Spontaneous generation of entangled exciton in quantum dot systems

We calculate the time evolution of single-exciton states prepared for ensembles of two to four quantum dots. Each dot is considered a two-level system, but with slightly different excitation energies and dipole moments. The dots interact via a tunnel coupling which induces excitation transfer between single emitters, but conserves the total occupation of the system. We show that the initial exciton may evolve towards a steady state where the energy is partially trapped due to the formation of the subradiant (dark) states of the system. In the steady state the individual populations of each dot have permanent oscillations with frequencies given by the energy separation between the subradiant eigenstates.