qualitative and quantitative modification of the resonance fluorescence spectrum.
In a vapor cell, [Formula: see text] is the average velocity of the moving atoms. When [Formula: see text], the in-homogeneous broadening of the atomic spectral lines is important when taking into account thermal Doppler broadening. We also discover that the narrowing mechanism for inter-atomic with different components has more influence on the Doppler line-shape. Thus, the spectral line broadening of two-level and three-level multi-mer [Formula: see text] atom is not only influenced by the in-homogeneous Doppler broadening, but also affected by the Dicke narrowing effect. The fluorescence spectrum affords a good possibility for a detailed study of Dicke narrowing effect and thermal Doppler broadening effect. We analyze the influence of multi-mer [Formula: see text] atomic system component on resonance fluorescence spectrum (RFS). Based on the quantum regression theorem, we develop a method and derive a general analytical expression for the two-dimensional (2D) fluorescence correlation spectrum of three-level [Formula: see text] atomic system.