Dynamics of Bose-Einstein condensates in double-well potentials

We study the dynamics of Bose-Einstein condensates in symmetric double-well potentials following a sudden change of the potential from the Mott-insulator to the superfluid regime. We introduce a continuum approximation that maps that problem onto the wave-packet dynamics of a particle in an anharmonic effective potential. For repulsive two-body interactions the visibility of interference fringes that result from the superposition of the two condensates following a stage of ballistic expansion exhibits a collapse of coherent oscillations onto a background value whose magnitude depends on the amount of squeezing of the initial state. Strong attractive interactions are found to stabilize the relative number dynamics. We visualize the dynamics of the system in phase space using a quasiprobability distribution that allows for an intuitive interpretation of the various types of dynamics.

Bifurcations and bistability in cavity-assisted photoassociation of Bose-Einstein-condensed molecules

We study the photoassociation of Bose-Einstein condensed atoms into molecules using an optical cavity field. The driven cavity field introduces a dynamical degree of freedom into the photoassociation process, whose role in determining the stationary behavior has not previously been considered. The semiclassical stationary solutions for the atom and molecules as well as the intracavity field are found and their stability and scaling properties are determined in terms of experimentally controllable parameters including driving amplitude of the cavity and the nonlinear interactions between atoms and molecules. For weak cavity driving, we find a bifurcation in the atom and molecule number occurs that signals a transition from a stable steady state to nonlinear Rabi oscillations. For a strongly driven cavity, there exists bistability in the atom and molecule number.

Compositeness effects in the Bose-Einstein condensation

Small deviations from purely bosonic behaviour of trapped atomic Bose-Einstein condensates are investigated with the help of the quon algebra, which interpolates between bosonic and fermionic statistics. A previously developed formalism is employed to obtain a generalized version of the Gross-Pitaeviskii equation. The depletion of the amount of condensed atoms for the case of repulsive forces between atoms in the trap can be accounted for by a universal fitting of the deformation parameter.

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.

Finite-well potential in the 3D nonlinear Schrodinger equation: application to Bose-Einstein condensation

Using variational and numerical solutions we show that stationary negative-energy localized (normalizable) bound states can appear in the three-dimensional nonlinear Schrodinger equation with a finite square-well potential for a range of nonlinearity parameters. Below a critical attractive nonlinearity, the system becomes unstable and experiences collapse. Above a limiting repulsive nonlinearity, the system becomes highly repulsive and cannot be bound. The system also allows nonnormalizable states of infinite norm at positive energies in the continuum. The normalizable negative-energy bound states could be created in BECs and studied in the laboratory with present knowhow.

Limits of validity for a semiclassical mean-field two-fluid model for Bose-Einstein condensation thermodynamics

We reinvestigate the Bose-Einstein condensation (BEC) thermodynamics of a weakly interacting dilute Bose gas under the action of a trap using a semi-classical two-fluid mean-field model in order to find the domain of applicability of the model. Such a model is expected to break down once the condition of diluteness and weak interaction is violated. We find that this breakdown happens for values of coupling and density near the present experimental scenario of BEG. With the increase of the interaction coupling and density the model may lead to unphysical results for thermodynamic observables. (C) 2000 Published by Elsevier B.V. B.V, All rights reserved.

Atomic Bose-Einstein condensation with three-body interactions and collective excitations

The stability of a Bose-Einstein condensed state of trapped ultra-cold atoms is investigated under the assumption of an attractive two-body and a repulsive three-body interaction. The Ginzburg-Pitaevskii-Gross (GPG) nonlinear Schrodinger equation is extended to include an effective potential dependent on the square of the density and solved numerically for the s-wave. The lowest collective mode excitations are determined and their dependences on the number of atoms and on the strength of the three-body force are studied. The addition of three-body dynamics can allow the number of condensed atoms to increase considerably, even when the strength of the three-body force is very small compared with the strength of the two-body force. We study in detail the first-order liquid-gas phase transition for the condensed state, which can happen in a critical range of the effective three-body force parameter.

Positronium-positronium interaction: resonance, scattering length, and Bose-Einstein condensation

The low-energy scattering of ortho positronium (Ps) by ortho Ps has been studied in a full quantum mechanical coupled-channel approach. In the singlet channel (total spin s(T) = 0) we find S- and P-wave resonances at 3.35 eV (width 0.02 eV) and 5.05 eV (width 0.04 eV), respectively, and a binding of 0.43 eV of Ps(2). The scattering length for s(T) = 0 is 3.95 Angstrom and for s(T) = 2 is 0.83 Angstrom. The small s(T) = 2 scattering length makes the spin-polarized ortho Ps atoms an almost noninteracting ideal gas which may undergo Bose-Einstein condensation. (C) 2002 Elsevier B.V. B.V. All rights reserved.

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.

Superconductivity as a Bose-Einstein condensation?

Bose-Einstein condensation (BEC) in two dimensions (2D) (e.g., to describe the quasi-2D cuprates) is suggested as the possible mechanism widely believed to underlie superconductivity in general. A crucial role is played by nonzero center-of-mass momentum Cooper pairs (CPs) usually neglected in BCS theory. Also vital is the unique linear dispersion relation appropriate to weakly-coupled bosonic CPs moving in the Fermi sea-rather than in vacuum where the dispersion would be quadratic but only for very strong coupling, and for which BEC is known to be impossible in 2D.

Bose-Einstein condensation and free DKP field

The thermodynamical partition function of the Duffin-Kemmer-Petiau theory is evaluated using the imaginary-time formalism of quantum field theory at finite temperature and path integral methods. The DKP partition function displays two features: (i) full equivalence with the partition function for charged scalar particles and charged massive spin 1 particles; and (ii) the zero mode sector which is essential to reproduce the well-known relativistic Bose-Einstein condensation for both theories. (C) 2003 Published by Elsevier B.V.

Bose-Einstein condensates in 2D with time-periodic scattering length

We discuss two-dimensional Bose-Einstein Condensates (BEC) under time-periodic variation of the scattering length. In particular we argue that for high-frequency variation there exist stable self-confined condensates without an external trap, when the do component of the scattering length is negative. Our results are based on a variational approximation, on direct averaging of the Gross-Pitaevskii equation and on numerical simulations.

Bright solitons in coupled defocusing NLS equation supported by coupling: Application to Bose-Einstein condensation

We demonstrate the formation of bright solitons in coupled self-defocusing nonlinear Schrodinger (NLS) equation supported by attractive coupling. As an application we use a time-dependent dynamical mean-field model to study the formation of stable bright solitons in two-component repulsive Bose-Einstein condensates (BECs) supported by interspecies attraction in a quasi one-dimensional geometry. When all interactions are repulsive, there cannot be bright solitons. However, bright solitons can be formed in two-component repulsive BECs for a sufficiently attractive interspecies interaction, which induces an attractive effective interaction among bosons of same type. (c) 2005 Elsevier B.V. All rights reserved.

Macroscopic quantum tunneling and resonances in coupled Bose-Einstein condensates with oscillating atomic scattering length

We study the macroscopic quantum tunneling, self-trapping phenomena in two weakly coupled Bose-Einstein condensates with periodically time-varying atomic scattering length.The resonances in the oscillations of the atomic populations are investigated. We consider oscillations in the cases of macroscopic quantum tunneling and the self-trapping regimes. The existence of chaotic oscillations in the relative atomic population due to overlaps between nonlinear resonances is showed. We derive the whisker-type map for the problem and obtain the estimate for the critical amplitude of modulations leading to chaos. The diffusion coefficient for motion in the stochastic layer near separatrix is calculated. The analysis of the oscillations in the rapidly varying case shows the possibility of stabilization of the unstable pi-mode regime. (C) 2000 Published by Elsevier B.V. B.V. PACS: 03.75.Fi; 05.30.Jp.

Formation of soliton trains in Bose-Einstein condensates as a nonlinear Fresnel diffraction of matter waves

The problem of generation of atomic soliton trains in elongated Bose-Einstein condensates is considered in framework of Whitham theory of modulations of nonlinear waves. Complete analytical solution is presented for the case when the initial density distribution has sharp enough boundaries. In this case the process of soliton train formation can be viewed as a nonlinear Fresnel diffraction of matter waves. Theoretical predictions are compared with results of numerical simulations of one- and three-dimensional Gross-Pitaevskii equation and with experimental data on formation of Bose-Einstein bright solitons in cigar-shaped traps. (C) 2003 Elsevier B.V. All rights reserved.