Decay and persistence of spatial coherence during phonon-assisted relaxation in double quantum dots

We present a theoretical study of the evolution of spatial coherence during relaxation between delocalized exciton states in a pair of vertically stacked semiconductor quantum dots coupled to acoustic phonons. We show that spatial coherence can be transferred to the ground state even in a system of uncoupled non-identical quantum dots if a particular kind of degeneracy between the inter-level energy splittings is present. The phonon-assisted mechanism of coherence transfer leads to a dependence of the amount of the resulting coherence on the inter-dot distance and temperature. We analyze also the impact of carrier-phonon dynamics on a coupled system, where spatial coherence is present in the delocalized ground state.