  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.
