Control of Dephasing and Phonon Emission in Coupled Quantum Dots

We predict that phonon subband quantization can be detected in the non-linear electron current through double quantum dot qubits embedded into nano-size semiconductor slabs, acting as phonon cavities. For particular values of the dot level splitting $\mathrm{\Delta }$, piezo-electric or deformation potential scattering is either drastically reduced as compared to the bulk case, or strongly enhanced due to phonon van Hove singularities. By tuning $\mathrm{\Delta }$ via gate voltages, one can either control dephasing, or strongly increase emission into phonon modes with characteristic angular distributions.