We consider a single-impurity atom confined to an optical lattice and immersed in a homogeneous Bose-Einstein condensate (BEC). Interaction of the impurity with the phonon modes of the BEC leads to the formation of a stable quasiparticle, the polaron. We use a variational mean-field approach to study dispersion renormalization and derive equations describing nonequilibrium dynamics of polarons by projecting equations of motion into mean-field-type wave functions. As a concrete example, we apply our method to study dynamics of impurity atoms in response to a suddenly applied force and explore the interplay of coherent Bloch oscillations and incoherent drift. We obtain a nonlinear dependence of the drift velocity on the applied force, including a sub-Ohmic dependence for small forces for dimensionality $d>1$ of the BEC. For the case of heavy impurity atoms, we derive a closed analytical expression for the drift velocity. Our results show considerable differences with the commonly used phenomenological Esaki-Tsu model.

• Received 9 October 2014

DOI:https://doi.org/10.1103/PhysRevA.90.063610