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Annalen der Physik

Cooperative Spontaneous Emission from a Single‐quantum Excited Three‐atom System

Th. Richter

Published Jan 1, 1981• 12 citations
Publisher

Abstract

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.

DOI
10.1002/andp.19814930204

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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.
The cooperative spontaneous emission from three identical, initially excited two-level atoms separated by distances much smaller than the resonance wavelength is studied taking into account the dipole-dipole near-field interaction. Approximate expressions are obtained for the time evolution of the atomic system, the radiated intensity and the one-time intensity correlation function. As a new result the authors find that the near-field interaction may lead to the occurrence of beats in the intensity. Moreover, the destructive effect of the near-field interaction on the coherence properties of the emitted radiation is discussed.
The interaction between electromagnetic radiation and two three-level atoms is investigated. The atom-atom separation is assumed to be smaller than the corresponding mean resonance wavelength. The total radiance rate of the atomic system is calculated as a function of time. Explicit results are given for several different initial states of the atomic system. Some of them exhibit superradiance, and some act as photon-trapping states. Instead of exponential decay, the oscillations appear in the time evolution of the radiation rate due to the correlation between atoms. The decay constants and coupling decay constants show strong effects on the emission rates. Completely differing from two identical double-level atoms, the cooperative effects always exist in the three-level atomic system except for the case in which the coupling decay constants ${\ensuremath{\gamma}}_{12}$ and ${\ensuremath{\gamma}}_{21}$ are zero.
We study cooperative single-photon spontaneous emission from three multilevel atoms with one of them being excited for different atomic configurations in optical vector theory. The dynamic evolution is solved by finding the eigenvalues of a 3 \ifmmode\times\else\texttimes\fi{} 3 matrix, and then the relevant decay rates and Lamb shifts are obtained analytically. It is shown that the symmetry of atomic configuration has a big influence on the super-radiance of the system. To obtain strong super-radiance requires not only the distances among the three atoms to be much shorter than the wavelength, but also to have symmetrical distribution. We also calculate the emission spectra and find that it normally has three peaks, but it has two peaks under the equilateral-triangle configuration.
Spontaneous emission from two non-identical two-level atoms is examined from the viewpoint of quantum beats and super-radiant effects. Our analytical solution, illustrated graphically, shows that the total radiation rate exhibits temporal sinusoidal modulation (beats). The beats result from the fact that the atoms have different transition frequencies and different natural linewidths. For small interatomic separations, the total radiation rate is greater than its initial value. This ‘super-radiant’ property is absent in the case of noninteracting atoms, as well as for two identical atoms. In the case when the atoms are separated by distances much smaller than the resonant wavelength, the population trapping effect can take place in such a system.