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Physical Review A

Two-atom resonance fluorescence including the dipole-dipole interaction

R. D. Griffin, Samuel M. Harris

Published Mar 1, 1982• 29 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.25.1528

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Physical Review A•Apr 1, 1977•159 citations
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.
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.
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.
The authors investigate the dipole-dipole interaction role in the resonance fluorescence of two identical two-level atoms, which are confined to a region much smaller than the resonant wavelength and which are damped by a squeezed vacuum. The spectrum consists of seven or five lines, depending on the relative phase between the driving field and the squeezed vacuum, whereas the spectrum without the dipole-dipole interaction displays three lines. The widths of these lines depend on the parameters of the squeezed vacuum and can be subnatural or supernatural depending on the phase. The central line and additional sidebands at double the Rabi frequency can have intensities larger than in the normal vacuum but the intensities of lines at one Rabi frequency are always less than in the normal vacuum.
The equal-time intensity correlation function and variances of the in-phase and out-of-phase components of the electric field radiated by a system of two interacting atoms in the process of resonance fluorescence are calculated analytically for arbitrary values of the field strength, interatomic interaction, and detuning and are illustrated graphically. It is shown that not only photon antibuching but also squeezing can occur in two-atom resonance fluorescence. The influence of dipole-dipole interaction between the atoms on both nonclassical effects is discussed. It is shown that a considerable amount of photon antibunching and squeezing can be obtained for finite detuning of the laser frequency from atomic resonance, especially when the detuning and dipole-dipole interaction parameters cancel out mutually. The maximum value of squeezing for interacting atoms is shown to be less, however, than that for noninteracting atoms. Very strong dipole-dipole interaction reduces the squeezing effect to zero.
The excitation spectrum arising from photon density-density correlations has been considered in a system of two interacting identical atoms. The two-level atoms are pumped near resonance by a strong electromagnetic field while they interact through their dipole-dipole interaction and radiate to each other as well. In such a system the photon density-density correlations arise from the interference spectrum due to the beating of the frequency of the pump field and the atomic transition frequency, as well as from the spectrum induced by the dipole-dipole and radiative interactions between the atoms. The spectral function of this system has been calculated in the limit of high photon densities. It consists of four terms describing four bands which are similar to those appearing in the two-atom resonance fluorescence spectrum for the symmetric modes when the central peak is missing. The collective behavior as well as the dynamics of the system are discussed in detail. By using the spectral function, an expression for the photon density-density correlation function at different times has been derived where thermal effects have been also included.
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.