Dynamics and Bloch oscillations of mobile impurities in one-dimensional quantum liquids

► A mobile impurity in a one-dimensional quantum liquid acquires a periodic dispersion. ► Under the action of a force, the impurity may perform Bloch oscillations (BO). ► Due to phonon coupling, the impurity exhibits uniform drift along with renormalized BO. ► The drift strongly depends on the temperature and impurity-liquid interactions. ► We predict a wide range of forces where drifted BO can be observed in current experiments.