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Periodically driven systems can lead to a directed motion of particles. Weinvestigate this ratchet effect for a bosonic Mott insulator where both astaggered hopping and a staggered local potential vary periodically in time. Ifdriving frequencies are smaller than the interaction strength and the densityof excitations is small, one obtains effectively a one-particle quantum ratchetdescribing the motion of doubly occupied sites (doublons) and empty sites(holes). Such a simple quantum machine can be used to manipulate theexcitations of the Mott insulator. For suitably chosen parameters, for example,holes and doublons move in opposite direction. To investigate whether theperiodic driving can be used to move particles "uphill", i.e., against anexternal force, we study the influence of a linear potential $- g x$. For longtimes, transport is only possible when the driving frequency $\omega$ and theexternal force $g$ are commensurate, $n_0 g = m_0 \omega$, with$\frac{n_0}{2},m_0 \in \mathbb{Z}$.

Directed motion of doublons and holes in periodically driven Mott insulators