Resonance fluorescence from aj=12toj=12transition

The calculation is given of the spectral distribution of resonance fluorescence from an atom that is driven near a $j=\frac{1}{2}$ to $j=\frac{1}{2}$ transition by a monochromatic, $x$-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 $x$ 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 $y$ and $z$ 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 $x$ component and to the $y$ or $z$ component mainly differ in the heights and widths of their central incoherent band and their Rabi-precession-frequency-shifted side bands.