The theoretical group approach is applied to the study of collective properties of concrete multiparticle systems. The Dicke theory of coherent spontaneous radiation is generalized to the caae of multilevel emitters. The effects of superradiation and photon echoes in multilevel systems are investigated. Two generalizations of the coherent state of oscillators are examined: 1) coherent states of unitary spin obeying the classical limitations in the Dicke problem and 2) coherent states for systems with non-equidistant spectra (using an example of a rotating A description is given of the coherent properties of beams of particles of different nature. It is shown that the correlation between particles of the incident beam can lead to significant increase of the probability of their interaction with the scatterer. (tr-auth)
The present state of theoretical and experimental research on collective spontaneous emission (superradiance) in a system of radiators (atoms, molecules, or nuclei) is reviewed. The distinction between superradiance and the amplification of spontaneous emission is discussed. There is also a discussion of conditions under which the effect can be observed and of various theoretical methods for describing superradiance: the quantum single-mode and multimode models and the semiclassical approach. Theoretical papers on superradiance in systems with dimensions smaller than the wavelength of the radiation and also in extended systems are reviewed. It is shown that superradiance may occur in weakly amplifying media. A situation in which the superradiance is oscillatory is described. The possible use of superradiance to generate coherent emission in the x-ray and ? ranges is discussed. The superradiance accompanying Raman scattering of light in atomic and molecular media is studied. The theoretical results are compared with experimental observations of superradiance in the optical range. In an appendix, the nature of the phase transition in a system of radiators interacting through an electromagnetic field is discussed.
Phenomena of coherent resonant propagation can be considered as resulting from the cooperative interaction of a certain number of excited two-level systems. It is shown that these phenomena can be characterized by a specific "maximum cooperation number" and by the associated "cooperation time." These are defined for the superradiant state, but their meaning and usefulness can be extended to other situations. The alternative description of of superradiance as a spontaneous or as a stimulated effect is also discussed and it is shown that with the help of the new concepts, the Dicke quantum perturbative treatment can be reconciled with the semiclassical theories.
In this paper we discuss the quantum features of cooperative radiation processes in a two-level system taking into account non-Markovian effects. If the initial condition is spatially uniform, the many-mode atom-field master equation which has been derived and semiclassically discussed in a previous paper, reduces to the well-known single-mode model laser master equation. Hence, using a suitable projection operator, we derive a generalized non-Markovian master equation which turns out to be correct already in the first Born approximation. This master equation incorporates the effects both of stimulated emission and absorption and of spontaneous emission. When stimulated processes can be neglected, it reduces to a previously known Markovian superradiance master equation, whereas in general it describes non-Markovian oscillations of the radiated intensity. Finally we derive a linear system of equations for the probability of occupation of the Dicke states which generalizes a previously discussed system, taking into account the contribution of stimulated processes.
We give a general nonperturbative treatment of cooperative emission in systems of
N two-level atoms, starting from first principles and including inhomogeneous broadening. In particular, we study superfluorescence, which is defined as the cooperative spontaneous emission, i.e., radiation rate proportional to
N2, from an atomic system initially excited with zero macroscopic dipole moment and a uniform population difference between the excited and the fundamental states. The atomic system is described by means of collective dipole operators. A fundamental justification is given for the existence of damped "quasimodes" of the mirrorless active volume. The damping of such modes is simply due to the propagation of the Maxwell field, which escapes from the active volume. A general atom-field master equation is derived for the system atoms plus field inside the active volume, described, respectively, in terms of collective dipole operators and quasimode operators. An important feature of this equation is that inhomogeneous broadening simply appears via a time-dependent atom-field coupling constant. In this paper we give a semiclassical treatment of such a master equation. For a pencil-shaped geometry of the active volume, generalized Maxwell-Bloch equations are derived for the envelopes of the radiation inside the active volume and polarization. Such equations take into account the two directions of propagation of the radiation and the inhomogeneous broadening. Suitably phrasing our initial condition in semiclassical terms, we find that propagation effects can be neglected at all times and the generalized Maxwell-Bloch equations reduce to a simple pendulum equation. On the basis of the discussion of the pendulum equation, we conclude that superfluorescence occurs when (i) the length
L of the active volume is much larger than a suitable threshold length
LT (this condition ensures that the dephasing atomic processes occur on a time scale much larger than the times characteristic of the cooperative emission); (ii) the length
L is smaller or of the same order of a suitable cooperation length
Lc (this condition ensures that cooperative spontaneous emission dominates stimulated processes, which give radiation proportional to
N). For $L\ensuremath{\ll}{L}_{c}$, one has a hyperbolic-secant superfluorescent pulse; for $L\ensuremath{\approx}{L}_{c}$, as one has in the recent experiments of Skribanowitz et al., one finds oscillations in the cooperative decay and in the radiation emission. Such oscillations are due to the contribution of stimulated processes. For $L\ensuremath{\gg}{L}_{c}$, this contribution increases. As a consequence one gets more oscillations in the radiated intensity, which becomes proportional to
N, so that superfluorescence effects disappear.
In this paper the possibility of cooperative effects in Cerenkov radiation will be discussed theoretically. A crude sketch is given of a possible capture of photons from a part of the rather broadband Cerenkov spectrum in a high quality resonator. We then introduce a classical Markoffian master equation for the system, accounting for Cerenkov emission as well as reabsorption. Both elementary quantum theory and classical electrodynamics provide us with the same formula for the transition rate of the stimulated Cerenkov process. At present we restrict ourselves to the macroscopic evolutions. The stationary electron distribution is calculated explicitly, as well as the equation governing the photon numbers. A non-equilibrium second order phase transition will be seen to occur for a critical value of the electronic input current density. Rough estimates are presented for threshold parameters. © 1977.