Chirped Bloch-harmonic oscillations in a parametrically forced optical lattice

Abstract

The acceleration theorem for wave packet propagation in periodic potentials disentangles the k-space dynamics and real space dynamics. This is well known and understood for Bloch oscillations and super Bloch oscillations in the presence of position-independent forces. Here, we analyze the dynamics of a model system in which the k-space dynamics and the real space dynamics are inextricably intertwined due to a position-dependent force provided by a parabolic trap. We demonstrate that this coupling gives rise to significantly modified and rich dynamics when the lattice is shaken by a modulated parabolic potential. The dynamics range from chirped Bloch-harmonic oscillations to asymmetric spreading oscillations. We analyze these findings by tracing the spatiotemporal dynamics in real space and by visualizing the relative phase in the k-space dynamics which leads to an accurate explanation of the obtained phenomena. We also compare our numerical results to a local acceleration model and obtain very good agreement for the case of coherent oscillations, however, deviations for oscillations with spreading dynamics which altogether supports the interpretations of our findings.