Generation of nonground-state Bose-Einstein condensates by modulating atomic interactions

A technique is proposed for creating nonground-state Bose-Einstein condensates in a trapping potential by means of the temporal modulation of atomic interactions. Applying a time-dependent spatially homogeneous magnetic field modifies the atomic scattering length. A modulation of the scattering length excites the condensate, which, under special conditions, can be transferred to an excited nonlinear coherent mode. It is shown that a phase-transition-like behavior occurs in the time-averaged population imbalance between the ground and excited states. The application of the technique is analyzed and it is shown that the considered effect can be realized for experimentally available condensates.

Growth of Bose-Einstein condensates from thermal vapor

We report on a quantitative study of the growth process of 87Rb Bose-Einstein condensates. By continuous evaporative cooling we directly control the thermal cloud from which the condensate grows. We compare the experimental data with the results of a theoretical model based on quantum kinetic theory. We find quantitative agreement with theory for the situation of strong cooling, whereas in the weak cooling regime a distinctly different behavior is found in the experiment.

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.

Dynamical quantum noise in trapped Bose-Einstein condensates

We introduce the study of dynamical quantum noise in Bose-Einstein condensates through numerical simulation of stochastic partial differential equations obtained using phase-space representations. We derive evolution equations for a single trapped condensate in both the positive-P and Wigner representations and perform simulations to compare the predictions of the two methods. The positive-P approach is found to be highly susceptible to the stability problems that have been observed in other strongly nonlinear, weakly damped systems. Using the Wigner representation, we examine the evolution of several quantities of interest using from a variety of choices of initial stare for the condensate and compare results to those for single-mode models. [S1050-2947(98)06612-8].

Dynamics of trapped Bose-Einstein condensates: Beyond the mean-field

Since dilute Bose gas condensates were first experimentally produced, the Gross-Pitaevskii equation has been successfully used as a descriptive tool. As a mean-field equation, it cannot by definition predict anything about the many-body quantum statistics of condensate. We show here that there are a class of dynamical systems where it cannot even make successful predictions about the mean-field behavior, starting with the process of evaporative cooling by which condensates are formed. Among others are parametric processes, such as photoassociation and dissociation of atomic and molecular condensates.

Weakly linked binary mixtures of F = 1 87Rb Bose-Einstein condensates

We present a study of binary mixtures of Bose-Einstein condensates confined in a double-well potential within the framework of the mean field Gross-Pitaevskii (GP) equation. We re-examine both the single component and the binary mixture cases for such a potential, and we investigate what are the situations in which a simpler two-mode approach leads to an accurate description of their dynamics. We also estimate the validity of the most usual dimensionality reductions used to solve the GP equations. To this end, we compare both the semi-analytical two-mode approaches and the numerical simulations of the one-dimensional (1D) reductions with the full 3D numerical solutions of the GP equation. Our analysis provides a guide to clarify the validity of several simplified models that describe mean-field nonlinear dynamics, using an experimentally feasible binary mixture of an F = 1 spinor condensate with two of its Zeeman manifolds populated, m = ±1.

Weakly linked binary mixtures of F = 1 87Rb Bose-Einstein condensates

We present a study of binary mixtures of Bose-Einstein condensates confined in a double-well potential within the framework of the mean field Gross-Pitaevskii (GP) equation. We re-examine both the single component and the binary mixture cases for such a potential, and we investigate what are the situations in which a simpler two-mode approach leads to an accurate description of their dynamics. We also estimate the validity of the most usual dimensionality reductions used to solve the GP equations. To this end, we compare both the semi-analytical two-mode approaches and the numerical simulations of the one-dimensional (1D) reductions with the full 3D numerical solutions of the GP equation. Our analysis provides a guide to clarify the validity of several simplified models that describe mean-field nonlinear dynamics, using an experimentally feasible binary mixture of an F = 1 spinor condensate with two of its Zeeman manifolds populated, m = ±1.

Spinor Bose-Einstein Condensates and Topological Defects

This thesis concentrates on the topological defects of spin-1 and spin-2 Bose-Einstein condensates, the ground states of spin-3 condensates, and the inert states of spinor condensates with arbitrary spin. Our work is based on the description of a spinor condensate of spin-S atoms in terms of a state vector of a spin-S particle. The results of the homotopy theory are used to study the existence and structure of the topological defects in spinor condensates. We construct examples of defects, study their energetics, and examine how their stability is affected by the presence of an external magnetic field. The ground states of spin-3 condensates are calculated using analytical and numerical means. Special emphasis is put on the ground states of a chromium condensate, whose dependence on the magnetic dipole-dipole interaction is studied. A simple geometrical method for the calculation of inert states of spinor condensates is presented. This method is used to find candidates for the ground states of spin-S condensates.

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 dynamics from the numerical solution of the Gross-Pitaevskii equation

We study certain stationary and time-evolution problems of trapped Bose-Einstein condensates using the numerical solution of the Gross-Pitaevskii (GP) equation with both spherical and axial symmetries. We consider time-evolution problems initiated by suddenly changing the interatomic scattering length or harmonic trapping potential in a stationary condensate. These changes introduce oscillations in the condensate which are studied in detail. We use a time iterative split-step method for the solution of the time-dependent GP equation, where all nonlinear and linear non-derivative terms are treated separately from the time propagation with the kinetic energy terms. Even for an arbitrarily strong nonlinear term this leads to extremely accurate and stable results after millions of time iterations of the original equation.

Effects of time-periodic linear coupling on two-component Bose-Einstein condensates in two dimensions

We examine two-component Gross-Pitaevskii equations with nonlinear and linear couplings, assuming self-attraction in one species and self-repulsion in the other, while the nonlinear inter-species coupling is also repulsive. For initial states with the condensate placed in the self-attractive component, a sufficiently strong linear coupling switches the collapse into decay (in the free space). Setting the linear-coupling coefficient to be time-periodic (alternating between positive and negative values, with zero mean value) can make localized states quasi-stable for the parameter ranges considered herein, but they slowly decay. The 2D states can then be completely stabilized by a weak trapping potential. In the case of the high-frequency modulation of the coupling constant, averaged equations are derived, which demonstrate good agreement with numerical solutions of the full equations. (C) 2007 Elsevier B.V. All rights reserved.

Bose-Einstein condensation for general dispersion relations

Bose-Einstein condensation in an ideal (i.e. interactionless) boson gas can be studied analytically, at university-level statistical and solid state physics, in any positive dimensionality (d > 0) for identical bosons with any positive-exponent (s > 0) energy-momentum (i.e. dispersion) relation. Explicit formulae with arbitrary dls are discussed for: the critical temperature (non-zero only if d/s > 1); the condensate fraction; the internal energy; and the constant-volume specific heat (found to possess a jump discontinuity only if d/s > 2) Classical results are recovered at sufficiently high temperatures. Applications to ordinary' Bose-Einstein condensation, as well as to photons, phonons, ferro-and antiferromagnetic magnons, and (very specially) to Cooper pairs in superconductivity, are mentioned.

Liquid-gas phase transition in Bose-Einstein condensates with time evolution

We study the effects of a repulsive three-body interaction on a system of trapped ultracold atoms in a Bose-Einstein condensed state. The stationary solutions of the corresponding s-wave nonlinear Schrödinger equation suggest a scenario of first-order liquid-gas phase transition in the condensed state up to a critical strength of the effective three-body force. The time evolution of the condensate with feeding process and three-body recombination losses has a different characteristic pattern. Also, the decay time of the dense (liquid) phase is longer than expected due to strong oscillations of the mean-squared radius.