  Single-electron tunneling processes through a double quantum dot can induce a
lasing state in an electromagnetic resonator which is coupled coherently to the
dot system. Here we study the noise properties of the transport current in the
lasing regime, i.e., both the zero-frequency shot noise as well as the noise
spectrum. The former shows a remarkable super-Poissonian behavior when the
system approaches the lasing transition, but sub-Poissonian behavior deep in
the lasing state. The noise spectrum contains information about the coherent
dynamics of the coupled dot-resonator system. It shows pronounced structure at
a frequency matching that of the resonator due to the excitation of photons.
For strong interdot Coulomb interaction we find asymmetries in the
auto-correlation noise spectra of the left and right junctions, which we trace
back to asymmetries in the incoherent tunneling channels.
