Dicke effect in the tunnel current through two double quantum dots

We calculate the stationary current through two double quantum dots which are interacting via a common phonon environment. Numerical and analytical solutions of a master equation in the stationary limit show that the current can be increased as well as decreased due to a dissipation mediated interaction. This effect is closely related to collective, spontaneous emission of phonons (Dicke super-radiance and subradiance effect), and the generation of a ``cross-coherence'' with entanglement of charges in singlet or triplet states between the dots. Furthermore, we discuss an inelastic ``current switch'' mechanism by which one double dot controls the current of the other.