Abstract
A density-matrix approach is developed to provide a theoretical description of the intensity, angular distribution, and polarization of superradiative emission from an ensemble of many-electron atomic systems. The many-electron atomic systems are described as cooperatively interacting by means of forces that can be long range. Particular emphasis is given to the coherent excitation of the collective atomic-ensemble states, which may be produced by incident laser radiation. The initial excitation and spontaneous emission processes may be described as independent. Both frequency-domain and time-domain formulations of the density-matrix approach are developed. The collective atomic-ensemble states are specified in a detailed hyperfine representation, corresponding to successively coupling the individual hyperfine angular momenta F pertaining to the many-electron atoms. A less detailed fine-structure angular-momentum representation may also be used. In the density-operator approach, account can be taken of the coherent excitation of a particular subspace of the initial atomic-ensemble states. For a comprehensive and unified development of time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations, a reduced-density-matrix (quantum-open-systems) approach is introduced. The non-equilibrium atomic-ensemble-state kinetics and the homogeneous spectral-line shapes can thereby be systematically and self-consistently determined. The collective atomic-ensemble states may be obtained using a variety of different methods. These states can be determined using a dressed-state approach, in which the required states are calculated in the presence of an electromagnetic field.
Highlights
Superradiant emission was first described by Dicke [1]
The angular distribution and polarization measurements can provide more detailed information, which would be unobtainable in a spectroscopy measurement of only the total intensity
In the density-matrix description of the intensity, angular distribution, and polarization of superradiant emission, account can be taken of a general set of steady-state or time-varying atomic-ensemble excitation and de-excitation processes
Summary
Superradiant emission was first described by Dicke [1]. Due to the cooperative nature of the interaction among the individual members of an ensemble of N quantum systems, e. g., many-electron atoms, the intensity of superradiant emission can be proportional to N2. A. Density-Matrix Approach By means of a density-matrix approach, a general quantum-mechanical description of the intensity, angular distribution, and polarization of superradiant emission from an ensemble of N many-electron atomic systems can be developed. In the density-matrix description of the intensity, angular distribution, and polarization of superradiant emission, account can be taken of a general set of steady-state or time-varying (possibly coherent) atomic-ensemble excitation and de-excitation processes. A compact formulation is achieved by adopting the Liouville-space operator representation This formulation can provide a detailed non-equilibrium quantum-statistical description of the angular distribution and polarization of radiative emission from an atomic ensemble for a general set of steady-state or time-varying (possibly coherent) excitation and de-excitation processes involving the atomic-ensemble states, under the influence of environmental collisional and radiative decoherence and relaxation processes.
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