Wenhua Hai

Spatial chaos of trapped Bose–Einstein condensate in one-dimensional weak optical lattice potential

The spatially chaotic attractor in an elongated cloud of Bose-Einstein condensed atoms perturbed by a weak optical lattice potential is studied. The analytical insolvability and numerical incomputability of the atomic number density are revealed by a perturbed solution that illustrates the unpredictability of the deterministic chaos. Although this could lead the nonphysical explosion and unboundedness to the numerical solution, the theoretical analysis offers a criterion to avoid them. Moreover, the velocity field is investigated that exhibits the superfluid property of the chaotic system.

Chaotic atomic tunneling between two periodically driven Bose–Einstein condensates

The chaotic coherent atomic tunneling between two periodically driven and weakly coupled Bose-Einstein condensates has been investigated. The perturbed correction to the homoclinic orbit is constructed and its boundedness conditions are established that contain the Melnikov criterion for the onset of chaos. We analytically reveal that the chaotic coherent atomic tunneling is deterministic but not predictable. Our numerical calculation shows good agreement with the analytical result and exhibits nonphysically numerical instability. By adjusting the initial conditions, we propose a method to control the unboundedness, which leads the quantum coherent atomic tunneling to predictable periodical oscillation.

An analytical study for controlling unstable periodic motion in magneto-elastic chaos☆

Abstract A magneto-elastic beam system is described by the Duffing equation with delay feedback term. The perturbation technique leads to a general unstable periodic solution near the homoclinic orbit of the equation. A necessary and sufficient condition for stabilizing the solution is given as the relation between control parameters and initial constants. It is shown that sensitivity of the solution to initial constants implies chaos and fitting the parameters to the condition can control the chaos. Good agreement is found between the analytical results and previous experimental facts.

Current–voltage characteristic of the Josephson chaos

Abstract Perturbed correction to the heteroclinic orbit of a rf-driven Josephson system is derived from a direct perturbation technique. Theoretical analysis reveals that boundedness conditions of the orbit contain Melnikov criterion for the onset of chaos. Current–voltage characteristic associated with the bounded chaotic orbit is obtained, which implies current steps and shows qualitative agreement between the analytical results and experimental data. The results supply a more detailed analytical criterion for chaos in the system.

Transitions between chaos and order in rf-driven Josephson junction

We investigate transitions between the chaotic and regular states through a perturbed chaotic solution of a rf-driven Josephson system. It is shown that the transition from order to chaos may occur when the system initially near the heteroclinic points. The chaotic solution tends to an unstable periodic one for the initial values sufficiently nearing the heteroclinic orbit but going beyond the heteroclinic points. Thus the Josephson chaos can be analytically and numerically controlled, by adjusting the initial conditions.

Analytically bounded and numerically unbounded compound pendulum chaos

Abstract A compound pendulum with deterministically periodic perturbation is treated. In the analytical approximation, chaotic solution initially near the homoclinic one is constructed and its boundedness conditions are established. It is shown that the chaotic solution is analytically bounded and numerically unbounded, which describes a non-periodical vibration around unstable equilibrium of the corresponding unperturbed system.

Discrete chaotic states of a Bose-Einstein condensate

We examine spatial chaos in a one-dimensional attractive Bose-Einstein condensate interacting with a Gaussian-like laser barrier and perturbed by a weak optical lattice. For a low laser barrier, chaotic regions of the parameters are demonstrated and the chaotic and regular states are illustrated numerically. In the high-barrier case, bounded perturbed solutions that describe a set of discrete chaotic states are constructed for discrete barrier heights and magic numbers of condensed atoms. Chaotic density profiles are exhibited numerically for the lowest quantum number, and analytically bounded but numerically unbounded Gaussian-like configurations are confirmed. It is shown that the chaotic wave packets can be controlled experimentally by adjusting the laser barrier potential.

Dynamic chaos and stability of a weakly open Bose-Einstein condensate in a double-well trap

We investigate the dynamics of a weakly open Bose-Einstein condensate with attractive interaction in a magneto-optical double-well trap. A set of time-dependent ordinary differential equations describing the complex dynamics are derived by using a two-mode approximation. The stability of the stationary solution is analyzed and some stability regions on the parameter space are displayed. In the symmetric well case, the numerical calculations reveal that by adjusting the feeding from the nonequilibrium thermal cloud or the two-body dissipation rate, the system could transit among the periodic motions, chaotic self-trapping states of the Lorenz model, and the steady states with the zero relative atomic population or with the macroscopic quantum self-trapping (MQST). In the asymmetric well case, we find the periodic orbit being a stable two-sided limited cycle with MQST. The results are in good agreement with that of the direct numerical simulations to the Gross-Pitaevskii equation.

CHAOTIC SOLUTION OF THE rf-DRIVEN JOSEPHSON SYSTEM WITH QUADRATIC DAMPING

The method of direct perturbation is applied to a rf-driven Josephson junction with strong and quadratic damping resistor. Perturbed correction to the heteroclinic orbit is constructed and its boundedness conditions are established to contain the Melnikov criterion for the onset of chaos. The result shows that the corrected heteroclinic orbit is unbounded, unless it is chaotic. The analytically deterministic chaotic solution exposes the incomputability of chaotic orbits, which is numerically demonstrated.

Phase-controlled localization and directed transport in an optical bipartite lattice.

We investigate coherent control of a single atom interacting with an optical bipartite lattice via a combined high-frequency modulation. Our analytical results show that the quantum tunneling and dynamical localization can depend on phase difference between the modulation components, which leads to a different route for the coherent destruction of tunneling and a convenient phase-control method for stabilizing the system to implement the directed transport of atom. The similar directed transport and the phase-controlled quantum transition are revealed for the corresponding many-particle system. The results can be referable for experimentally manipulating quantum transport and transition of cold atoms in the tilted and shaken optical bipartite lattice or of analogical optical two-mode quantum beam splitter, and also can be extended to other optical and solid-state systems.