  We demonstrate a fundamental breakdown of the photonic spontaneous emission
(SE) formula derived from Fermi's golden rule, in absorptive and amplifying
media, where one assumes the SE rate scales with the local photon density of
states, an approach often used in more complex, semiclassical nanophotonics
simulations. Using a rigorous quantization of the macroscopic Maxwell equations
in the presence of arbitrary linear media, we derive a corrected Fermi's golden
rule and master equation for a quantum two-level system (TLS) that yields a
quantum pumping term and a modified decay rate that is net positive. We show
rigorous numerical results of the temporal dynamics of the TLS for an example
of two coupled microdisk resonators, forming a gain-loss medium, and
demonstrate the clear failure of the commonly adopted formulas based solely on
the local density of states.
