  We study a system of two quantum dots, each with several discrete levels,
which are coherently coupled to a microwave oscillator. They are attached to
electronic leads and coupled to a phonon bath, both leading to inelastic
processes. For a simpler system with a single level in each dot it has been
shown that a population inversion can be created by electron tunneling, which
in a resonance situation leads to lasing-type properties of the oscillator. In
the multi-level system several resonance situations may arise, some of them
relying on a sequence of tunneling processes which also involve non-resonant,
inelastic transitions. The resulting photon number in the oscillator and the
current-voltage characteristic are highly sensitive to these properties and
accordingly can serve as a probe for microscopic details.
