  We analyze how a multilevel many-electron system in a photon cavity
approaches the steady state when coupled to external leads. When a plunger gate
is used to lower cavity photon dressed one- and two-electron states below the
bias window defined by the external leads, we can identify one regime with
nonradiative transitions dominating the electron transport, and another regime
with radiative transitions. Both transitions trap the electrons in the states
below the bias bringing the system into a steady state. The order of the two
regimes and their relative strength depends on the location of the bias window
in the energy spectrum of the system and the initial conditions.
