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Journal of Physics B Atomic and Molecular Physics

Radiation rate and spectrum of a continuously pumped three-atom system

Heinz Steudel

Published Oct 28, 1979• 5 citations
Publisher

Abstract

Radiation properties of three atoms continuously pumped by an incoherent excitation mechanism are investigated by using Lehmberg's master equation (1970) and the quantum fluctuation-regression theorem. The main results are: (i) the radiation rate of three atoms within a volume of diameter very much less than lambda essentially depends on their arrangement; (ii) the effect for two atoms, i.e. that an increasing radiation rate can be accompanied by a decreasing spectral width, becomes even more pronounced for three atoms.

DOI
10.1088/0022-3700/12/20/011

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Radiation properties of three atoms continuously pumped by an incoherent excitation mechanism are investigated by using Lehmberg's master equation (1970) and the quantum fluctuation-regression theorem. The main results are: (i) the radiation rate of three atoms within a volume of diameter very much less than lambda essentially depends on their arrangement; (ii) the effect for two atoms, i.e. that an increasing radiation rate can be accompanied by a decreasing spectral width, becomes even more pronounced for three atoms.
The intensity correlation function of the cooperative radiation from a continuously pumped three-atom system is calculated using Lehmberg's master equation supplemented by an incoherent-pumping term. Cooperative effects are found to change drastically the intensity fluctuations of the emitted radiation. Particularly, if the pumping rate is adjusted to three times the single-atom spontaneous decay rate, increased radiation, compared with that from three independently emitting atoms, should be observed, exhibiting a reduced intensity fluctuation.
Abstract The total radiation rate of the cooperative spontaneous emission from an initially single‐quantum excited three‐atom system is calculated using Lehmberg's master equation and taking into account dipole‐dipole near field interaction. We find a strong influence of the precise configuration of the atomic dipoles and of the position of the initially excited atom on the temporal behaviour of the total radiation rate, especially if the atoms are separated by distances much smaller than the resonance wavelength.
The emission spectrum is found for transitions between a pair of atomic levels which are coupled by a coherent applied field, in the case in which decay to other levels of lower energy takes place during the emission process. The problem is solved by first finding the spectral distribution of radiation emitted by an atom which is initially prepared in some combination of the two coupled states, and which then decays to states of lower energy. (The solution found to this initial-value problem is valid even when many photons are emitted before the decay takes place.) It is then shown how the solution so obtained may be used to describe the case in which the atom is continually excited to the pair of levels in question by a weak, incoherent pumping mechanism. Limiting cases are discussed and compared with those which apply when no decay out of the two-dimensional subspace of coupled states takes place. The method of solution, which is based on an evaluation of the appropriate atomic correlation function by means of the quantum fluctuation-regression theorem, is compared to the method of simply adding imaginary terms, proportional to the decay constants, to the state energies. The latter method is of far more restricted validity, in that it depends on a particular strong inequality which must be assumed to hold between the decay constants.
We suggest that the statistical properties of the scattered radiation in resonance-fluorescence experiments may be affected significantly by the existence of atomic correlations. The scattered light spectrum from two- and three-atom collective systems has been calculated and compared with the one-atom spectrum. The differences are quite significant for weak fields, but become less pronounced as the intensity of the driving field is increased. In addition, we have calculated the scattered intensity correlation function for collectively interacting systems, and found that its behavior is very different from that of the single-atom intensity correlation function, both for weak and strong incident fields. The implications of our findings for the observation of photon antibunching are also discussed.