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 Experimental and Theoretical Physics

Exchange dipole interaction in a multilevel cooperative system of atoms

E. V. Orlenko, Boris G. Matisov

Published Jan 1, 2004• 1 citation
Publisher

Abstract

Atomic systems with three or more equidistant energy levels, in which a cascade process is possible, are considered. Hamiltonians obtained for such systems are analogous to Heisenberg Hamiltonians, but for systems with integral spins. For Dicke states in multilevel systems, quantum-mechanical mean values of the energy of a cooperative system are calculated taking into account weak interactions between atoms. The type of emission preceding superradiant avalanche emission of the system is analyzed. It can be expected that a coherent state may be formed, in which collective processes affect one another not only via population of the intermediate common layer, but also via phasing of pure quantum states. The single superfluorescence pulse that can be formed in this case is not a simple superposition of two or more pulses of sequential superradiant transitions in two-level systems.

DOI
10.1134/1.1648098

Related papers

Enhanced superradiance effect in a system of interacting two-level atoms and crossover from coherent to many-atom multiphoton relaxation regime

Sergei P. Lukyanets, Dmytro Bevzenko

We study effects of direct interatomic interaction on cooperative processes in atom-photon dynamics. Using a model of two-level atoms with Ising-type interaction as an example, it is demonstrated that interparticle interaction can promote cooperative radiative relaxation. For small number of atoms this results in inhibition of incoherent spontaneous decay leading to the regime of collective pulse relaxation. Above superradiance threshold increase in delay time and enhancement of superradiance is occurred. In the case of strong interaction (as compared to excitation energy of an atom) transition to the regime of multiphoton relaxation occurs, which we discuss using a simple model of two atoms in a high-Q single mode cavity. It is shown that such transition is accompanied by Rabi oscillations involving many-atom multiphoton states. Dephasing effect of dipole-dipole interaction and solitonic mechanism of relaxation are discussed as well.

Optics and Spectroscopy•Nov 1, 2011•3 citations

Effects of quantum interference in spectra of cascade spontaneous emission from multilevel systems

A.A. Makarov, Vladimir I. Yudson

A general expression for the spectrum of cascade spontaneous emission from an arbitrary multilevel system is presented. Effects of the quantum interference of photons emitted in different transitions are analyzed. These effects are especially essential when the transition frequencies are close. Several examples are considered: (i) Three-level system; (ii) Harmonic oscillator; (iii) System with equidistant levels and equal rates of the spontaneous decay for all the transitions; (iv) Dicke superradiance model.

EPJ Web of Conferences•Dec 13, 2016•0 citations

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

Effects of interatomic interaction on cooperative relaxation of two-level atoms

Sergei P. Lukyanets, Dmytro Bevzenko

We study effects of direct interatomic interaction on cooperative processes in atom-photon dynamics. Using a model of two-level atoms with Ising-type interaction as an example, it is demonstrated that interparticle interaction combined with atom-field coupling can introduce additional interatomic correlations acting as a phase synchronizing factor. For the case of weakly interacting atoms with $J<\ensuremath{\hbar}{\ensuremath{\omega}}_{0}$, where $J$ is the interparticle coupling constant and ${\ensuremath{\omega}}_{0}$ is the atomic frequency, dynamical regimes of cooperative relaxation of atoms are analyzed in the Born-Markov approximation both numerically and using the mean field approximation. We show that interparticle correlations induced by the direct interaction result in inhibition of incoherent spontaneous decay leading to the regime of collective pulse relaxation which differs from superradiance in nature. For superradiant transition, the synchronizing effect of interatomic interaction is found to manifest itself in enhancement of superradiance. When the interaction is strong and $J>\ensuremath{\hbar}{\ensuremath{\omega}}_{0}$, one-particle one-photon transitions are excluded and transition to the regime of multiphoton relaxation occurs. Using a simple model of two atoms in a high-$Q$ single mode cavity we show that such transition is accompanied by Rabi oscillations involving many-atom multiphoton states. Dephasing effects of dipole-dipole interaction and solitonic mechanism of relaxation are discussed.

arXiv:quant-ph/0607023•Physical Review A•Nov 9, 2006•10 citations

Theory of cooperative spontaneous emission

Anatolii V Andreev

An analysis is made of the deexcitation kinetics of strongly excited extended systems of initially uncorrelated two-level radiators. The possibility of partially cooperative states of the system is predicted when the radiation intensity acquires values intermediate between the spontaneous decay intensity and the Dicke superradiance intensity. The conditions for the onset of cooperative processes are obtained. The threshold for the oscillatory emission conditions is determined and the oscillation frequency is found. Modulation of the emission intensity is predicted with different modulation frequencies before and after the superradiant pulse. The modulation frequencies are determined. Formulas are derived for the superradiant pulse delay times and intensities. The possibility of weakly anisotropic cooperative emission is predicted.

Soviet Journal of Quantum Electronics•Apr 30, 1978•3 citations

Coherent population trapping in an ensemble of three-level atoms in the presence of cooperative relaxation

Boris G. Matisov, I. A. Grigorenko, I. E. Mazets

We derive equations that describe the dynamics of three-level atoms with a cascade system of levels interacting with two resonant coherent fields in conditions where cooperative relaxation dominates over incoherent spontaneous emission. We calculate the temporal dynamics of the values of the atomic populations. The possibility of coherent population trapping in the presence of the cooperative decay is established. Finally, we calculate the averaged population of the intermediate level as a function of detuning for different values of the coupling constant.

Journal of Experimental and Theoretical Physics•Sep 1, 1997•0 citations
Atomic systems with three or more equidistant energy levels, in which a cascade process is possible, are considered. Hamiltonians obtained for such systems are analogous to Heisenberg Hamiltonians, but for systems with integral spins. For Dicke states in multilevel systems, quantum-mechanical mean values of the energy of a cooperative system are calculated taking into account weak interactions between atoms. The type of emission preceding superradiant avalanche emission of the system is analyzed. It can be expected that a coherent state may be formed, in which collective processes affect one another not only via population of the intermediate common layer, but also via phasing of pure quantum states. The single superfluorescence pulse that can be formed in this case is not a simple superposition of two or more pulses of sequential superradiant transitions in two-level systems.
We study effects of direct interatomic interaction on cooperative processes in atom-photon dynamics. Using a model of two-level atoms with Ising-type interaction as an example, it is demonstrated that interparticle interaction can promote cooperative radiative relaxation. For small number of atoms this results in inhibition of incoherent spontaneous decay leading to the regime of collective pulse relaxation. Above superradiance threshold increase in delay time and enhancement of superradiance is occurred. In the case of strong interaction (as compared to excitation energy of an atom) transition to the regime of multiphoton relaxation occurs, which we discuss using a simple model of two atoms in a high-Q single mode cavity. It is shown that such transition is accompanied by Rabi oscillations involving many-atom multiphoton states. Dephasing effect of dipole-dipole interaction and solitonic mechanism of relaxation are discussed as well.
A general expression for the spectrum of cascade spontaneous emission from an arbitrary multilevel system is presented. Effects of the quantum interference of photons emitted in different transitions are analyzed. These effects are especially essential when the transition frequencies are close. Several examples are considered: (i) Three-level system; (ii) Harmonic oscillator; (iii) System with equidistant levels and equal rates of the spontaneous decay for all the transitions; (iv) Dicke superradiance model.
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.
We study effects of direct interatomic interaction on cooperative processes in atom-photon dynamics. Using a model of two-level atoms with Ising-type interaction as an example, it is demonstrated that interparticle interaction combined with atom-field coupling can introduce additional interatomic correlations acting as a phase synchronizing factor. For the case of weakly interacting atoms with $J<\ensuremath{\hbar}{\ensuremath{\omega}}_{0}$, where JJJ is the interparticle coupling constant and ${\ensuremath{\omega}}_{0}$ is the atomic frequency, dynamical regimes of cooperative relaxation of atoms are analyzed in the Born-Markov approximation both numerically and using the mean field approximation. We show that interparticle correlations induced by the direct interaction result in inhibition of incoherent spontaneous decay leading to the regime of collective pulse relaxation which differs from superradiance in nature. For superradiant transition, the synchronizing effect of interatomic interaction is found to manifest itself in enhancement of superradiance. When the interaction is strong and $J>\ensuremath{\hbar}{\ensuremath{\omega}}_{0}$, one-particle one-photon transitions are excluded and transition to the regime of multiphoton relaxation occurs. Using a simple model of two atoms in a high-QQQ single mode cavity we show that such transition is accompanied by Rabi oscillations involving many-atom multiphoton states. Dephasing effects of dipole-dipole interaction and solitonic mechanism of relaxation are discussed.
An analysis is made of the deexcitation kinetics of strongly excited extended systems of initially uncorrelated two-level radiators. The possibility of partially cooperative states of the system is predicted when the radiation intensity acquires values intermediate between the spontaneous decay intensity and the Dicke superradiance intensity. The conditions for the onset of cooperative processes are obtained. The threshold for the oscillatory emission conditions is determined and the oscillation frequency is found. Modulation of the emission intensity is predicted with different modulation frequencies before and after the superradiant pulse. The modulation frequencies are determined. Formulas are derived for the superradiant pulse delay times and intensities. The possibility of weakly anisotropic cooperative emission is predicted.
We derive equations that describe the dynamics of three-level atoms with a cascade system of levels interacting with two resonant coherent fields in conditions where cooperative relaxation dominates over incoherent spontaneous emission. We calculate the temporal dynamics of the values of the atomic populations. The possibility of coherent population trapping in the presence of the cooperative decay is established. Finally, we calculate the averaged population of the intermediate level as a function of detuning for different values of the coupling constant.