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Canadian Journal of Physics

Cooperative fluorescence by three-level atoms in a strong excitation field

Helen S. Freedhoff

Published Jan 1, 1985• 4 citations
Publisher

Abstract

When a system of two-level atoms interacts with a very intense field, the phenomena associated with superradiance do not appear in the fluorescent radiation. The question has been raised, "Can pumping by an intense field inhibit the occurrence of superradiance in the fluorescence of a system of three-level atoms to the third (nonresonant) level?" In this paper, we calculate the fluorescence spectrum of 2 three-level atoms. We find that superradiance, while absent in that part of the radiation corresponding to resonance fluoresence, is present in the radiation to the nonresonant level.

DOI
10.1139/p85-018

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Canadian Journal of Physics•Nov 1, 1980•13 citations
When a system of two-level atoms interacts with a very intense field, the phenomena associated with superradiance do not appear in the fluorescent radiation. The question has been raised, "Can pumping by an intense field inhibit the occurrence of superradiance in the fluorescence of a system of three-level atoms to the third (nonresonant) level?" In this paper, we calculate the fluorescence spectrum of 2 three-level atoms. We find that superradiance, while absent in that part of the radiation corresponding to resonance fluoresence, is present in the radiation to the nonresonant level.
We consider the possible physical processes that may arise in a three-level atom when only two of its levels interact with a strong electromagnetic field and when the atomic transition frequency is nearly equal to once and twice the frequency of the laser field, respectively. There have been found pronounced cooperative effects in the spectrum of the two-level system, which is in resonance with the laser field, arising from the presence of the third level. The excitation spectra describing the transitions from the first excited state into the second excited state and from that to the ground state consist, apart from the two central peaks, of two pairs of sidebands which are induced by the laser field of the neighbouring system. Detailed expressions of the spectral functions for the physical processes of one- and two-photon resonance fluorescence have been derived and discussed in the limit of high photon densities. The excitation spectrum of the low frequency modes has been considered and discussed in detail. It is found that quantum beats in spontaneous emission may appear in the spectra of the one- and two-photon resonance fluorescence arising from the interference between the two atomic transition frequencies and the frequency of the laser field. The importance of the low frequency modes that occur in the processes in question has been pointed out.
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.
The fluorescence spectrum of a system of a large number of two-level atoms driven by a strong resonant field has been treated, so far, for atoms contained in a region that is small compared to a wavelength. For high laser intensities resonances displaced from the line center by twice the Rabi frequency were predicted1-3 in addition to the usual Stark sidebands.4 We show that the explicit spatial distribution of the two-level atoms affects the shape of the radiation spectra and leads to the appearance of additional sidebands.
We have studied the fluorescence spectra arising from the interaction of a three-level atom with two strong electromagnetic fields whose initially populated modes are equal to the two atomic transition frequencies, respectively. The Green's function formalism has been used to calculate the excitation spectrum of the system. An expression for the spectral function describing the excitation spectrum of the system has been derived in a closed form in the limit of high photon densities. Numerical computation of the expression for the spectral function indicates that at each transition frequency there may exist either one pair or two pairs or three pairs of sidebands, in addition to the central peak, depending upon the relative strength of the Rabi frequencies involved.