We probe acoustic phonon mediated relaxation between tunnel coupled exciton states in an individual quantum dot molecule in which the interdot quantum coupling and energy separation between exciton states is continuously tuned using static electric field. Time resolved and temperature dependent optical spectroscopy are used to probe interlevel relaxation around the point of maximum coupling. The radiative lifetimes of the coupled excitonic states can be tuned from similar to 2 ns to similar to 10 ns as the spatially direct and indirect character of the wave function is varied by detuning from resonance. Acoustic phonon mediated interlevel relaxation is shown to proceed over time scales comparable to the direct exciton radiative lifetime, indicative of a relaxation bottleneck for level spacings in the range Delta E similar to 3-6 meV.
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