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Annalen der Physik

Radiation Properties of Systems of Three and Four Continuously Pumped Atoms

Heinz Steudel

Published Jan 1, 1981• 6 citations
Publisher

Abstract

Abstract Radiation properties of three and four atoms continuously pumped by an incoherent excitation mechanism are investigated by using Lehmberg's master equation and the quantum fluctuation‐regression theorem. For proper configurations we found in comparison with independent atoms simultaneously (i) an enlargement of the radiation rate, (ii) a spectral narrowing and (iii) a reduction of intensity fluctuations.

DOI
10.1002/andp.19814930203

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Quantum Theory of Radiation. II. Statistical Aspects of Laser Light

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We have solved a master equation to obtain the diagonal elements of the density matrix for laser light. The master equation represents a generalization of a master equation derived earlier for a single radiation mode interacting with $N$ stationary two-level atoms. The generalization takes into account the pumping scheme which characterizes a three-level laser. For positive temperatures and a lossless cavity, the equilibrium solution of the master equation gives the correct statistical-mechanical description of the atoms and radiation. For negative temperatures, the distribution function for the number of photons in the mode is either exponential or peaked, depending on whether the laser is operating below or above threshold. The calculated intensity fluctuations are in good agreement with semiclassical results for lasers operating slightly above threshold.

Physical Review•Mar 10, 1967•4 citations
Abstract Radiation properties of three and four atoms continuously pumped by an incoherent excitation mechanism are investigated by using Lehmberg's master equation and the quantum fluctuation‐regression theorem. For proper configurations we found in comparison with independent atoms simultaneously (i) an enlargement of the radiation rate, (ii) a spectral narrowing and (iii) a reduction of intensity fluctuations.
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.
Abstract Using Lehmberg's master equation and taking into account dipole‐dipole near‐field interaction the time‐dependent intensity pattern, intensity – and angular correlations of the cooperative spontaneous radiation from an initially fully excited system of three identical two‐level atoms are calculated. The intensity pattern developes lobes in different directions at different times in such a way that contrary to the two‐atom system the spatial distribution of the total number of the emitted photons differs from that of the single‐atom radiation pattern. In particular three atoms placed in proper distances on a straight line emit preferentially their energy along this line. At the beginning of the emission process the probability to find two photons simultaneously in the same (or geometrical equivalent) direction is always highest but in the course of time, contrary to the two‐atom case, it may well happen that the probability of finding two photons in quite different directions becomes more favoured.
We have solved a master equation to obtain the diagonal elements of the density matrix for laser light. The master equation represents a generalization of a master equation derived earlier for a single radiation mode interacting with NNN stationary two-level atoms. The generalization takes into account the pumping scheme which characterizes a three-level laser. For positive temperatures and a lossless cavity, the equilibrium solution of the master equation gives the correct statistical-mechanical description of the atoms and radiation. For negative temperatures, the distribution function for the number of photons in the mode is either exponential or peaked, depending on whether the laser is operating below or above threshold. The calculated intensity fluctuations are in good agreement with semiclassical results for lasers operating slightly above threshold.