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

Level-degeneracy effects in super-radiance theory. Calculations for j=12 to j′=12 dipole transition

A. Crubellier, Marie-Gabrielle Schweighofer

Published Nov 1, 1978• 24 citations
Publisher

Abstract

We study here level-degeneracy effects in super-radiance, using the quantum "small-system" model whose interest and limitations are discussed. First, we show that this model allows one to understand the physical origin of these effects and to describe their qualitative influence on the properties of the emitted light. We also present and analyze numerical results obtained for the case of a dipole transition between two degenerate levels of angular momenta \textonehalf{}. We show that in this particular case one can define a basis of collective states which is well adapted to the invariance properties of the master equation. It is then possible to solve the master equation and to compute expectation values for the radiated field (intensity radiated with a given polarization, quantum fluctuations of this intensity) for various initial conditions and for small but already significant values of the number of individual systems. A detailed analysis of these results and a comparison with analogous calculations in the case where the degeneracy is supposed to be removed allows us to estimate the individual influence of the different types of effects (interference effects and the two sorts of competition effects, inhibition and initiation). We also compare the total intensity radiated to the intensity radiated by the same number of two (nondegenerate) level atoms. This comparison can be simply understood if one studies the partition of the population of the collective energy levels between the different states of these levels, and it appears that the most populated states are these which are able to radiate the most. Finally, it is shown how level degeneracy affects the quantum fluctuations of the intensity.

DOI
10.1103/physreva.18.1797

Related papers

Level-degeneracy effects in superradiance theory

A. Crubellier

Up to now, the problem of the influence of level degeneracy on superradiance has been neglected. We describe here a first approach to this problem, in the frame of "small system" quantum model, generalized to the case of a collection of atoms with two degenerate levels of angular momenta $j$ and ${j}^{\ensuremath{'}}$ connected by an electric or magnetic dipole transition. The differences between this case and the well-known case of two (nondegenerate) level atoms are of two types. The first type is due to the competition between different transitions sharing a common state: superradiant emission on a transition inhibits or initiates superradiance on transitions with smaller transition probability, depending upon which state, upper or lower, is the common one. This effect does not come from the equality of the different wavelengths and would also appear with the same states even if the degeneracy were removed; its qualitative influence on the features of the superradiant pulse can be easily estimated. The second type of differences is quite specific to level degeneracy and consists in interferences between the transitions of the collective system having the same frequency and polarization. In analogy with the description of collections of two-level atoms as spin-\textonehalf{} systems, a group-theoretical description of the considered collection of atoms is found suitable; the problem of the determination of a basis of collective states and its group-theoretical implications are discussed; in particular, it is found that the isotropic character of spontaneous emission allows us to use tensorial formalism and simplifies the formal description of the problem.

Physical Review A•Jun 1, 1977•22 citations

The influence of dipole–dipole inter-atomic coupling upon super-radiance

M. G. Benedict, A. M. Ermolaev, Viktor A. Malyshev +2 more

The influence of the dipole–dipole inter-atomic coupling on collective spontaneous emission has been considered by many authors using both semiclassical and quantum theories. Specific results have been obtained for simple cases of regular atomic systems with a finite number of atoms. For disordered systems it has been found that the dipole–dipole coupling causes relaxation of the polarization phase (the effect of de-phasing), thus suppressing super-radiance. The main object of this chapter will be a regular linear chain of identical two-level atoms fully excited in the initial moment of time. The chapter considers the super-radiance of a regular linear chain of atoms. Such a system is the limiting case of a multi-atomic system characterized by a small Fresnel number. The dipole–dipole inter-atomic coupling modifies the super-radiance dynamics only slightly, but has a strong effect on the shape and width of the spectrum.

CRC Press eBooks•Mar 29, 2018•0 citations

Super-radiance from degenerate levels

Решетов Владимир Александрович

The polarization properties and the temporal shapes of the super-radiance pulses formed on degenerate levels are studied theoretically in a semiclassical approximation. The dependence of the super-radiance pulse polarization on the values of the total angular momenta of resonant levels and on the polarization and area of the pumping pulse is examined in detail. Non-linear equations describing the temporal shapes of the super-radiance pulses with different polarizations are obtained. Some examples with low values of angular momenta of the levels are discussed. It is shown that, in general, the temporal shape of the super-radiance pulse differs from hyperbolic secant.

Journal of Physics B Atomic Molecular and Optical Physics•Nov 14, 1993•4 citations

Optical properties of degenerate atomic gases

Janne Ruostekoski

We study interactions of light with a sample of two-level atoms. Quantum statistical effects of degenerate boson and fermion gases are described by using the quantum field theory of atom-photon interactions, fully including the angular momentum degeneracies. Coupled propagation equations are given for light and matter fields, and plausible general simplifications are enumerated.^ In the limit of large atom-field detuning, multiple scattering of light and QED linewidths and line shifts may be ignored, and the propagation equations of light and matter fields may be decoupled. A general expression for the spectrum of the scattered light is derived, complete with the dependence on atomic level scheme, on various light polarizations, and on the geometry of the experiment. With these simplifications we are able to find distinct qualitative features in the spectrum of the scattered light in the case of both fermions and bosons that depend on the statistics of atoms. This is because for bosons (fermions), those scattering events in which an atom recoils to an already occupied state are enhanced (inhibited).^ As the driving light gets closer to the atomic resonance, multiple scattering and vacuum fluctuations of the electromagnetic fields should also be taken into account. We write the equations of motion for the excited state field operators by eliminating the vacuum electromagnetic field. It is always assumed that the driving external laser field is in the coherent state. We find in the limit of low light intensity, a hierarchy of equations of motion for correlation functions that contain one excited-atom field and one, two, three, etc., ground state atom fields. It is conjectured that the entire linear hierarchy may be solved by solving numerically the classical equations for the coupled system of electromagnetic fields and charged harmonic oscillators. We discuss the emergence of resonant dipole-dipole interactions and collective linewidths, and delineate the limits of validity of the column density approach in terms of non-cooperative atoms by presenting a mathematical example in which this approach is exact. ^

•Jan 1, 1996•0 citations

Correlation in superradiance: A closed-form approach to cooperative effects

Susanne F. Yelin, Kostrun, M., T. Wang +1 more

We have developed a novel method to describe superradiance and related cooperative and collective effects in a closed form. Using the method we derive a two-atom master equation in which any complexity of atomic levels, semiclassical coupling fields and quantum fluctuations in the fields can be included, at least in principle. As an example, we consider the dynamics of an initially inverted two-level system and show how even such in a simple system phenomena such as the initial radiation burst or broadening due to dipole-dipole interactions occur, but it is also possible to estimate the population of the subradiant state during the radiative decay. Finally, we find that correlation only, not entanglement is responsible for superradiance.

arXiv:quant-ph/0509184•Sep 26, 2005•3 citations

Effects of diffraction upon super-radiance

M. G. Benedict, A. M. Ermolaev, Viktor A. Malyshev +2 more

This chapter investigates both diffraction and fluctuation effects on super-radiance within the framework of two models. Firstly, the two-dimensional theory of super-radiance of an extended system is developed. Secondly, the chapter considers the super-radiance of a 'sheet of paper' volume. However, quantum fluctuations of the initial polarization give rise to transverse inhomogeneity of atomic and field characteristics, which manifests itself in a change in the shape of the pulse and in the radiation polar diagram. The ringing of the envelope, which is typical of the one-dimensional model, becomes smoother. The super-radiance polar diagram has a ray structure, of which the angular size of individual components (rays) is of the order of the diffraction angle. The angular size of the ray is close to the diffraction angle, and its form changes relatively little from one realization of the initial polarization distribution to another.

CRC Press eBooks•Mar 29, 2018•0 citations
We study here level-degeneracy effects in super-radiance, using the quantum "small-system" model whose interest and limitations are discussed. First, we show that this model allows one to understand the physical origin of these effects and to describe their qualitative influence on the properties of the emitted light. We also present and analyze numerical results obtained for the case of a dipole transition between two degenerate levels of angular momenta \textonehalf{}. We show that in this particular case one can define a basis of collective states which is well adapted to the invariance properties of the master equation. It is then possible to solve the master equation and to compute expectation values for the radiated field (intensity radiated with a given polarization, quantum fluctuations of this intensity) for various initial conditions and for small but already significant values of the number of individual systems. A detailed analysis of these results and a comparison with analogous calculations in the case where the degeneracy is supposed to be removed allows us to estimate the individual influence of the different types of effects (interference effects and the two sorts of competition effects, inhibition and initiation). We also compare the total intensity radiated to the intensity radiated by the same number of two (nondegenerate) level atoms. This comparison can be simply understood if one studies the partition of the population of the collective energy levels between the different states of these levels, and it appears that the most populated states are these which are able to radiate the most. Finally, it is shown how level degeneracy affects the quantum fluctuations of the intensity.
Up to now, the problem of the influence of level degeneracy on superradiance has been neglected. We describe here a first approach to this problem, in the frame of "small system" quantum model, generalized to the case of a collection of atoms with two degenerate levels of angular momenta jjj and ${j}^{\ensuremath{'}}$ connected by an electric or magnetic dipole transition. The differences between this case and the well-known case of two (nondegenerate) level atoms are of two types. The first type is due to the competition between different transitions sharing a common state: superradiant emission on a transition inhibits or initiates superradiance on transitions with smaller transition probability, depending upon which state, upper or lower, is the common one. This effect does not come from the equality of the different wavelengths and would also appear with the same states even if the degeneracy were removed; its qualitative influence on the features of the superradiant pulse can be easily estimated. The second type of differences is quite specific to level degeneracy and consists in interferences between the transitions of the collective system having the same frequency and polarization. In analogy with the description of collections of two-level atoms as spin-\textonehalf{} systems, a group-theoretical description of the considered collection of atoms is found suitable; the problem of the determination of a basis of collective states and its group-theoretical implications are discussed; in particular, it is found that the isotropic character of spontaneous emission allows us to use tensorial formalism and simplifies the formal description of the problem.
The influence of the dipole–dipole inter-atomic coupling on collective spontaneous emission has been considered by many authors using both semiclassical and quantum theories. Specific results have been obtained for simple cases of regular atomic systems with a finite number of atoms. For disordered systems it has been found that the dipole–dipole coupling causes relaxation of the polarization phase (the effect of de-phasing), thus suppressing super-radiance. The main object of this chapter will be a regular linear chain of identical two-level atoms fully excited in the initial moment of time. The chapter considers the super-radiance of a regular linear chain of atoms. Such a system is the limiting case of a multi-atomic system characterized by a small Fresnel number. The dipole–dipole inter-atomic coupling modifies the super-radiance dynamics only slightly, but has a strong effect on the shape and width of the spectrum.
The polarization properties and the temporal shapes of the super-radiance pulses formed on degenerate levels are studied theoretically in a semiclassical approximation. The dependence of the super-radiance pulse polarization on the values of the total angular momenta of resonant levels and on the polarization and area of the pumping pulse is examined in detail. Non-linear equations describing the temporal shapes of the super-radiance pulses with different polarizations are obtained. Some examples with low values of angular momenta of the levels are discussed. It is shown that, in general, the temporal shape of the super-radiance pulse differs from hyperbolic secant.
We study interactions of light with a sample of two-level atoms. Quantum statistical effects of degenerate boson and fermion gases are described by using the quantum field theory of atom-photon interactions, fully including the angular momentum degeneracies. Coupled propagation equations are given for light and matter fields, and plausible general simplifications are enumerated.^ In the limit of large atom-field detuning, multiple scattering of light and QED linewidths and line shifts may be ignored, and the propagation equations of light and matter fields may be decoupled. A general expression for the spectrum of the scattered light is derived, complete with the dependence on atomic level scheme, on various light polarizations, and on the geometry of the experiment. With these simplifications we are able to find distinct qualitative features in the spectrum of the scattered light in the case of both fermions and bosons that depend on the statistics of atoms. This is because for bosons (fermions), those scattering events in which an atom recoils to an already occupied state are enhanced (inhibited).^ As the driving light gets closer to the atomic resonance, multiple scattering and vacuum fluctuations of the electromagnetic fields should also be taken into account. We write the equations of motion for the excited state field operators by eliminating the vacuum electromagnetic field. It is always assumed that the driving external laser field is in the coherent state. We find in the limit of low light intensity, a hierarchy of equations of motion for correlation functions that contain one excited-atom field and one, two, three, etc., ground state atom fields. It is conjectured that the entire linear hierarchy may be solved by solving numerically the classical equations for the coupled system of electromagnetic fields and charged harmonic oscillators. We discuss the emergence of resonant dipole-dipole interactions and collective linewidths, and delineate the limits of validity of the column density approach in terms of non-cooperative atoms by presenting a mathematical example in which this approach is exact. ^
We have developed a novel method to describe superradiance and related cooperative and collective effects in a closed form. Using the method we derive a two-atom master equation in which any complexity of atomic levels, semiclassical coupling fields and quantum fluctuations in the fields can be included, at least in principle. As an example, we consider the dynamics of an initially inverted two-level system and show how even such in a simple system phenomena such as the initial radiation burst or broadening due to dipole-dipole interactions occur, but it is also possible to estimate the population of the subradiant state during the radiative decay. Finally, we find that correlation only, not entanglement is responsible for superradiance.
This chapter investigates both diffraction and fluctuation effects on super-radiance within the framework of two models. Firstly, the two-dimensional theory of super-radiance of an extended system is developed. Secondly, the chapter considers the super-radiance of a 'sheet of paper' volume. However, quantum fluctuations of the initial polarization give rise to transverse inhomogeneity of atomic and field characteristics, which manifests itself in a change in the shape of the pulse and in the radiation polar diagram. The ringing of the envelope, which is typical of the one-dimensional model, becomes smoother. The super-radiance polar diagram has a ray structure, of which the angular size of individual components (rays) is of the order of the diffraction angle. The angular size of the ray is close to the diffraction angle, and its form changes relatively little from one realization of the initial polarization distribution to another.