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- 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.