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Generalized single-atom Maxwell-Bloch equations for optically dense media arederived taking into account non-cooperative radiative atom-atom interactions.Applying a Gaussian approximation and formally eliminating the degrees offreedom of the quantized radiation field and of all but a probe atom leads toan effective time-evolution operator for the probe atom. The mean coherentamplitude of the local field seen by the atom is shown to be given by theclassical Lorentz-Lorenz relation. The second-order correlations of the fieldlead to terms that describe relaxation or pump processes and level shifts dueto multiple scattering or reabsorption of spontaneously emitted photons. In theMarkov limit a nonlinear and nonlocal single-atom density matrix equation isderived. To illustrate the effects of the quantum corrections we discussamplified spontaneous emission and radiation trapping in a dense ensemble ofinitially inverted two-level atoms and the effects of radiative interactions onintrinsic optical bistability in coherently driven systems.Comment: 16 pages, 12 figures, subm. to PR

Radiative atom-atom interactions in optically dense media: Quantum corrections to the Lorentz-Lorenz formula