Macroscopic dynamics of a trapped Bose-Einstein condensate in the presence of 1D and 2D optical lattices

The hydrodynamic equations of superfluids for a weakly interacting Bose gas are generalized to include the effects of periodic optical potentials produced by stationary laser beams. The new equations are characterized by a renormalized interaction coupling constant and by an effective mass accounting for the inertia of the system along the laser direction. For large laser intensities the effective mass is directly related to the tunneling rate between two consecutive wells. The predictions for the frequencies of the collective modes of a condensate confined by a magnetic harmonic trap are discussed for both 1D and 2D optical lattices and compared with recent experimental data.Comment: 4 pages, 2 postscript figure

Atom trapping and two-dimensional Bose-Einstein condensates in field-induced adiabatic potentials

We discuss a method to create two-dimensional traps as well as atomic shell, or bubble, states for a Bose-Einstein condensate initially prepared in a conventional magnetic trap. The scheme relies on the use of time-dependent, radio frequency-induced adiabatic potentials. These are shown to form a versatile and robust tool to generate novel trapping potentials. Our shell states take the form of thin, highly stable matter-wave bubbles and can serve as stepping-stones to prepare atoms in highly-excited trap eigenstates or to study `collapse and revival phenomena'. Their creation requires gravitational effects to be compensated by applying additional optical dipole potentials. However, in our scheme gravitation can also be exploited to provide a route to two-dimensional atom trapping. We demonstrate the loading process for such a trap and examine experimental conditions under which a 2D condensate may be prepared.Comment: 16 pages, 10 figure

't Hooft-Polyakov Monopoles in an Antiferromagnetic Bose-Einstein Condensate

We show that an antiferromagnetic spin-1 Bose-Einstein condensate, which can for instance be created with Na-23 atoms in an optical trap, has not only singular line-like vortex excitations, but also allows for singular point-like topological excitations, i.e., 't Hooft-Polyakov monopoles. We discuss the static and dynamic properties ofthese monopoles.Comment: Four pages of ReVTeX and 1 postscript figur

Resonant and Non-Resonant Modulated Amplitude Waves for Binary Bose-Einstein Condensates in Optical Lattices

We consider a system of two Gross-Pitaevskii (GP) equations, in the presence of an optical-lattice (OL) potential, coupled by both nonlinear and linear terms. This system describes a Bose-Einstein condensate (BEC) composed of two different spin states of the same atomic species, which interact linearly through a resonant electromagnetic field. In the absence of the OL, we find plane-wave solutions and examine their stability. In the presence of the OL, we derive a system of amplitude equations for spatially modulated states which are coupled to the periodic potential through the lowest-order subharmonic resonance. We determine this averaged system's equilibria, which represent spatially periodic solutions, and subsequently examine the stability of the corresponding solutions with direct simulations of the coupled GP equations. We find that symmetric (equal-amplitude) and asymmetric (unequal-amplitude) dual-mode resonant states are, respectively, stable and unstable. The unstable states generate periodic oscillations between the two condensate components, which is possible only because of the linear coupling between them. We also find four-mode states, but they are always unstable. Finally, we briefly consider ternary (three-component) condensates.Comment: 16 pages, 4 figures (some of which have multiple parts), to appear in Physica D; streamlined paper; added some references and discussion concerning experimental realizations of this work; higher-resolution copies of a couple figures are available on the version of the document downloadable from http://www.math.gatech.edu/~mason

Identification of Extracellular d-Catenin Accumulation for Prostate Cancer Detection

BACKGROUND—Prostate cancer is the second leading cause of cancer death in men, and early detection is essential to reduce mortality and increase survival. δ-Catenin is a unique β-catenin superfamily protein primarily expressed in the brain but is upregulated in human prostatic adenocarcinomas. Despite its close correlation with the disease, it is unclear whether δ-catenin presents the potential in prostate cancer screening because it is an intracellular protein. In this study, we investigated the hypothesis of δ-catenin accumulation in the urine of prostate cancer patients and its potential pathways of excretion into extracellular milieu. METHODS—Prostate cancer cell cultures, human tissue biopsies, and voided urines were characterized to determine extracellular δ-catenin accumulation and co-isolation with exosomes/ prostasomes. RESULTS—We identified δ-catenin in culture media and in the stroma of human prostate cancer tissues. In PC-3 cells in culture, δ-catenin was partially co-localized and co-isolated with raftassociated membrane protein caveolin-1 and glycosylphosphatidylinositol-anchored protein CD59, suggesting its potential excretion into extracellular milieu through exosome/prostasome associated pathways. Interference with endocytic pathway using wortmannin did not block prostasome excretion, but δ-catenin overexpression promoted the extracellular accumulation of caveolin-1. δ- Catenin, caveolin-1, and CD59 were all detected in cell-free human voided urine prostasomes. δ- Catenin immunoreactivity was significantly increased in the urine of prostate cancer patients (p<0.0005). CONCLUSIONS—This study demonstrated, for the first time, the extracellular accumulation of δ-catenin in urine supporting its potential utility for non-invasive prostate cancer detection. Originally published The Prostate, Vol. 69, No. 4, March 1 200

Multicomponent Bright Solitons in F = 2 Spinor Bose-Einstein Condensates

We study soliton solutions for the Gross--Pitaevskii equation of the spinor Bose--Einstein condensates with hyperfine spin F=2 in one-dimension. Analyses are made in two ways: by assuming single-mode amplitudes and by generalizing Hirota's direct method for multi-components. We obtain one-solitons of single-peak type in the ferromagnetic, polar and cyclic states, respectively. Moreover, twin-peak type solitons both in the ferromagnetic and the polar state are found.Comment: 15 pages, 8 figure

Magnetism in a lattice of spinor Bose condensates

We study the ground state magnetic properties of ferromagnetic spinor Bose-Einstein condensates confined in a deep optical lattices. In the Mott insulator regime, the ``mini-condensates'' at each lattice site behave as mesoscopic spin magnets that can interact with neighboring sites through both the static magnetic dipolar interaction and the light-induced dipolar interaction. We show that such an array of spin magnets can undergo a ferromagnetic or anti-ferromagnetic phase transition under the magnetic dipolar interaction depending on the dimension of the confining optical lattice. The ground-state spin configurations and related magnetic properties are investigated in detail

Matter-Wave Solitons in an F=1 Spinor Bose-Einstein Condensate

Following our previous work [J. Ieda, T. Miyakawa, M. Wadati, cond-mat/0404569] on a novel integrable model describing soliton dynamics of an F=1 spinor Bose--Einstein condensate, we discuss in detail the properties of the multi-component system with spin-exchange interactions. The exact multiple bright soliton solutions are obtained for the system where the mean-field interaction is attractive (c_0 < 0) and the spin-exchange interaction is ferromagnetic (c_2 < 0). A complete classification of the one-soliton solution with respect to the spin states and an explicit formula of the two-soliton solution are presented. For solitons in polar state, there exists a variety of different shaped solutions including twin peaks. We show that a "singlet pair" density can be used to distinguish those energetically degenerate solitons. We also analyze collisional effects between solitons in the same or different spin state(s) by computing the asymptotic forms of their initial and final states. The result reveals that it is possible to manipulate the spin dynamics by controlling the parameters of colliding solitons.Comment: 12 pages, 9 figures, to appear in J. Phys. Soc. Jpn. Vol.73 No.11 (2004

Trematodes of the Great Barrier Reef, Australia: emerging patterns of diversity and richness in coral reef fishes

The Great Barrier Reef holds the richest array of marine life found anywhere in Australia, including a diverse and fascinating parasite fauna. Members of one group, the trematodes, occur as sexually mature adult worms in almost all Great Barrier Reef bony fish species. Although the first reports of these parasites were made 100 years ago, the fauna has been studied systematically for only the last 25 years. When the fauna was last reviewed in 1994 there were 94 species known from the Great Barrier Reef and it was predicted that there might be 2,270 in total. There are now 326 species reported for the region, suggesting that we are in a much improved position to make an accurate prediction of true trematode richness. Here we review the current state of knowledge of the fauna and the ways in which our understanding of this fascinating group is changing. Our best estimate of the true richness is now a range, 1,100–1,800 species. However there remains considerable scope for even these figures to be incorrect given that fewer than one-third of the fish species of the region have been examined for trematodes. Our goal is a comprehensive characterisation of this fauna, and we outline what work needs to be done to achieve this and discuss whether this goal is practically achievable or philosophically justifiable

Evolution of the RNA polymerase II C-terminal domain

In recent years a great deal of biochemical and genetic research has focused on the C-terminal domain (CTD) of the largest subunit (RPB1) of DNA-dependent RNA polymerase II. This strongly conserved domain of tandemly repeated heptapeptides has been linked functionally to important steps in the initiation and processing of mRNA transcripts in both animals and fungi. Although they are absolutely required for viability in these organisms, C-terminal tandem repeats do not occur in RPB1 sequences from diverse eukaryotic taxa. Here we present phylogenetic analyses of RPB1 sequences showing that canonical CTD heptads are strongly conserved in only a subset of eukaryotic groups, all apparently descended from a single common ancestor. Moreover, eukaryotic groups in which the most complex patterns of ontogenetic development occur are descended from this CTD-containing ancestor. Consistent with the results of genetic and biochemical investigations of CTD function, these analyses suggest that the enhanced control over RNA polymerase II transcription conveyed by acquired CTD protein interactions was an important step in the evolution of intricate patterns of gene expression that are a hallmark of large, developmentally complex eukaryotic organisms. Originally published Proc Natl Acad Sci, Vol. 99, No. 9, Apr 200