Qiongtao Xie

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.

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.

Chaos enhancing tunneling in a coupled Bose–Einstein condensate with a double driving

We study the effects of chaotic dynamics on atomic tunneling between two weakly coupled Bose-Einstein condensates driven by a double-frequency periodic field. Under the Melnikovs chaos criterion, we divide the parameter space into three parts of different types, regular region, low-chaoticity region, and high-chaoticity region, and give the accurate boundaries between the different regions. It is found that the atomic tunneling can be enhanced in the presence of chaos. Particularly, in the high-chaoticity regions, the chaos-induced inversion of the population imbalance is observed numerically.

Exact Solutions for Hydrogenic Impurity States in Quantum Dots

According to the hydrogenic-effective-mass theory and assumed finite barrier height for a confining potential, the analytical solutions and quantum energy-level structure for a hydrogenic impurity located at the center of a spherical quantum dot (SQD) are obtained. The calculated results reveal that because of the spatial confinement of the quantum dots, the energy, quantum numbers and radius of the SQD must satisfy a certain relation which arises from the boundary conditions. Given a barrier height or energy, the relation allows for the existence of bound states only for some discrete values of the radius of the SQD. On the other hand, for a fixed radius the energies of the bound states are discrete.

Nonlinear localized eigenmodes for a Bose Einstein condensate in a double-well potential

In this paper, we investigate the nonlinear localized eigenmodes for a Bose–Einstein condensate in a double-well potential. For a specific choice of the potential parameters, certain exact analytical solutions for nonlinear localized eigenmodes are presented. By applying the linear stability analysis, the stability regions of these exact nonlinear localized eigenmodes are obtained numerically. It is shown that under certain conditions, the unstable nonlinear localized modes display the breathing behavior characterized by repeated appearance of symmetric and asymmetric distributions in the two potentials. This breathing behavior is shown to arise from the symmetry breaking for these nonlinear localized eigenmodes.

Different routes from a matter wavepacket to spatiotemporal chaos

We investigate the dynamics of a quasi-one-dimensional Bose-Einstein condensate confined in a double-well potential with spatiotemporally modulated interaction. A variety of phenomena is identified in different frequency regimes, including the self-compression, splitting, breathing-like, and near-fidelity of the matter wavepacket, which are associated with different routes for the onset of spatiotemporal chaos. The results also reveal that chaos can retain space-inversion symmetry of the system.