Decoherence of adiabatically steered quantum systems

We study the effect of Markovian environmental noise on the dynamics of a two-level quantum system which is steered adiabatically by an external driving field. We express the master equation taking consistently into account all the contributions to the lowest non-vanishing order in the coupling to the Markovian environment. We study the master equation numerically and analytically and we find that, in the adiabatic limit, a zero-temperature environment does not affect the ground state evolution. As a physical application, we discuss extensively how the environment affects Cooper pair pumping. The adiabatic ground state pumping appears to be robust against environmental noise. In fact, the relaxation due to the environment is required to avoid the accumulation of small errors from each pumping cycle. We show that neglecting the non-secular terms in the master equation leads to unphysical results, such as charge non-conservation. We discuss also a possible way to control the environmental noise in a realistic physical setup and its influence on the pumping process.