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A dressed state of an atom and its driving field. Within the rotating-wave approximation, the paired configurations $|e,n⟩$ and $|g,n+1⟩$ mix. A classical-drive rotating-frame Hamiltonian $H=\hslash (-\Delta {\sigma }_z+\Omega {\sigma }_x)/2$ has eigenvalues $\pm \hslash \sqrt{{\Delta }^2+{\Omega }^2}/2$. At resonance its eigenvectors are equal-weight combinations of the two bare configurations. Radiative transitions between neighboring manifolds explain the Mollow triplet.

An atom-field dressed state is an eigenstate of the coupled atom and drive, rather than an eigenstate of the isolated atom. A strong near-resonant field mixes the bare two-level states and changes the transition spectrum. In a frame rotating at the drive frequency, the rotating-wave approximation gives, for one convenient convention,Here $\Omega$ is the resonant Rabi frequency. The two eigenvalues areAt resonance, the dressed states are equal-weight symmetric and antisymmetric combinations of the bare atom–field configurations. For a quantized drive, the appropriate paired configurations are $|e,n⟩$ and $|g,n+1⟩$; their coupling scales as $\sqrt{n+1}$. A strong coherent drive gives the familiar approximately classical Rabi frequency over its occupied photon-number range.

Radiative transitions connect neighboring dressed manifolds. Same-branch transitions have frequency near ${\omega }_L$, while opposite-branch transitions give sidebands near ${\omega }_L\pm {\Omega }_R$. Under sufficiently strong resonant driving this produces the Mollow triplet in resonance fluorescence, with sidebands separated from the center by $\Omega$. Radiation damping determines widths and weights; detuning changes the relative intensities. Sidebands must be sufficiently separated compared with the decay scale to be resolved.^[ref]

A fluorescence experiment drives the transition with a narrow-band laser, collects scattered light away from the intense drive beam, and resolves its spectrum. Changing drive intensity changes $\Omega$ and hence the splitting. This measures transitions of the interacting system, not merely a population oscillation in time. The emitted spectrum can include an elastic coherent contribution as well as the inelastic fluorescence peaks, so the observed line shape needs the specified drive, damping and detection model.

Published in Physical Review 188, starting at page 1969, on 25 December 1969: journals.aps.org/pr/abstract/10.1103/PhysRev.188.1969

The primary calculation obtains the near-resonant driven-atom fluorescence spectrum from two-time atomic dipole correlations, with radiation damping included through coupling to the quantized electromagnetic field. It provides the source for the Mollow triplet.