Numerical study of the spherically symmetric Gross-Pitaevskii equation in two space dimensions

The Gross-Pitaevskii equation for Bose-Einstein condensation (BEC) in two space dimensions under the action of a harmonic oscillator trap potential for bosonic atoms with attractive and repulsive interparticle interactions was numerically studied by using time-dependent and time-independent approaches. In both cases, numerical difficulty appeared for large nonlinearity. Nonetheless, the solution of the time-dependent approach exhibited intrinsic oscillation with time iteration which is independent of space and time steps used in discretization.

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)

Interference pattern with a dark center from two atoms driven by a coherent laser field

In a recent paper Meyer and Yeoman [Phys. Rev. Lett. 79, 2650 (1997)] have shown that the resonance fluorescence from two atoms placed in a cavity and driven by an incoherent field can produce an interference pattern with a dark center. We study the fluorescence from two coherently driven atoms in free space and show that this system can also produce an interference pattern with a dark center. This happens when the atoms are in nonequivalent positions in the driving: field, i.e., the atoms experience different intensities and phases of the driving field. We discuss the role of the interatomic interactions in this process and find that the interference pattern with a dark center results from the participation of the antisymmetric state in the dynamics of the driven two-atom system.

Interference pattern with a dark center in resonance fluorescence from two atoms driven by a squeezed vacuum field

We study the resonance fluorescence from two interacting atoms driven by a squeezed vacuum field and show that this system produces an interference pattern with a dark center. We discuss the role of the interatomic interactions in this process and find that the interference pattern results from an unequal population of the symmetric and antisymmetric states of the two-atom system. We also identify intrinsically nonclassical effects versus classical squeezed field effects, (C) 1998 Elsevier Science B.V. All rights reserved.

Theory of a mode-locked atom laser with toroidal geometry

We consider a possible technique for mode locking an atom laser, based on the generation of a dark soliton in a ring-shaped Bose-Einstein condensate, with repulsive atomic interactions. The soliton is a kink, with angular momentum per particle equal to (h) over bar /2. It emerges naturally when the condensate is stirred at the soliton velocity and cleansed with a periodic out coupler. The result is a replicating coherent field inside the atom laser, stabilized by topology. We give a numerical demonstration of the generation and stabilization of the soliton.

Colloidal assembly on magnetically vibrated stripes

We investigate the collective organization of paramagnetic colloidal particles externally driven above the periodic stripes of a uniaxial ferrimagnetic garnet film. An external field modulation induces vibration of the stripe walls and produces random motion of the particles. Defects in the stripe pattern break the symmetry of the potential and favor particle nucleation into large clusters above a critical density. Mismatch between particle size and pattern wavelength generates assemblies with different morphological order. At even higher field strengths, repulsive dipolar interactions between the particles induce cluster melting. We propose a novel approach to generate and externally control a variety of colloidal assemblies.

Magnetic Resonance Experiments with Atomic Hydrogen

In this thesis three experiments with atomic hydrogen (H) at low temperatures T<1 K are presented. Experiments were carried out with two- (2D) and three-dimensional (3D) H gas, and with H atoms trapped in solid H2 matrix. The main focus of this work is on interatomic interactions, which have certain specific features in these three systems considered. A common feature is the very high density of atomic hydrogen, the systems are close to quantum degeneracy. Short range interactions in collisions between atoms are important in gaseous H. The system of H in H₂ differ dramatically because atoms remain fixed in the H₂ lattice and properties are governed by long-range interactions with the solid matrix and with H atoms. The main tools in our studies were the methods of magnetic resonance, with electron spin resonance (ESR) at 128 GHz being used as the principal detection method. For the first time in experiments with H in high magnetic fields and at low temperatures we combined ESR and NMR to perform electron-nuclear double resonance (ENDOR) as well as coherent two-photon spectroscopy. This allowed to distinguish between different types of interactions in the magnetic resonance spectra. Experiments with 2D H gas utilized the thermal compression method in homogeneous magnetic field, developed in our laboratory. In this work methods were developed for direct studies of 3D H at high density, and for creating high density samples of H in H₂. We measured magnetic resonance line shifts due to collisions in the 2D and 3D H gases. First we observed that the cold collision shift in 2D H gas composed of atoms in a single hyperfine state is much smaller than predicted by the mean-field theory. This motivated us to carry out similar experiments with 3D H. In 3D H the cold collision shift was found to be an order of magnitude smaller for atoms in a single hyperfine state than that for a mixture of atoms in two different hyperfine states. The collisional shifts were found to be in fair agreement with the theory, which takes into account symmetrization of the wave functions of the colliding atoms. The origin of the small shift in the 2D H composed of single hyperfine state atoms is not yet understood. The measurement of the shift in 3D H provides experimental determination for the difference of the scattering lengths of ground state atoms. The experiment with H atoms captured in H2 matrix at temperatures below 1 K originated from our work with H gas. We found out that samples of H in H2 were formed during recombination of gas phase H, enabling sample preparation at temperatures below 0.5 K. Alternatively, we created the samples by electron impact dissociation of H₂ molecules in situ in the solid. By the latter method we reached highest densities of H atoms reported so far, 3.5(5)x10¹⁹ cm^-3. The H atoms were found to be stable for weeks at temperatures below 0.5 K. The observation of dipolar interaction effects provides a verification for the density measurement. Our results point to two different sites for H atoms in H2 lattice. The steady-state nuclear polarizations of the atoms were found to be non-thermal. The possibility for further increase of the impurity H density is considered. At higher densities and lower temperatures it might be possible to observe phenomena related to quantum degeneracy in solid.

Formation et propriétés des cristaux colloïdaux issus de l’auto-assemblage de microsphères de polymère

Le besoin pour des biocapteurs à haute sensibilité mais simples à préparer et à utiliser est en constante augmentation, notamment dans le domaine biomédical. Les cristaux colloïdaux formés par des microsphères de polymère ont déjà prouvé leur fort potentiel en tant que biocapteurs grâce à l’association des propriétés des polymères et à la diffraction de la lumière visible de la structure périodique. Toutefois, une meilleure compréhension du comportement de ces structures est primordiale avant de pouvoir développer des capteurs efficaces et polyvalents. Ce travail propose d’étudier la formation et les propriétés des cristaux colloïdaux résultant de l’auto-assemblage de microsphères de polymère en milieu aqueux. Dans ce but, des particules avec différentes caractéristiques ont été synthétisées et caractérisées afin de corréler les propriétés des particules et le comportement de la structure cristalline. Dans un premier temps, des microsphères réticulées de polystyrène anioniques et cationiques ont été préparées par polymérisation en émulsion sans tensioactif. En variant la quantité de comonomère chargé, le chlorure de vinylbenzyltriméthylammonium ou le sulfonate styrène de sodium, des particules de différentes tailles, formes, polydispersités et charges surfaciques ont été obtenues. En effet, une augmentation de la quantité du comonomère ionique permet de stabiliser de façon électrostatique une plus grande surface et de diminuer ainsi la taille des particules. Cependant, au-dessus d’une certaine concentration, la polymérisation du comonomère en solution devient non négligeable, provoquant un élargissement de la distribution de taille. Quand la polydispersité est faible, ces microsphères chargées, même celles non parfaitement sphériques, peuvent s’auto-assembler et former des cristaux colloïdaux diffractant la lumière visible. Il semble que les répulsions électrostatiques créées par les charges surfaciques favorisent la formation de la structure périodique sur un grand domaine de concentrations et améliorent leur stabilité en présence de sel. Dans un deuxième temps, le besoin d’un constituant stimulable nous a orientés vers les structures cœur-écorce. Ces microsphères, synthétisées en deux étapes par polymérisation en émulsion sans tensioactif, sont formées d’un cœur de polystyrène et d’une écorce d’hydrogel. Différents hydrogels ont été utilisés afin d’obtenir des propriétés différentes : le poly(acide acrylique) pour sa sensibilité au pH, le poly(N-isopropylacrylamide) pour sa thermosensibilité, et, enfin, le copolymère poly(N-isopropylacrylamide-co-acide acrylique) donnant une double sensibilité. Ces microsphères forment des cristaux colloïdaux diffractant la lumière visible à partir d’une certaine concentration critique et pour un large domaine de concentrations. D’après les changements observés dans les spectres de diffraction, les stimuli ont un impact sur la structure cristalline mais l’amplitude de cet effet varie avec la concentration. Ce comportement semble être le résultat des changements induits par la transition de phase volumique sur les interactions entre particules plutôt qu’une conséquence du changement de taille. Les interactions attractives de van der Waals et les répulsions stériques sont clairement affectées par la transition de phase volumique de l’écorce de poly(N-isopropylacrylamide). Dans le cas des microsphères sensibles au pH, les interactions électrostatiques sont aussi à considérer. L’effet de la concentration peut alors être mis en relation avec la portée de ces interactions. Finalement, dans l’objectif futur de développer des biocapteurs de glucose, les microsphères cœur-écorce ont été fonctionnalisées avec l’acide 3-aminophénylboronique afin de les rendre sensibles au glucose. Les effets de la fonctionnalisation et de la complexation avec le glucose sur les particules et leur empilement périodique ont été examinés. La structure cristalline est visiblement affectée par la présence de glucose, même si le mécanisme impliqué reste à élucider.

Synthesis and characterisation of novel nitrogen and fluorine containing spirobifluorene derivatives for electronic applications and crystal engineering

Among organic materials, spirobifluorene derivatives represent a very attractive class of materials for electronic devices. These compounds have high melting points, glass transitions temperatures and morphological stability, which makes these materials suitable for organic electronic applications. In addition, some of spirobifluorenes can form porous supramolecular associations with significant volumes available for the inclusion of guests. These molecular associations based on the spirobifluorenes are noteworthy because they are purely molecular analogues of zeolites and other microporous solids, with potential applications in separation, catalysis, sensing and other areas.

Conformational preferences for some 2-substituted N-methoxy-N-methylacetamides through spectroscopic and theoretical studies

The analysis of the IR carbonyl band of the 2-substituted N-methoxy-N-methylacetamides Y-CH(2)C(O)-N(OMe)Me (Y = F1, OMe 2, OPh 3, Cl 4), supported by B3LYP/6-311++G(3df, 3pd) calculations along with the NBO analysis for 1-4, indicated the existence of cis-gauche conformers i.e. (c) and (g) for 1 and 3, (c(1), c(2)) and (g(1), g(2)) for 2, and (c) and (g(1), g(2)) for 4. In the gas phase, the g conformer population prevails over the c one, for 1 and 3, the (c(1) + c(2)) population prevails over the (g(1) + g(2)) one for 2, and the (g(1) + g(2)) conformer population is more abundant than (c) one for 4. In n-hexane solution, the cis conformer is more abundant for 1-3. The occurrence of Fermi resonance in the nu(CO) region, in n-hexane, precludes the estimative of relative populations of the (c, g(1), g(2)) conformers for 4. The SCI-PCM calculations agree with the solvent effect on the nu(CO) band component relative intensities for 1-3. NBO analysis showed that the n(N) -> pi.(CO), orbital interaction is the main factor which stabilizes the gauche (g, g(1), g(2)) conformers for 1-4 into a larger extent relative to the cis (c, c(1), c(2)) ones. The n(y) -> pi(.)(Co,) sigma(C-Y) -> pi.(CO,) pi(CO) -> sigma(C-Y) and 7co orbital interactions still contribute, but into a minor extent for the stabilization of the gauche conformers relative to the cis ones. The existence of some pyramidalization at the nitrogen atom of the Weinreb amides 1-4 is responsible for the occurrence of Y(delta)-(4)center dot center dot center dot O(delta)-(9) and Y(delta)-(4)center dot center dot center dot N(delta)-(7) short contacts in the gauche (g, g(1), g(2)) conformers, which originates strong repulsive Coulombic interactions, acting in opposition to the large orbital stabilization of the gauche conformer with respect to the cis one. Therefore, a delicate balance of the Coulombic and orbital interactions seems to be responsible for the observed stabilization of the gauche (g, g(1), g(2)) and cis (c, c(1), c(2)) conformers, both in the gas phase and in the solution for 1-4. However, the cis conformer predominance, in non polar solvents, for the 2-substituted N-methoxy-N-methyl acetamides 1-3, bearing in a first raw (fluorine and oxygen) atoms, is in the opposite direction to the gauche conformer preference for the corresponding 2-substituted N,N-dialkyl-acetamides. (C) 2010 Elsevier B.V. All rights reserved.

Formation of bright solitons and soliton trains in a fermion-fermion mixture by modulational instability

We employ a time- dependent mean- field- hydrodynamic model to study the generation of bright solitons in a degenerate fermion - fermion mixture in a cigar- shaped geometry using variational and numerical methods. Due to a strong Pauli- blocking repulsion among identical spin- polarized fermions at short distances there cannot be bright solitons for repulsive interspecies interactions. Employing a linear stability analysis we demonstrate the formation of stable solitons due to modulational instability of a constant-amplitude solution of the model equations for a sufficiently attractive interspecies interaction. We perform a numerical stability analysis of these solitons and also demonstrate the formation of soliton trains by jumping the effective interspecies interaction from repulsive to attractive. These fermionic solitons can be formed and studied in laboratory with present technology.

Three-dimensional solitons in cross-combined linear and nonlinear optical lattices

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

Toward the Application of Three-Dimensional Approach to Few-body Atomic Bound States

The first step toward the application of an effective non partial wave (PW) numerical approach to few-body atomic bound states has been taken. The two-body transition amplitude which appears in the kernel of three-dimensional Faddeev-Yakubovsky integral equations is calculated as function of two-body Jacobi momentum vectors, i.e. as a function of the magnitude of initial and final momentum vectors and the angle between them. For numerical calculation the realistic interatomic interactions HFDHE2, HFD-B, LM2M2 and TTY are used. The angular and momentum dependence of the fully off-shell transition amplitude is studied at negative energies. It has been numerically shown that, similar to the nuclear case, the transition amplitude exhibits a characteristic angular behavior in the vicinity of He-4 dimer pole.

Numerical study of the coupled time-dependent Gross-Pitaevskii equation: Application to Bose-Einstein condensation

The Bose-Einstein condensate of several types of trapped bosons at ultralow temperature was described using the coupled time dependent Gross-Pitaevskii equation. Both the stationary and time evolution problems were analyzed using this approach. The ground state stationary wave functions were found to be sharply peaked near the origin for attractive interatomic interaction for larger nonlinearity while for a repulsive interatomic interaction the wave function extends over a larger region of space.

Stabilizing an attractive Bose-Einstein condensate by driving a surface collective mode

Bose-Einstein condensates with attractive interatomic interactions undergo collective collapse beyond a critical number. We show theoretically that if the low-lying collective modes of the condensate are excited, the radial breathing mode further destabilizes the condensate. Remarkably, excitation of the quadrupolar surface mode causes the condensate to become more stable, imparting quasiangular momentum to it. A significantly larger number of atoms may then occupy the condensate. Efforts are under way for the experimental realization of these effects. ©2001 The American Physical Society.