Manifestation of classical wave delays in a fully quantized model of the scattering of a single photon

We consider a fully quantized model of spontaneous emission, scattering, and absorption, and study propagation of a single photon from an emitting atom to a detector atom both with and without an intervening scatterer. We find an exact quantum analog to the classical complex analytic signal of an electromagnetic wave scattered by a medium of charged oscillators. This quantum signal exhibits classical phase delays. We define a time of detection which, in the appropriate limits, exactly matches the predictions of a classically defined delay for light propagating through a medium of charged oscillators. The fully quantized model provides a simple, unambiguous, and causal interpretation of delays that seemingly imply speeds greater than c in the region of anomalous dispersion.