Tunneling of quantum particle in parametrically driven double-well system

Controlling chaos-assisted directed transport via quantum resonance

We report on the first demonstration of chaos-assisted directed transport of a quantum particle held in an amplitude-modulated and tilted optical lattice, through a resonance-induced double-mean displacement relating to the true classically chaotic orbits. The transport velocity is controlled by the driving amplitude and the sign of tilt, and also depends on the phase of the initial state. The chaos-assisted transport feature can be verified experimentally by using a source of single atoms to detect the double-mean displacement one by one, and can be extended to different scientific fields.

Does chaos assist localization or delocalization?

We aim at a long-standing contradiction between chaos-assisted tunneling and chaos-related localization study quantum transport of a single particle held in an amplitude-modulated and tilted optical lattice. We find some near-resonant regions crossing chaotic and regular regions in the parameter space, and demonstrate that chaos can heighten velocity of delocalization in the chaos-resonance overlapping regions, while chaos may aid localization in the other chaotic regions. The degree of localization enhances with increasing the distance between parameter points and near-resonant regions. The results could be useful for experimentally manipulating chaos-assisted transport of single particles in optical or solid-state lattices.

Numerical study on dynamical behavior in oscillatory driven quantum double-well systems

We numerically investigate quantum dynamics in a one-dimensional double-well system emphasizing influence of a parametrically polychromatic perturbation on the dynamics. It is found that time dependence of transition probability for an initially localized wave packet between the wells shows two types of motion, coherent and incoherent motion, depending on the perturbation parameters. As the strength and/or the number of frequency components of the perturbation increase, coherent motion changes into incoherent one. The former is related to coherent tunneling of the wave packet due to coherence; the latter is related to a delocalized state caused by decoherence. In coherent motion, by virtue of coherence of the dynamics, the expectation value and the standard deviation of a dynamical variable such as the energy of the system show oscillatory time dependence around the initial values. On the contrary in incoherent motion, because of the decoherence, the time dependence fluctuates irregularly around a certain value after a rapid increase due to the resonance. We find that negativity of the Wigner function also show similar time dependence in each type of motion. We compare the classification of the quantum dynamics based on regularity of the time dependence with the one of corresponding classical dynamics based on the Lyapunov exponent. The classifications of the quantum and classical dynamics overlap well in the parameter space. Furthermore, we confirm decoherence of quantum dynamics in a kicked double-well system.