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.

Miscibility in a degenerate fermionic mixture induced by linear coupling

We consider a one-dimensional mean-field-hydrodynamic model of a two-component degenerate Fermi gas in an external trap, each component representing a spin state of the same atom. We demonstrate that the interconversion between them (linear coupling), imposed by a resonant electromagnetic wave, transforms the immiscible binary gas into a miscible state, if the coupling constant, kappa, exceeds a critical value, kappa(cr). The effect is predicted in a variational approximation, and confirmed by numerical solutions. Unlike the recently studied model of a binary Bose-Einsten condensate with the linear coupling, the components in the immiscible phase of the binary fermion mixture never fill two separated domains with a wall between them, but rather form antilocked (pi-phase-shifted) density waves. Another difference from the bosonic mixture is spontaneous breaking of symmetry between the two components in terms of the numbers of atoms in them, N(1) and N(2). The latter effect is characterized by the parameter nu equivalent to(N(1)-N(2))/(N(1)+N(2)) (only N(1)+N(2) is a conserved quantity), the onset of miscibility at kappa >=kappa(cr) meaning a transition to nu equivalent to 0. At kappa

Spatially-antisymmetric localization of matter wave in a bichromatic optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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.

Mean-field equations for cigar- and disc-shaped Bose and Fermi superfluids

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Numerical and variational solutions of the dipolar Gross-Pitaevskii equation in reduced dimensions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Josephson oscillation of a superfluid Fermi gas

Using the complete numerical solution of a time-dependent three-dimensional rnean-field model we study the Josephson oscillation of a superfluid Fermi gas (SFG) at zero temperature formed in a combined axially-symmetric harmonic plus one-dimensional periodic optical-lattice (OL) potentials after displacing the harmonic trap along the axial OL axis. We study the dependence of Josephson frequency on the strength of the OL potential. The Josephson frequency decreases with increasing strength as found in the experiment of Cataliotti et al. [Science 293, 843 (2001)] for a Bose-Einstein condensate and of the experiment of Pezze et al. [Phys. Rev. Lett. 93, 120401 (2004)] for an ideal Fermi gas. We demonstrate a breakdown of Josephson oscillation in the SFG for a large displacement of the harmonic trap. These features of Josephson oscillation of a SFG can be tested experimentally.

Integrable NLS equation with time-dependent nonlinear coefficient and self-similar attractive BEC

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

C programs for solving the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Positronium interaction and its Bose-Einstein condensation

We present the actual state of affairs and future perspectives in the study of a quantum system of a collection of positronium (Ps) atoms. The interaction of a Ps atom with other atoms and molecules and specially with another Ps atom is described in some detail as Ps-Ps interaction should play a crucial role in the dynamics of an assembly of Ps atoms. Using a simple model-exchange potential, we could describe the available experimental results of Ps scattering reasonably well. The present scenario of the observation of Ps2 molecule, Ps Bose-Einstein condensate (BEC) and the annihilation laser from a Ps BEC is presented. Possibilities of a Ps BEC formation via laser cooling of Ps atoms and via Ps formation in cavities are considered and difficulties with each procedure discussed (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Chiral symmetry breaking in QCD-like gauge theories with a confining propagator and dynamical gauge boson mass generation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Extension of the Nambu-Jona-Lasinio model predictions at high densities and temperatures using an implicit regularization scheme

Traditional cutoff regularization schemes of the Nambu-Jona-Lasinio model limit the applicability of the model to energy-momentum scales much below the value of the regularizing cutoff. In particular, the model cannot be used to study quark matter with Fermi momenta larger than the cutoff. In the present work, an extension of the model to high temperatures and densities recently proposed by Casalbuoni, Gatto, Nardulli, and Ruggieri is used in connection with an implicit regularization scheme. This is done by making use of scaling relations of the divergent one-loop integrals that relate these integrals at different energy-momentum scales. Fixing the pion decay constant at the chiral symmetry breaking scale in the vacuum, the scaling relations predict a running coupling constant that decreases as the regularization scale increases, implementing in a schematic way the property of asymptotic freedom of quantum chromodynamics. If the regularization scale is allowed to increase with density and temperature, the coupling will decrease with density and temperature, extending in this way the applicability of the model to high densities and temperatures. These results are obtained without specifying an explicit regularization. As an illustration of the formalism, numerical results are obtained for the finite density and finite temperature quark condensate and applied to the problem of color superconductivity at high quark densities and finite temperature.

Bekenstein bound in asymptotically free field theory

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices

The properties of the localized states of a two-component Bose-Einstein condensate confined in a nonlinear periodic potential (nonlinear optical lattice) are investigated. We discuss the existence of different types of solitons and study their stability by means of analytical and numerical approaches. The symmetry properties of the localized states with respect to nonlinear optical lattices are also investigated. We show that nonlinear optical lattices allow the existence of bright soliton modes with equal symmetry in both components and bright localized modes of mixed symmetry type, as well as dark-bright bound states and bright modes on periodic backgrounds. In spite of the quasi-one-dimensional nature of the problem, the fundamental symmetric localized modes undergo a delocalizing transition when the strength of the nonlinear optical lattice is varied. This transition is associated with the existence of an unstable solution, which exhibits a shrinking (decaying) behavior for slightly overcritical (undercritical) variations in the number of atoms.