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 the interaction between different channels together with phonon emission and absorption are responsible for the shot noise characteristics. The observed asymmetry of the peaks at low temperatures stems from spontaneous emission.
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