  Generalized single-atom Maxwell-Bloch equations for optically dense media are
derived taking into account non-cooperative radiative atom-atom interactions.
Applying a Gaussian approximation and formally eliminating the degrees of
freedom of the quantized radiation field and of all but a probe atom leads to
an effective time-evolution operator for the probe atom. The mean coherent
amplitude of the local field seen by the atom is shown to be given by the
classical Lorentz-Lorenz relation. The second-order correlations of the field
lead to terms that describe relaxation or pump processes and level shifts due
to multiple scattering or reabsorption of spontaneously emitted photons. In the
Markov limit a nonlinear and nonlocal single-atom density matrix equation is
derived. To illustrate the effects of the quantum corrections we discuss
amplified spontaneous emission and radiation trapping in a dense ensemble of
initially inverted two-level atoms and the effects of radiative interactions on
intrinsic optical bistability in coherently driven systems.
