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Physical Review A

Observables and moments of cooperative resonance fluorescence

P. D. Drummond

Published Sep 1, 1980• 58 citations
Publisher

Abstract

The moments of the fluorescent radiation of a ${J}^{2}$-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.

DOI
10.1103/physreva.22.1179

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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 \ensuremathΩc=J\ensuremathγ{\ensuremath{\Omega}}_{c}=J\ensuremath{\gamma}\ensuremathΩc​=J\ensuremathγ in the cooperative limit of J\ensuremath→\ensuremath∞J\ensuremath{\rightarrow}\ensuremath{\infty}J\ensuremath→\ensuremath∞. 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.
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 spectrum of resonance fluorescence and the second-order correlation function are calculated for a system of two identical two-level cooperative systems interacting via the dipole-dipole interaction. The results are valid for arbitrary incident-field strengths and for atomic separations much less than the resonant wavelength. The intensity of the sidebands at the Rabi frequency is diminished by the dipole interaction, whereas that of the sidebands at twice the Rabi frequency is enhanced. Both the cooperative behavior and the dipole-dipole interaction act to diminish the photon antibunching, as shown by the second-order correlation function.
The experimental conditions under which the intensity correlation function from a single atom undergoing resonance fluorescence may be observed are studied. As was pointed out by Jakeman et al. (1977), even under optimum conditions the number of fluctuations in the atomic beam prevent a direct observation of photon antibunching under the subsequent normalisation scheme used by Kimble et al. (1977). However, a direct observation of photon antibunching is possible in principle by adopting alternative normalisation schemes of the intensity correlation function.
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 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.