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Optica Acta International Journal of Optics

Power Broadening and Two-photon Correlations in Two-atom Resonance Fluorescence

Thomas Richter

Published Mar 1, 1982• 25 citations
Publisher

Abstract

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.

DOI
10.1080/713820845

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Physical Review A•Mar 1, 1979•58 citations
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 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 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 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.
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.
Resonance fluorescence of two two-level atoms driven by a coherent laser field propagating parallel to the interatomic axis is examined, taking into account the dipole-dipole interaction. We show that the number of peaks in the fluorescence intensity depends on the direction of observation with respect to the interatomic axis and on whether the system is driven by a standing-wave or a running-wave laser field. When the system is driven by the standing-wave field the fluorescence intensity shows two peaks and a dip for an observation direction perpendicular to the interatomic axis and three peaks in the direction parallel to it. When the system is driven by the running-wave field only two peaks are observed for the perpendicular direction. We explain these features in terms of the collective states of the system and show that the directional effect can be attributed to the fact that the antisymmetric state of the system does not radiate in the direction perpendicular to the interatomic axis. Photon statistics also demonstrate the directional effect for the standing-wave field. Frequency regimes are found where sub-Poissonian photon statistics occur. Depending on the direction of the observation, a state close to a Fock state can occur for one or two frequencies of the driving field, corresponding to zero-photon-number fluctuations or maximum sub-Poissonian behavior. The fluorescence spectrum is found to depend on the direction of observation and the interatomic separation. For small interatomic separations and a standing-wave driving field the spectrum exhibits seven lines for the perpendicular direction and 13 lines in the direction parallel to the interatomic axis. For the running-wave field the spectrum shows 13 lines independent of the direction of observation. Moreover, we show that for particular interatomic separations dark regimes appear in the spectrum. We discuss the effect of the dipole-dipole interaction on the dark states and explain the spectral features in terms of the dressed-atom model. We also consider the absorption spectrum of a weak probe beam illuminating the two-atom system. We show that apart from a weak dispersion structure, the spectrum shows large peaks as one of the atoms is moved to successive nodes of the field.
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〉.