  We show that quantum electromagnetic transitions to high orders are essential
to describe the time-dependent path of a nanoscale electron system in a Coulomb
blockage regime when coupled to external leads and placed in a
three-dimensional rectangular photon cavity. The electronic system consists of
two quantum dots embedded asymmetrically in a short quantum wire. The two
lowest in energy spin degenerate electron states are mostly localized in each
dot with only a tiny probability in the other dot. In the presence of the leads
we identify a slow high order transition between the ground states of the two
quantum dots. The Fourier power spectrum for photon-photon correlations in the
steady state shows a Fano-type of a resonance for the frequency of the slow
transition. Full account is taken of the geometry of the multi-level electronic
system, and the electron-electron Coulomb interactions together with the para-
and diamagnetic electron-photon interactions are treated with step wise exact
numerical diagonalization and truncation of appropriate many-body Fock spaces.
The matrix elements for all interactions are computed analytically or
numerically exactly.
