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Phonon-mediated decoherence in triple quantum dot interferometers

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