Quantum-field dynamics of expanding and contracting Bose-Einstein condensates

We analyze the dynamics of quantum statistics in a harmonically trapped Bose-Einstein condensate, whose two-body interaction strength is controlled via a Feshbach resonance. From an initially non-interacting coherent state, the quantum field undergoes Kerr squeezing, which can be qualitatively described with a single mode model. To render the effect experimentally accessible, we propose a homodyne scheme, based on two hyperfine components, which converts the quadrature squeezing into number squeezing. The scheme is numerically demonstrated using a two-component Hartree-Fock-Bogoliubov formalism.Comment: 9 pages, 4 figure

A search on Dirac equation

The solutions, in terms of orthogonal polynomials, of Dirac equation with analytically solvable potentials are investigated within a novel formalism by transforming the relativistic equation into a Schrodinger like one. Earlier results are discussed in a unified framework and certain solutions of a large class of potentials are given.Comment: 9 page

Interaction of matter-wave gap solitons in optical lattices

We study mobility and interaction of gap solitons in a Bose-Einstein condensate (BEC) confined by an optical lattice potential. Such localized wavepackets can exist only in the gaps of the matter-wave band-gap spectrum and their interaction properties are shown to serve as a measure of discreteness imposed onto a BEC by the lattice potential. We show that inelastic collisions of two weakly localized near-the-band-edge gap solitons provide simple and effective means for generating strongly localized in-gap solitons through soliton fusion.Comment: 12 pages, 7 figure

Relativistic shape invariant potentials

Dirac equation for a charged spinor in electromagnetic field is written for special cases of spherically symmetric potentials. This facilitates the introduction of relativistic extensions of shape invariant potential classes. We obtain the relativistic spectra and spinor wavefunctions for all potentials in one of these classes. The nonrelativistic limit reproduces the usual Rosen-Morse I & II, Eckart, Poschl-Teller, and Scarf potentials.Comment: Corrigendum: The last statement above equation (1) is now corrected and replaced by two new statement

Dynamical formation and interaction of bright solitary waves and solitons in the collapse of Bose-Einstein condensates with attractive interactions

We model the dynamics of formation of multiple, long-lived, bright solitary waves in the collapse of Bose-Einstein condensates with attractive interactions as studied in the experiment of Cornish et al. [Phys. Rev. Lett. 96 (2006) 170401]. Using both mean-field and quantum field simulation techniques, we find that while a number of separated wave packets form as observed in the experiment, they do not have a repulsive \pi phase difference that has been previously inferred. We observe that the inclusion of quantum fluctuations causes soliton dynamics to be predominantly repulsive in one dimensional simulations independent of their initial relative phase. However, indicative three-dimensional simulations do not support this conclusion and in fact show that quantum noise has a negative impact on bright solitary wave lifetimes. Finally, we show that condensate oscillations, after the collapse, may serve to deduce three-body recombination rates, and that the remnant atom number may still exceed the critical number for collapse for as long as three seconds independent of the relative phases of the bright solitary waves.Comment: 14 pages, 5 figure

Maternal stress during pregnancy and neurodevelopmental outcomes of children during the first 2 years of life

AIM: A growing body of literature documents associations between maternal stress in pregnancy and child development, but findings across studies are often inconsistent. The aim of this study was to estimate the association between exposure to different kinds of prenatal stress and child psychomotor development. METHODS: The study population consisted of 372 mother-child pairs from Polish Mother and Child Cohort. The analysis was restricted to the women who worked at least 1 month during pregnancy period. Maternal psychological stress during pregnancy was assessed based on: the Subjective Work Characteristics Questionnaire, Perceived Stress Scale and Social Readjustment Rating Scale. The level of satisfaction with family functioning and support was evaluated by APGAR Family Scale. Child psychomotor development was assessed at the 12th and 24th months of age by Bayley Scales of Infant and Toddler Development. RESULTS: Negative impact on child cognitive development at the age of two was observed for the Perceived Stress Scale (β = -0.8; P = 0.01) and the Social Readjustment Rating Scale (β = -0.4; P = 0.03) after adjusting for the variety of confounders. Occupational stress, as well as satisfaction with family functioning, was not significantly associated with child psychomotor development (P > 0.05). CONCLUSIONS: The study supports the findings that prenatal exposure to maternal stress is significantly associated with decreased child cognitive functions. In order to further understand and quantify the effects of prenatal stress on child neurodevelopment further studies are needed. This will be important for developing interventions that provide more assistance to pregnant women, including emotional support or help to manage psychological stress

Quantum switches and quantum memories for matter-wave lattice solitons

We study the possibility of implementing a quantum switch and a quantum memory for matter wave lattice solitons by making them interact with "effective" potentials (barrier/well) corresponding to defects of the optical lattice. In the case of interaction with an "effective" potential barrier, the bright lattice soliton experiences an abrupt transition from complete transmission to complete reflection (quantum switch) for a critical height of the barrier. The trapping of the soliton in an "effective" potential well and its release on demand, without loses, shows the feasibility of using the system as a quantum memory. The inclusion of defects as a way of controlling the interactions between two solitons is also reported

Charged particle production in the Pb+Pb system at 158 GeV/c per nucleon

Charged particle multiplicities from high multiplicity central interactions of 158 GeV/nucleon Pb ions with Pb target nuclei have been measured in the central and far forward projectile spectator regions using emulsion chambers. Multiplicities are significantly lower than predicted by Monte Carlo simulations. We examine the shape of the pseudorapidity distribution and its dependence on centrality in detail.Comment: 17 pages text plus 12 figures in postscript 12/23/99 -- Add TeX version of sourc

Generalized Morse Potential: Symmetry and Satellite Potentials

We study in detail the bound state spectrum of the generalized Morse potential~(GMP), which was proposed by Deng and Fan as a potential function for diatomic molecules. By connecting the corresponding Schr\"odinger equation with the Laplace equation on the hyperboloid and the Schr\"odinger equation for the P\"oschl-Teller potential, we explain the exact solvability of the problem by an $so(2,2)$ symmetry algebra, and obtain an explicit realization of the latter as $su(1,1) \oplus su(1,1)$. We prove that some of the $so(2,2)$ generators connect among themselves wave functions belonging to different GMP's (called satellite potentials). The conserved quantity is some combination of the potential parameters instead of the level energy, as for potential algebras. Hence, $so(2,2)$ belongs to a new class of symmetry algebras. We also stress the usefulness of our algebraic results for simplifying the calculation of Frank-Condon factors for electromagnetic transitions between rovibrational levels based on different electronic states.Comment: 23 pages, LaTeX, 2 figures (on request). one LaTeX problem settle