  We report on linewidth analysis of optical transitions in InAs/GaAs coupled
quantum dots as a function of bias voltage, temperature, and tunnel coupling
strength. A significant line broadening up to 100 $\mu$eV is observed at hole
tunneling resonances where the coherent tunnel coupling between spatially
direct and indirect exciton states is maximized, corresponding to a
phonon-assisted transition rate of 150 ns${}^{-1}$ at 20 K. With increasing
temperature, the linewidth shows broadening characteristic of single-phonon
transitions. The linewidth as a function of tunnel coupling strength tracks the
theoretical prediction of linewidth broadening due to phonon-assisted
transitions, and is maximized with an energy splitting between the two exciton
branches of 0.8$-$0.9 meV. This report highlights the linewidth broadening
mechanisms and fundamental aspects of the interaction between these systems and
the local environment.
