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

TL;DR

This paper explores wave packet dynamics in parabolic optical lattices, revealing how quantum states can exhibit mixed classical-quantum behavior and enabling controlled long-range tunneling with potential applications in quantum control.

Contribution

It introduces a detailed phase space analysis of wave packet dynamics in parabolic optical lattices, highlighting the creation of non-classical states and controlled dynamical tunneling phenomena.

Findings

Quantum states can exhibit mixed dynamics near the separatrix.

Controlled long-range dynamical tunneling can be achieved.

Quantum beating between rotating pendulum states is observed.

Abstract

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 non-classical 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.