  We study the transport properties of two double quantum dots in a parallel
arrangement at temperatures of a few Kelvin. Thereby, we show that decoherence
entailed by the substrate phonons affects the shot noise. For asymmetric
coupling between the dots and the respective lead, the current noise is
sub-Poissonian for resonant tunneling, but super-Poissonian in the vicinity of
the resonances. Our results indicate that phonon emission and absorption is
responsible for the shot noise enhancement. The observed asymmetry of the peaks
at low temperatures stems from spontaneous emission.
