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Optica Acta International Journal of Optics

Cooperative Resonance Fluorescence from Two Atoms Experiencing Different Driving Fields

Th. Richter

Published Dec 1, 1983• 14 citations
Publisher

Abstract

The inclusion of the coupling of the antisymmetric state to the driving field, if the atoms are in inequivalent positions, can change the steady-state total scattering intensity as a function of field strength from one monotonically approaching the saturation intensity 2 n to one which at first runs through a maximum above 2 n at intermediate field strengths. Moreover, under suitable conditions the scattering spectrum can exhibit three distinct peaks, and depending on the detuning, photon bunching and antibunching can occur in the scattered radiation.

DOI
10.1080/713821122

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•Mar 1, 1982•0 citations
The inclusion of the coupling of the antisymmetric state to the driving field, if the atoms are in inequivalent positions, can change the steady-state total scattering intensity as a function of field strength from one monotonically approaching the saturation intensity 2 n to one which at first runs through a maximum above 2 n at intermediate field strengths. Moreover, under suitable conditions the scattering spectrum can exhibit three distinct peaks, and depending on the detuning, photon bunching and antibunching can occur in the scattered radiation.
The cooperative resonance fluorescence radiation from two atoms separated by an arbitrary distance and driven by a coherent laser field is studied, taking into account the dipole-dipole near-field interaction. The steady-state total scattering intensity, as a function of laser frequency and field strength, differs considerably from the single-atom one for sufficiently small distances. Photon bunching and antibunching occur in the scattered radiation depending on the laser frequency. Practically a full antibunching effect is found, especially if the laser is tuned to resonance with a transition frequency of the two-atom system. This is in contrast to a recent result of Agarwal et al., who studied the two-atom system but neglected the frequency splitting due to the dipole-dipole near-field interaction.
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.
The moments of the fluorescent radiation of a J2{J}^{2}J2-invariant, cooperative fluorescent group of atoms are calculated exactly. Both photon bunching and antibunching can occur in the fluorescent radiation. All finite-order moments have a critical-point behavior at ${\ensuremath{\Omega}}_{c}=J\ensuremath{\gamma}$ in the cooperative limit of $J\ensuremath{\rightarrow}\ensuremath{\infty}$. The maximum normalized intensity correlation is 6/5 which shows greatly reduced intensity fluctuations compared to noncooperative resonance fluorescence. Enhanced antibunching in all the fluorescent correlation functions occurs in the threshold region.
We study the correlation between photons in the fluorescence light scattered from an atom driven by an intense bichromatic field having one strong and one weak component, with or without the use of frequency filters in front of the photodetectors. Depending on the filters used and on the spectral components selected, we predict signals corresponding either to bunching or to antibunching, and modulations at the driving field Rabi frequencies as well as at their sum and difference. In contrast with the case of monochromatic driving, the antibunching can occur between photons emitted into different (as well as the same) lines of the fluorescence spectrum.
The normalised intensity correlation function of resonance fluorescence radiation from two-level atoms is studied in various respects. In the first part of the paper the author discusses only interference effects for several uncoupled, linearly arranged, atoms. It is shown that, depending on the distance between the atoms, the direction of observation and the strength of the driving field, an antibunching effect as well as a very big bunching effect may be observed. In the second part of the paper he studies for the case of two atoms and weak external fields the influence of the interaction between the atoms by means of a perturbation theory. It is shown that the coupling between the atoms strongly modifies the normalised intensity correlation function in comparison with the case of uncoupled atoms. He takes as the driving field a coherent external field as well as laser light and thermal light.
We have calculated the spectrum of resonance fluorescence and the second-order correlation function for a system of two two-level atoms interacting via the dipole-dipole interaction and via radiative coupling. The method employed is the "master equation" for the reduced atomic density operator. The scattered spectrum is symmetric about the resonant frequency and is altered significantly by the presence of the dipole-dipole term. For large incident field strengths pairs of sidebands are displaced from resonance by (+OR-)(omega)(,R) and (+OR-)2(omega)(,R), where (omega)(,R) is the Rabi frequency. Additional peaks arise when the dipole-dipole interaction is of the same order as the atom-field interaction. For weak incident fields the spectrum consists of a central peak and two peaks displaced symmetrically by (omega)(,d), the strength of the dipole-dipole interaction. The spectrum when averaged over the atomic separation and orientation consists of the central peak and two pairs of sidebands displaced by (+OR-)(omega)(,R) and (+OR-)2(omega)(,R). The central and first pair of sidebands become weaker and broader as the number density increases, whereas the second pair of sidebands is enhanced and broadened. The first effect is probably observable for suitable atomic number densities. Perhaps the second pair of sidebands could also be observed in a careful experiment. The second-order correlation function of this system predicts incomplete antibunching for strong incident field strengths. At weak field strengths the antibunching depends strongly on the dipole-dipole energy.