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Physical Review A

Collective atomic effects in resonance fluorescence: The "scaling factor"

Helen S. Freedhoff

Published Jul 1, 1982• 20 citations
Publisher

Abstract

In this Comment we study the resonance fluorescence of a system of two atoms separated by an arbitrary distance $R$ in an on-resonance laser field. The steady-state spectrum is calculated in the strong-field limit both for negligible and for non-negligible dipole-dipole interaction. The singlet state of the system is included throughout, even for small interatomic separations. We show that the so-called "scaling factor," or the enhancement of the integrated fluorescence by $N$ atoms (above the expected factor of $N$), predicted in the literature by many authors, does not, in fact, exist.

DOI
10.1103/physreva.26.684

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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.

•Mar 1, 1982•0 citations
In this Comment we study the resonance fluorescence of a system of two atoms separated by an arbitrary distance RRR in an on-resonance laser field. The steady-state spectrum is calculated in the strong-field limit both for negligible and for non-negligible dipole-dipole interaction. The singlet state of the system is included throughout, even for small interatomic separations. We show that the so-called "scaling factor," or the enhancement of the integrated fluorescence by NNN atoms (above the expected factor of NNN), predicted in the literature by many authors, does not, in fact, exist.
The resonance fluorescence of a two-atom system interacting collectively with an intense driving field is studied. The first-order dispersion forces, or dipole-dipole interaction, between the atoms is included as well. The scattered-light spectrum is found to differ considerably from the single-atom spectrum even for very intense driving fields, in direct contrast with the results obtained by Agarwal et al., who studied the two-atom system but neglected the dipole-dipole interaction. The effects of collective scattering are calculated on the fluorescence spectra of idealized beams of atoms moving with uniform velocity, for a number of different number densities 〈N〉〈N〉〈N〉.
The exact steady-state solution is presented for the reduced atomic density operator describing the cooperative resonance fluorescence from a system of two atoms separated by an arbitrary distance in an off-resonance laser field, with the dipole-dipole near-field interaction between the atoms included. It is shown that the destructive effect of the dipole-dipole interaction on the formation of squeezing in two-atom resonance fluorescence found recently by Ficek et al. can be compensated to a very large extent by an appropriate choice of the detuning between the laser frequency and the single-atom transition frequency.
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 investigate the resonance fluorescence features of a small ensemble of closely packed and moderately laser-pumped two-level emitters at resonance. The mean distance between any two-level radiators is smaller than the corresponding emission wavelength, such that the dipole-dipole interactions are not negligible. We have found that under the secular approximation, the collective resonance fluorescence spectrum consists of 2 N + 1 spectral lines, where N is the number of emitters from the sample. The 2 N spectral sidebands, symmetrically located around the generalized Rabi frequency with respect to the central line at the laser frequency, are distinguishable if the dipole-dipole coupling strength is larger than the collective spontaneous decay rate. This way, one can estimate the radiators number within the ensemble via measuring of the spontaneously scattered collective resonance fluorescence spectrum. Contrarily, if the dipole-dipole coupling is of the order of or smaller than the cooperative spontaneous decay rate, but still non-negligible, the spectrum turns into a Mollow-like fluorescence spectrum, where the two sidebands' spectral lines broaden proportional to the dipole-dipole coupling strength. Published by the American Physical Society 2024
Resonance-fluorescence power spectrum of two-level atoms driven by a strong monochromatic laser field is discussed, taking into account effects due to the dipole-dipole interaction between the atoms. For two atoms confined to a region smaller than the wavelength of the driving field, we predict significant deviations of the power spectrum from the single-atom case. The two-atom spectrum is nonsymmetric, the wing peaks are shifted from their Rabi-frequency positions, and additional maxima may appear.
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.