Non-Markovian dynamics of a double quantum dot charge qubit with static bias

We have studied the dynamics of charge qubit with the static bias by a perturbation treatment based on unitary transformations. The approach can be practiced for various forms of the spectral density and the usual Ohmic and piezoelectric spectra are used in our calculations. Analytical results of the quantum dynamics, described by the population inversion P(t), are obtained together with the damping rate and the oscillation frequency. We find that a weak coupling of the qubit to the environment leads to a higher coherence oscillation frequency and a longer coherence time. For a fixed tunneling between the double quantum dots, the finite bias enhances the oscillation frequency effectively but its effect on the damping rate is relatively small. This is a possible way to maintain quantum coherence.