Nonlinear Schrodinger equation for a superfluid Bose gas from weak coupling to unitarity: Study of vortices

We introduce a nonlinear Schrodinger equation to describe the dynamics of a superfluid Bose gas in the crossover from the weak-coupling regime, where an(1/3)<<1 with a the interatomic s-wave scattering length and n the bosonic density, to the unitarity limit, where a ->+infinity. We call this equation the unitarity Schrodinger equation (USE). The zero-temperature bulk equation of state of this USE is parametrized by the Lee-Yang-Huang low-density expansion and Jastrow calculations at unitarity. With the help of the USE we study the profiles of quantized vortices and vortex-core radius in a uniform Bose gas. We also consider quantized vortices in a Bose gas under cylindrically symmetric harmonic confinement and study their profile and chemical potential using the USE and compare the results with those obtained from the Gross-Pitaevskii-type equations valid in the weak-coupling limit. Finally, the USE is applied to calculate the breathing modes of the confined Bose gas as a function of the scattering length.

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.

Dipolar Bose-Einstein condensates with large scattering length

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

Dimensional effects on the momentum distribution of bosonic trimer states

The momentum distribution is a powerful probe of strongly interacting systems that are expected to display universal behavior. This is contained in the contact parameters which relate few- and many-body properties. Here we consider a Bose gas in two dimensions and explicitly show that the two-body contact parameter is universal and then demonstrate that the momentum distribution at next-to-leading order has a logarithmic dependence on momentum which is vastly different from the three-dimensional case. Based on this, we propose a scheme for measuring the effective dimensionality of a quantum many-body system by exploiting the functional form of the momentum distribution. © 2013 American Physical Society.

Advances on statistical/thermodynamical models for unpolarized structure functions

During the eights and nineties many statistical/thermodynamical models were proposed to describe the nucleons' structure functions and distribution of the quarks in the hadrons. Most of these models describe the compound quarks and gluons inside the nucleon as a Fermi / Bose gas respectively, confined in a MIT bag[1] with continuous energy levels. Another models considers discrete spectrum. Some interesting features of the nucleons are obtained by these models, like the sea asymmetries d̄/ū and d̄-ū. © 2013 American Institute of Physics.

Bose-Einstein condensation thermodynamics of a trapped gas with attractive interaction

We study the Bose-Einstein condensation of an interacting gas with attractive interaction confined in a harmonic trap using a semiclassical two-fluid mean-field model. The condensed state is described by the converged numerical solution of the Gross-Pitaevskii equation. By solving the system of coupled equations of this model iteratively we obtain the converged results for the temperature dependencies of the condensate fraction, chemical potential, and internal energy for the Bose-Einstein condensate of Li-7 atoms. (C) 2000 Elsevier B.V. B.V. All rights reserved.

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.

Chaos in collapsing Bose-condensed gas

We reinvestigate the dynamics of the grow and collapse of Bose-Einstein condensates in a system of trapped ultracold atoms with negative scattering lengths, and found a new behavior in the long time scale evolution: the number of atoms can go far beyond the static stability limit. The condensed state is described by the solution of the time-dependent nonlinear Schrödinger equation, in a model that includes atomic feeding and three-body dissipation. Our results for the model show that, by changing the feeding parameter and when a substantial depletion of the ground-state exists, a chaotic behavior is found. We consider a criterion proposed by Deissler and Kaneko [Phys. Lett. A 119, 397 (1987)] to diagnose spatiotemporal chaos. ©2000 The American Physical Society.

Self-trapping of Fermi and Bose gases under spatially modulated repulsive nonlinearity and transverse confinement

We show that self-localized ground states can be created in the spin-balanced gas of fermions with repulsion between the spin components, whose strength grows from the center to periphery, in combination with the harmonic-oscillator (HO) trapping potential acting in one or two transverse directions. We also consider the ground state in the noninteracting Fermi gas under the action of the spatially growing tightness of the one- or two-dimensional (1D or 2D) HO confinement. These settings are considered in the framework of the Thomas-Fermi-von Weizsäcker (TF-vW) density functional. It is found that the vW correction to the simple TF approximation (the gradient term) is nearly negligible in all situations. The properties of the ground state under the action of the 2D and 1D HO confinement with the tightness growing in the transverse directions are investigated too for the Bose-Einstein condensate with the self-repulsive nonlinearity. © 2013 American Physical Society.

A novel ozone gas sensor based on one-dimensional (1D) alpha-Ag2WO4 nanostructures

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

Tightly bound gap solitons in a Fermi gas

Within the framework of the mean-field hydrodynamic model of a degenerate Fermi gas ( DFG), we study, by means of numerical methods and variational approximation ( VA), the formation of fundamental gap solitons ( FGSs) in a DFG ( or in a BCS superfluid generated by weak interaction between spin- up and spin- down fermions), which is trapped in a periodic optical- lattice ( OL) potential. An effectively one- dimensional ( 1D) con. guration is considered, assuming strong transverse confinement; in parallel, a proper 1D model of the DFG ( which amounts to the known quintic equation for the Tonks- Girardeau gas in the OL) is considered too. The FGSs found in the first two bandgaps of the OL- induced spectrum ( unless they are very close to edges of the gaps) feature a ( tightly bound) shape, being essentially confined to a single cell of the OL. In the second bandgap, we also find antisymmetric tightly bound subfundamental solitons ( SFSs), with zero at the midpoint. The SFSs are also confined to a single cell of the OL, but, unlike the FGSs, they are unstable. The predicted solitons, consisting of similar to 10(4) - 10(5) atoms, can be created by available experimental techniques in the DFG of Li-6 atoms.

Anisotropic sound and shock waves in dipolar Bose-Einstein condensate

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

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

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