Phonon decoherence in a double dot qubit embedded inside a suspended phonon cavity

The phonon-induced decoherence in a double dot charge qubit embedded inside a semiconductor slab is investigated theoretically. We employ the Redfield formalism to solve the density matrix in the Born-Markov approximation. Our calculations show some interesting results in the presence of slab cavity. In particular, the decoherence behaves significantly due to particular phonon couplings such as the van Hove singularity and vanishing deformation potential.