Dynamics of bright matter-wave solitons in a Bose-Einstein condensate with inhomogeneous scattering length

We investigate dynamical effects of a bright soliton in Bose-Einstein condensed (BEC) systems with local and smooth space variations of the two-body atomic scattering length. It includes a discussion about the possible observation of a new type of standing nonlinear atomic matter wave in cigar-type traps. A rich dynamics is observed in the interaction between the soliton and an inhomogeneity. By considering an analytical time-dependent variational approach and also full numerical simulation of one-dimensional and three-dimensional Gross-Pitaevskii equations, we study processes such as trapping, reflection and transmission of the bright matter soliton due to the impurity. We also derive conditions for the collapse of the bright solitary wave, considering a quasi-one-dimensional BEC with attractive local inhomogeneity.

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.

Periodic waves and solitons in a nonlinear fibre with resonant impurities

We shall consider a coupled nonlinear Schrodinger equation- Bloch system of equations describing the propagation of a single pulse through a nonlinear dispersive waveguide in the presence of resonances; this could be, for example, a doped optical fibre. By making use of the integrability of the dynamic equations, we shall apply the finite-gap integration method to obtain periodic solutions for this system. Next, we consider the problem of the formation of solitons at a sharp front pulse and, by means of the Whitham modulational theory, we derive the amplitude and velocity of the largest soliton.

Free expansion of fermionic dark solitons in a boson-fermion mixture

We use a time-dependent dynamical mean-field-hydrodynamic model to study the formation of fermionic dark solitons in a trapped degenerate Fermi gas mixed with a Bose-Einstein condensate in a harmonic as well as a periodic optical-lattice potential. The dark soliton with a 'notch' in the probability density with a zero at the minimum is simulated numerically as a nonlinear continuation of the first vibrational excitation of the linear mean-field-hydrodynamic equations, as suggested recently for pure bosons. We study the free expansion of these dark solitons as well as the consequent increase in the size of their central notch and discuss the possibility of experimental observation of the notch after free expansion.

Dynamics of quasi-one-dimensional bright and vortex solitons of a dipolar Bose-Einstein condensate with repulsive atomic interaction

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

Gap solitons in fermion superfluids

We consider a dynamical model of a superfluid Fermi gas in the Bardeen-Cooper-Schrieffer regime trapped in a periodic optical lattice (OL) potential. The model is based on an equation for complex order parameter phi of the superfluid, which is derived from the relevant energy density and includes a self-repulsive term similar to phi(7/3). By means of the variational approximation (VA) and numerical simulations, we find families of stable one- and two-dimensional (I D and 2D) gap solitons (GSs) in this model. Chiefly, they are compact objects trapped in a single cell of the OL. Families of stable even and odd bound states of these GSs are also found in one dimension. A 3D GS family is constructed too, but solely within the framework of the VA. In the linear limit, the VA predicts an almost exact position of the left edge of the first band-gap in the OL-induced spectrum. The full VA provides an accurate description of families of I D and 2D fundamental GSs. We also demonstrate that a I D GS can be safely transported by an OL moving at a moderate velocity. (C) 2009 IMACS. Published by Elsevier B.V. All rights reserved.

Dipolar Bose-Einstein condensate soliton on a two-dimensional optical lattice

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

Effective potential of two coupled binary matter wave bright solitons with spatially modulated nonlinearity

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

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.

Soliton dynamics at an interface between a uniform medium and a nonlinear optical lattice

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

Symbiotic gap and semigap solitons in Bose-Einstein condensates

Using the variational approximation and numerical simulations, we study one-dimensional gap solitons in a binary Bose-Einstein condensate trapped in an optical-lattice potential. We consider the case of interspecies repulsion, while the intraspecies interaction may be either repulsive or attractive. Several types of gap solitons are found: symmetric or asymmetric; unsplit or split, if centers of the components coincide or separate; intragap (with both chemical potentials falling into a single band gap) or intergap, otherwise. In the case of the intraspecies attraction, a smooth transition takes place between solitons in the semi-infinite gap, those in the first finite band gap, and semigap solitons (with one component in a band gap and the other in the semi-infinite gap).

Gap solitons in superfluid boson-fermion mixtures

Using coupled equations for the bosonic and fermionic order parameters, we construct families of gap solitons (GSs) in a nearly one-dimensional Bose-Fermi mixture trapped in a periodic optical-lattice (OL) potential, the boson and fermion components being in the states of the Bose-Einstein condensation and Bardeen-Cooper-Schrieffer superfluid, respectively. Fundamental GSs are compact states trapped, essentially, in a single cell of the lattice. Full families of such solutions are constructed in the first two band gaps of the OL-induced spectrum, by means of variational and numerical methods, which are found to be in good agreement. The families include both intragap and intergap solitons, with the chemical potentials of the boson and fermion components falling in the same or different band gaps, respectively. Nonfundamental states, extended over several lattice cells, are constructed too. The GSs are stable against strong perturbations.

An intercomparison of bio-optical techniques for detecting dominant phytoplankton size class from satellite remote sensing

Satellite remote sensing of ocean colour is the only method currently available for synoptically measuring wide-area properties of ocean ecosystems, such as phytoplankton chlorophyll biomass. Recently, a variety of bio-optical and ecological methods have been established that use satellite data to identify and differentiate between either phytoplankton functional types (PFTs) or phytoplankton size classes (PSCs). In this study, several of these techniques were evaluated against in situ observations to determine their ability to detect dominant phytoplankton size classes (micro-, nano- and picoplankton). The techniques are applied to a 10-year ocean-colour data series from the SeaWiFS satellite sensor and compared with in situ data (6504 samples) from a variety of locations in the global ocean. Results show that spectral-response, ecological and abundance-based approaches can all perform with similar accuracy. Detection of microplankton and picoplankton were generally better than detection of nanoplankton. Abundance-based approaches were shown to provide better spatial retrieval of PSCs. Individual model performance varied according to PSC, input satellite data sources and in situ validation data types. Uncertainty in the comparison procedure and data sources was considered. Improved availability of in situ observations would aid ongoing research in this field. (C) 2010 Elsevier B.V. All rights reserved.

Finite element analysis of anisotropic optical waveguide with arbitrary index profile

This work presents the application of a scalar finite element formulation for Ex (TE-like) modes in anisotropic planar and channel waveguides with diagonal permittivity tensor, diffused in both transversal directions. This extended formulation considers explicitly both the variations of the refractive index and their spatial derivates inside of each finite element. Dispersion curves for Ex modes in planar and channel waveguides are shown, and the results compared with solutions obtained by other formulations.

The dynamics of bright matter wave solitons in a quasi one-dimensional Bose-Einstein condensate with a rapidly varying trap

The dynamics of a bright matter wave soliton in a quasi one-dimensional Bose-Einstein condensate (BEC) with a periodically rapidly varying time trap is considered. The governing equation is based on averaging the fast modulations of the Gross-Pitaevskii (GP) equation. This equation has the form of a GP equation with an effective potential of a more complicated structure than an unperturbed trap. In the case of an inverted (expulsive) quadratic trap corresponding to an unstable GP equation, the effective potential can be stable. For the bounded space trap potential it is showed that bifurcation exists, i.e. the single-well potential bifurcates to the triple-well effective potential. The stabilization of a BEC cloud on-site state in the temporary modulated optical lattice is found. This phenomenon is analogous to the Kapitza stabilization of an inverted pendulum. The analytical predictions of the averaged GP equation are confirmed by numerical simulations of the full GP equation with rapid perturbations.