Resonance fluorescence and Raman line shapes produced by monochromatic laser fields: Effects of branching ratio and homogeneous broadening

Abstract

The Heitler-Ma damping theory is developed for a two level system in which the excited state is homogeneously, and irreversibly coupled to various continuum states with a total decay rate 1/τ. We give particular consideration to the channel consisting of a third, discrete, atomic level and a continuum of emitted photons, which simply corresponds to a spontaneous resonant Raman process. The theory applies to either a narrow, pulsed, laser beam, or injection of target atoms or molecules into a c.w. field. In this paper, we examine the t=∞ spectra as a function of field strength, detuning from resonance, and especially as a function of the upper state broadening, characterized by the branching ratio f A = τ/ t A , where τ - A is the natural resonance fluorescence lifetime. For strong fields, we obtain the usual resonance fluorescence spectrum centered at the incident, pumping frequency, with two symmetric side bands displaced by the Rabi frequency. If f A →0, the spectrum approaches the one-photon limit, with the height of the side bands equal to 1 2 that of the central peak and all of equal width. In this limit, the target predominantly decays into the Raman or other irreversible channels, and only a single laser photon contributes to the extremely weak resonance spectrum. At the opposite extreme, f A →1, the target scatters many photons out of the laser-field before it is optically pumped into a non-interacting state and the spectrum exhibits the infinite cascade properties obtained by Mollow. The side bands become broadened, with a height equal to 1 3 of the central peak. In this theory, we obtain a more complete interpretation of the elastically scattered delta function, which is an artifact of the infinite lifetime of the atom in the usual two-level theories. In both limits of f A , we obtain a Raman lineshape which is unchanged and is simply a function of the total width ℏ/τ of the excited state.