Phonon-induced decoherence and dissipation in donor-based charge qubits

We investigate the phonon-induced decoherence and dissipation in a donor-based charge quantum bit realized by the orbital states of an electron shared by two dopant ions which are implanted in a silicon host crystal. The dopant ions are taken from the group-V elements Bi, As, P, Sb. The excess electron is coupled to deformation potential acoustic phonons which dominate in the Si host. The particular geometry tailors a non-monotonous frequency distribution of the phonon modes. We determine the exact qubit dynamics under the influence of the phonons by employing the numerically exact quasi-adiabatic propagator path integral scheme thereby taking into account all bath-induced correlations. In particular, we have improved the scheme by completely eliminating the Trotter discretization error by a Hirsch-Fye extrapolation. By comparing the exact results to those of a Born-Markov approximation we find that the latter yields appropriate estimates for the decoherence and relaxation rates. However, noticeable quantitative corrections due to non-Markovian contributions appear.