Energy level statistics for models of coupled single-mode Bose-Einstein condensates

We study the distribution of energy level spacings in two models describing coupled single-mode Bose-Einstein condensates. Both models have a fixed number of degrees of freedom, which is small compared to the number of interaction parameters, and is independent of the dimensionality of the Hilbert space. We find that the distribution follows a universal Poisson form independent of the choice of coupling parameters, which is indicative of the integrability of both models. These results complement those for integrable lattice models where the number of degrees of freedom increases with increasing dimensionality of the Hilbert space. Finally, we also show that for one model the inclusion of an additional interaction which breaks the integrability leads to a non-Poisson distribution.

Quantum dynamics of a model for two Josephson-coupled Bose-Einstein condensates

In this work, we investigate the quantum dynamics of a model for two singlemode Bose-Einstein condensates which are coupled via Josephson tunnelling. Using direct numerical diagonalization of the Hamiltonian, we compute the time evolution of the expectation value for the relative particle number across a wide range of couplings. Our analysis shows that the system exhibits rich and complex behaviours varying between harmonic and non-harmonic oscillations, particularly around the threshold coupling between the delocalized and selftrapping phases. We show that these behaviours are dependent on both the initial state of the system and regime of the coupling. In addition, a study of the dynamics for the variance of the relative particle number expectation and the entanglement for different initial states is presented in detail.

Behaviour of the energy gap in a model of Josephson coupled Bose-Einstein condensates

In this work we investigate the energy gap between the ground state and the first excited state in a model of two single-mode Bose-Einstein condensates coupled via Josephson tunnelling. The ene:rgy gap is never zero when the tunnelling interaction is non-zero. The gap exhibits no local minimum below a threshold coupling which separates a delocalized phase from a self-trapping phase that occurs in the absence of the external potential. Above this threshold point one minimum occurs close to the Josephson regime, and a set of minima and maxima appear in the Fock regime. Expressions for the position of these minima and maxima are obtained. The connection between these minima and maxima and the dynamics for the expectation value of the relative number of particles is analysed in detail. We find that the dynamics of the system changes as the coupling crosses these points.

Classical and quantum dynamics of a model for atomic-molecular Bose-Einstein condensates

We study a model for a two-mode atomic-molecular Bose-Einstein condensate. Starting with a classical analysis we determine the phase space fixed points of the system. It is found that bifurcations of the fixed points naturally separate the coupling parameter space into four regions. The different regions give rise to qualitatively different dynamics. We then show that this classification holds true for the quantum dynamics.

Foil-based atom chip for Bose-Einstein condensates

We describe a novel method of fabricating atom chips that are well suited to the production and manipulation of atomic Bose–Einstein condensates. Our chip was created using a silver foil and simple micro-cutting techniques without the need for photolithography. It can sustain larger currents than conventional chips, and is compatible with the patterning of complex trapping potentials. A near pure Bose–Einstein condensate of 4 × 104 87Rb atoms has been created in a magnetic microtrap formed by currents through wires on the chip. We have observed the fragmentation of atom clouds in close proximity to the silver conductors. The fragmentation has different characteristic features to those seen with copper conductors.

Complex solitons in Bose-Einstein condensates with two- and three-body interactions

For the first time, we find the complex solitons for a quasi-one-dimensional Bose-Einstein condensate with two-and three-body interactions. These localized solutions are characterized by a power law behaviour. Both dark and right solitons can be excited in the experimentally allowed parameter domain, when two-and three-body interactions are,respectively, repulsive and attractive. The dark solitons travel with a constant speed, which is quite different from the Lieb mode, where profiles with different speeds, bounded above by sound velocity, can exist for specified interaction strengths. We also study the properties of these solitons in the presence of harmonic confinement with time-dependent nonlinearity and loss. The modulational instability and the Vakhitov-Kolokolov criterion of stability are also studied.

The quantum tunnelling between two-component Bose-Einstein condensates in a double-well configuration

We examine in terms of exact solutions of the time-dependent Schrodinger equation, the quantum tunnelling process in Bose-Einstein condensates of two interacting species trapped in a double well configuration. Based on the two series of time-dependent SU(2) gauge transformations, we diagonalize the Hamilton operator and obtain analytic time-evolution formulas of the population imbalance and the berry phase. the particle population imbalance (a(L)(+)aL - a(R)(+)a(R)) of species A between the two wells is studied analytically.

The quantum tunneling between two-component Bose-Einstein condensates in a double-well configuration

In terms of exact solution of the time-dependent Schrodinger equation. we examine the quantum tunneling process in Bose condensates of two interacting species trapped in a double well configuration. We use the two series of time-dependent SU(2) gauge transformation to diagonalize the Hamilton operator obtain analytic time-evolution formulas of the population imbalance and the berry phase. The particle population imbalance (a(L)(+)a(L) - a(R)(+)a(R)) of species A between the two wells is studied analytically.

Vortex entanglement in Bose-Einstein condensates coupled to Laguerre-Gauss beams

We study the establishment of vortex entanglement in remote Bose-Einstein condensates (BECs). We consider a two-mode photonic resource entangled in its orbital angular momentum (OAM) degree of freedom and, by exploiting the process of light-to-BEC OAM transfer, demonstrate that such entanglement can be efficiently passed to the matterlike systems. Our proposal thus represents a building block for novel dissipation-free and long-memory communication channels based on OAM. We discuss issues of practical realizability, stressing the feasibility of our scheme, and present an operative technique for the indirect inference of the set vortex entanglement.

Modulational instability criteria for two-component Bose-Einstein condensates

The stability of colliding Bose-Einstein condensates is investigated. A set of coupled Gross-Pitaevskii equations is thus considered, and analyzed via a perturbative approach. No assumption is made on the signs ( or magnitudes) of the relevant parameters like the scattering lengths and the coupling coefficients. The formalism is therefore valid for asymmetric as well as symmetric coupled condensate wave states. A new set of explicit criteria is derived and analyzed. An extended instability region, in addition to an enhanced instability growth rate, is predicted for unstable two component bosons, as compared to the individual ( uncoupled) state.

Vortex line and ring dynamics in trapped Bose-Einstein condensates

Vortex dynamics in inhomogeneous Bose-Einstein condensates are studied numerically in two and three dimensions. We simulate the precession of a single vortex around the center of a trapped condensate, and use the Magnus force to estimate the precession frequency. Vortex ring dynamics in a spherical trap are also simulated, and we discover that a ring undergoes oscillatory motion around a circle of maximum energy. The position of this locus is calculated as a function of the number of condensed atoms. In the presence of dissipation, the amplitude of the oscillation will increase, eventually resulting in self-annihilation of the ring.

Vortex shedding and drag in dilute Bose-Einstein condensates

Above a critical velocity, the dominant mechanism of energy transfer between a moving object and a dilute Bose-Einstein condensate is vortex formation. In this paper, we discuss the critical velocity for vortex formation and the link between vortex shedding and drag in both homogeneous and inhomogeneous condensates. We find that at supersonic velocities sound radiation also contributes significantly to the drag force.

Dissipationless shock waves in Bose-Einstein condensates with repulsive interaction between atoms

We consider formation of dissipationless shock waves in Bose-Einstein condensates with repulsive interaction between atoms. It is shown that for big enough initial inhomogeneity of density, interplay of nonlinear and dispersion effects leads to wave breaking phenomenon followed by generation of a train of dark solitons. Analytical theory is confirmed by numerical simulations.

Quantum coherent tunneling between two atomic-molecular Bose-Einstein condensates

We study the quantum coherent tunneling dynamics of two weakly coupled atomic-molecular Bose-Einstein condensates (AMBEC). A weak link is supposed to be provided by a double-well trap. The regions of parameters where the macroscopic quantum localization of the relative atomic population occurs are revealed. The different dynamical regimes are found depending on the value of nonlinearity, namely, coupled oscillations of population imbalance of atomic and molecular condensate, including irregular oscillations regions, and macroscopic quantum self trapping regimes. Quantum means and quadrature variances are calculated for population of atomic and molecular condensates and the possibility of quadrature squeezing is shown via stochastic simulations within P-positive phase space representation method. Linear tunnel coupling between two AMBEC leads to correlations in quantum statistics.

Gap solitons in Bose-Einstein condensates in linear and nonlinear optical lattices

Properties of localized states on array of BEC confined to a potential, representing superposition of linear and nonlinear optical lattices are investigated. For a shallow lattice case the coupled mode system has been derived. We revealed new types of gap solitons and studied their stability. For the first time a moving soliton solution has been found. Analytical predictions are confirmed by numerical simulations of the Gross-Pitaevskii equation with jointly acting linear and nonlinear periodic potentials. (c) 2007 Elsevier B.V. All rights reserved.