Wave packet dynamics in parabolic optical lattices: From Bloch oscillations to long-range dynamical tunneling

We investigate the dynamics of wave packets in a parabolic optical lattice formed by combining an optical lattice with a global parabolic trap. Our study examines the phase space representation of the system's eigenstates by comparing them to the classical phase space of a pendulum, to which the system effectively maps. The analysis reveals that quantum states can exhibit mixed dynamics by straddling the separatrix. A key finding is that the dynamics around the separatrix enables the controlled creation of highly nonclassical states, distinguishing them from the classical oscillatory or rotational dynamics of the pendulum. By considering a finite momentum of the initial wave packet, we demonstrate various dynamical regimes. Furthermore, a slight energy mismatch between nearly degenerate states localized at opposite turning points of the trap potential results in controlled long-range dynamical tunneling. These results can be interpreted as quantum beating between a clockwise rotating and a counterclockwise rotating pendulum.