Absorption Line Shape Function Research Articles

Stimulated Emission and Absorption near Resonance for Driven Systems

The rate of absorption of energy from a weak signal field by an atom driven by a strong pump field is evaluated. The pump field and the signal field are assumed to induce transitions between the same pair of states, and their frequencies are both assumed to lie near the atomic resonance frequency for the transition in question. We find that the signal-field absorption line-shape function takes on negative values, representing stimulated emission rather than absorption, even though population inversion does not occur. This amplification of the signal field, which is most pronounced at high pump intensities, is shown to occur primarily at the expense of the pump field, which suffers an increased rate of attenuation. The results are discussed in the context of a theorem which expresses the absorption line-shape function for general atomic systems in terms of a suitable atomic correlation function.

Absorption and Emission Line-Shape Functions for Driven Atoms

The effect of a driving or pump field on the emission and absorption line-shape functions for an atom is discussed. The pump field is assumed to oscillate at a frequency near the resonance frequency for transitions between a single pair of atomic states, and transitions between one of these states and any other state of the atom are analyzed. The pump field is treated classically, and atomic relaxation is treated in general terms. The emission and absorption line-shape function (the latter is defined as the rate of absorption of energy from a weak signal field, applied in addition to the pump field, as a function of the signal-field frequency) are found by evaluating the relevant two-time atomic correlation functions in the Markoff approximation. In the limit of high pump-field intensity, both the absorption and the emission spectra are doubly peaked at frequencies which differ from the usual resonance frequency by $\ifmmode\pm\else\textpm\fi{}\frac{1}{2} \ensuremath{\Omega}$, where $\ensuremath{\Omega}$ is the frequency of the pump-field-induced oscillations in the populations of the two strongly coupled states. The absorption and the emission spectra are represented by essentially the same function in the limit of high pump-field intensity, as they are also in the limit of vanishing pump-field intensity. For intermediate pump-field intensities, however, the two functions are quite different in form, and no simple proportionality exists between them.

NMR double quantum transitions: An alternative derivation

The general NMR absorption line shape function of Hoffman is used to derive the resonance condition for double quantum transitions. Strong absorption will occur at rf frequencies for which a pair of eigenvalues of the rotating frame Hamiltonian V lie close. It is shown how the eigenvalues of V may be found from a modified perturbation treatment, which is applicable also at near degeneracy of the eigenvalues. A small shift of the double quantum transition away from its first-order position may occur. The results obtained coincide with those of Anderson, Freeman, and Reilly with respect to the transition frequency and transition probability, but differ with respect to the eigenfunctions and eigenvalues obtained by these authors.

Infrared Absorption due to Substitutional Impurity in Cubic Crystals

The explicit expressions have been obtained for the absorption line-shape function due to one-phonon processes in some models of cubic crystals with impurities. All of them show pronounced resonance peaks in the low-frequency region for heavy impurities. Similar resonances also occur for light impurities when the force constants are reduced. An estimate is made of the change in force constant in the case of ${\mathrm{Li}}^{6}$ and ${\mathrm{Li}}^{7}$ in KBr, based on the experimental data of Sievers and Takeno.