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IEEE Journal of Quantum Electronics

Resonance fluorescence spectra of two driven two-level atoms

Y. Ben-Aryeh, C. M. Bowden

Published Jul 1, 1988• 11 citations
Publisher

Abstract

A theoretical analysis is developed for the spectrum of the light scattered by two two-level atoms driven near resonance by an external coherent electromagnetic field. The atoms are assumed to relax to equilibrium with the driving field as a result of radiation damping. The explicit dependence of the coherent dipole-dipole interactions on the distance between the two atoms is taken into account. For the case of two two-level atoms with a fixed distance smaller than a wavelength, an analytical result for the resonance fluorescence line shape is obtained, and the result is compared to previous work.>

DOI
10.1109/3.976

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Power Spectrum of Light Scattered by Two-Level Systems

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Physical Review•Dec 25, 1969•1,938 citations
A theoretical analysis is developed for the spectrum of the light scattered by two two-level atoms driven near resonance by an external coherent electromagnetic field. The atoms are assumed to relax to equilibrium with the driving field as a result of radiation damping. The explicit dependence of the coherent dipole-dipole interactions on the distance between the two atoms is taken into account. For the case of two two-level atoms with a fixed distance smaller than a wavelength, an analytical result for the resonance fluorescence line shape is obtained, and the result is compared to previous work.>
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.
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 calculation is given of the spectral distribution of resonance fluorescence from an atom that is driven near a j=12j=\frac{1}{2}j=21​ to j=12j=\frac{1}{2}j=21​ transition by a monochromatic, xxx-polarized electric field and that is subject to radiation damping only. In accordance with Mollow's results for a two-level system, the power spectrum of the scattered radiation corresponding to the xxx component of the dipole moment contains a coherent part for all driving-field intensities. The coherent part is absent in the fluorescence radiation corresponding to the yyy and zzz components of the dipole moment. For weak driving fields all power scattered by these latter components is present in a narrow Lorentzian. Consistent with energy conservation, the width of the Lorentzian corresponds to the probability of excitation of the atom out of its ground level due to the presence of the driving field. For strong driving fields the power spectra corresponding to the xxx component and to the yyy or zzz component mainly differ in the heights and widths of their central incoherent band and their Rabi-precession-frequency-shifted side bands.
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 power spectrum of the light scattered by a two-level atom driven near resonance by a monochromatic classical electric field is evaluated. The atom is assumed to relax to equilibrium with the driving field via radiation damping, which is treated by explicitly coupling the atom to the quantized electromagnetic field modes. The power spectrum of the scattered field is directly obtainable from the two-time atomic dipole moment correlation function, which is evaluated by a method based on a Markoff-type assumption analogous to that used to evaluate the time evolution of single-time atomic expectation values.