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We investigate decoherence in a triple quantum dot in ring configuration inwhich one dot is coupled to a damped phonon mode, while the other two dots areconnected to source and drain, respectively. In the absence of decoherence,single electron transport may get blocked by an electron falling into asuperposition decoupled from the drain and known as dark state. Phonon-mediateddecoherence affects this superposition and leads to a finite current. We studythe current and its shot noise numerically within a master equation approachfor the electrons and the dissipative phonon mode. A polaron transformationallows us to obtain a reduced equation for only the dot electrons whichprovides analytical results in agreement with numerical ones.

Phonon-mediated decoherence in triple quantum dot interferometers