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.

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).

Symmetry breaking in a localized interacting binary Bose-Einstein condensate in a bichromatic optical lattice

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

Self-trapping of a Fermi superfluid in a double-well potential in the Bose-Einstein-condensate-unitarity crossover

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

Localization of a Bose-Einstein-condensate vortex in a bichromatic optical lattice

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

First Measurement of Bose-Einstein Correlations in Proton-Proton Collisions at root s=0.9 and 2.36 TeV at the LHC

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dipolar Bose-Einstein condensates with large scattering length

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

Dipolar Bose-Einstein condensate in a ring or in a shell

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

Mixing, demixing, and structure formation in a binary dipolar Bose-Einstein condensate

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

Measurement of Bose-Einstein correlations in pp collisions at root s=0.9 and 7 TeV

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Solitons in Bose-Einstein condensates trapped in a double-well potential

We investigate, analytically and numerically, families of bright solitons in a system of two linearly coupled nonlinear Schrodinger/Gross-Pitaevskii equations, describing two Bose-Einstein condensates trapped in an asymmetric double-well potential, in particular, when the scattering lengths in the condensates have arbitrary magnitudes and opposite signs. The solitons are found to exist everywhere where they are permitted by the dispersion law. Using the Vakhitov-Kolokolov criterion and numerical methods, we show that, except for small regions in the parameter space, the solitons are stable to small perturbations. Some of them feature self-trapping of almost all the atoms in the condensate with no atomic interaction or weak repulsion is coupled to the self-attractive condensate. An unusual bifurcation is found, when the soliton bifurcates from the zero solution with vanishing amplitude and width simultaneously diverging but at a finite number of atoms in the soliton. By means of numerical simulations, it is found that, depending on values of the parameters and the initial perturbation, unstable solitons either give rise to breathers or completely break down into incoherent waves (radiation). A version of the model with the self-attraction in both components, which applies to the description of dual-core fibers in nonlinear optics, is considered too, and new results are obtained for this much studied system. (C) 2003 Elsevier B.V. All rights reserved.

The BCS-Bose crossover theory

We contrast four distinct versions of the BCS-Bose statistical crossover theory according to the form assumed for the electron-number equation that accompanies the BCS gap equation. The four versions correspond to explicitly accounting for two-hole-(2h) as well as two-electron-(2e) Cooper pairs (CPs), or both in equal proportions, or only either kind. This follows from a recent generalization of the Bose-Einstein condensation (GBEC) statistical theory that includes not boson-boson interactions but rather 2e- and also (without loss of generality) 2h-CPs interacting with unpaired electrons and holes in a single-band model that is easily converted into a two-band model. The GBEC theory is essentially an extension of the Friedberg-Lee 1989 BEC theory of superconductors that excludes 2h-CPs. It can thus recover, when the numbers of 2h- and 2e-CPs in both BE-condensed and non-condensed states are separately equal, the BCS gap equation for all temperatures and couplings as well as the zero-temperature BCS (rigorous-upper-bound) condensation energy for all couplings. But ignoring either 2h- or 2e-CPs it can do neither. In particular, only half the BCS condensation energy is obtained in the two crossover versions ignoring either kind of CPs. We show how critical temperatures T-c from the original BCS-Bose crossover theory in 2D require unphysically large couplings for the Cooper/BCS model interaction to differ significantly from the T(c)s of ordinary BCS theory (where the number equation is substituted by the assumption that the chemical potential equals the Fermi energy). (c) 2007 Published by Elsevier B.V.

Bose-Einstein correlations in W-pair decays

Bose-Einstein correlations are studied in semileptonic (WW → qq̄lv) and fully hadronic (WW → qq̄qq̄) W-pair decays with the ALEPH detector at LEP at centre-of-mass energies of 172, 183 and 189 GeV. They are compared with those made at the Z peak after correction for the different flavour compositions. A Monte Carlo model of Bose-Einstein correlations based on the JETSET hadronization scheme was tuned to the Z data and reproduces the correlations in the WW → qq̄lv events. The same Monte Carlo reproduces the correlations in the WW → qq̄qq̄ channel assuming independent fragmentation of the two W's. A variant of this model with Bose-Einstein correlations between decay products of different W's is disfavoured. (C) 2000 Published by Elsevier Science B.V.

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.

Coherent atomic oscillations and resonances between coupled Bose-Einstein condensates with time-dependent trapping potential

The atomic tunneling between two tunnel-coupled Bose-Einstein condensates (BECs) in a double-well time-dependent trap was studied. For the slowly varying trap, synchronization of oscillations of the trap with oscillations of the relative population was predicted. Using the Melnikov approach, the appearance of the chaotic oscillations in the tunneling phenomena between the condensates was confirmed.