Ultracold atoms confined in an optical lattice plus parabolic potential: a closed-form approach

We discuss interacting and non-interacting one dimensional atomic systems trapped in an optical lattice plus a parabolic potential. We show that, in the tight-binding approximation, the non-interacting problem is exactly solvable in terms of Mathieu functions. We use the analytic solutions to study the collective oscillations of ideal bosonic and fermionic ensembles induced by small displacements of the parabolic potential. We treat the interacting boson problem by numerical diagonalization of the Bose-Hubbard Hamiltonian. From analysis of the dependence upon lattice depth of the low-energy excitation spectrum of the interacting system, we consider the problems of "fermionization" of a Bose gas, and the superfluid-Mott insulator transition. The spectrum of the noninteracting system turns out to provide a useful guide to understanding the collective oscillations of the interacting system, throughout a large and experimentally relevant parameter regime.Comment: 19 pages, 15 figures Minor modification were done and new references were adde

Classical and quantum three-dimensional integrable systems with axial symmetry

We study the most general form of a three dimensional classical integrable system with axial symmetry and invariant under the axis reflection. We assume that the three constants of motion are the Hamiltonian, $H$, with the standard form of a kinetic part plus a potential dependent on the position only, the $z$-component of the angular momentum, $L$, and a Hamiltonian-like constant, $\widetilde H$, for which the kinetic part is quadratic in the momenta. We find the explicit form of these potentials compatible with complete integrability. The classical equations of motion, written in terms of two arbitrary potential functions, is separated in oblate spheroidal coordinates. The quantization of such systems leads to a set of two differential equations that can be presented in the form of spheroidal wave equations.Comment: 17 pages, 3 figure

Investigations on T violation and CPT symmetry in the neutral kaon system -- a pedagogical approach --

During the recent years experiments with neutral kaons have yielded remarkably sensitive results which are pertinent to such fundamental phenomena as CPT invariance (protecting causality), time-reversal invariance violation, coherence of wave functions, and entanglement of kaons in pair states. We describe the phenomenological developments and the theoretical conclusions drawn from the experimental material. An outlook to future experimentation is indicated.Comment: 41 pages, 9 figures. See arXiv:hep-ph/0603075 for an enlarged versio

Scalable register initialization for quantum computing in an optical lattice

The Mott insulator state created by loading an atomic Bose-Einstein condensate (BEC) into an optical lattice may be used as a means to prepare a register of atomic qubits in a quantum computer. Such architecture requires a lattice commensurately filled with atoms, which corresponds to the insulator state only in the limit of zero inter-well tunneling. We show that a lattice with spatial inhomogeneity created by a quadratic magnetic trapping potential can be used to isolate a subspace in the center which is impervious to hole-hoping. Components of the wavefunction with more than one atom in any well can be projected out by selective measurement on a molecular photo-associative transition. Maintaining the molecular coupling induces a quantum Zeno effect that can sustain a commensurately filled register for the duration of a quantum computation.Comment: 5 pages, 2 figure

2-Dust : a Dust Radiative Transfer Code for an Axisymmetric System

We have developed a general purpose dust radiative transfer code for an axisymmetric system, 2-Dust, motivated by the recent increasing availability of high-resolution images of circumstellar dust shells at various wavelengths. This code solves the equation of radiative transfer following the principle of long characteristic in a 2-D polar grid while considering a 3-D radiation field at each grid point. A solution is sought through an iterative scheme in which self-consistency of the solution is achieved by requiring a global luminosity constancy throughout the shell. The dust opacities are calculated through Mie theory from the given size distribution and optical properties of the dust grains. The main focus of the code is to obtain insights on (1) the global energetics of dust grains in the shell (2) the 2-D projected morphologies that are strongly dependent on the mixed effects of the axisymmetric dust distribution and inclination angle of the shell. Here, test models are presented with discussion of the results. The code can be supplied with a user-defined density distribution function, and thus, is applicable to a variety of dusty astronomical objects possessing the axisymmetric geometry.Comment: To be published in ApJ, April 2003 issue; 13 pages, 4 tables, 17 figures, 5-page appendix (no figures for the main text included in this preprint). For the complete preprint and code distribution, contact the author

Structure and Feedback in 30 Doradus I: Observations

We have completed a a new optical imaging and spectrophotometric survey of a 140 x 80 pc$^2$ region of 30 Doradus centered on R136, covering key optical diagnostic emission lines including \Ha, \Hb, \Hg, [O III] $\lambda\lambda$4363, 4959, 5007, [N II] $\lambda\lambda$6548, 6584, [S II] $\lambda\lambda$6717, 6731 [S III] $\lambda$6312 and in some locations [S III] $\lambda$9069. We present maps of fluxes and intensity ratios for these lines, and catalogs of isolated ionizing stars, elephant-trunk pillars, and edge-on ionization fronts. The final science-quality spectroscopic data products are available to the public. Our analysis of the new data finds that, while stellar winds and supernovae undoubtedly produce shocks and are responsible for shaping the nebula, there are no global spectral signatures to indicate that shocks are currently an important source of ionization. We conclude that the considerable region covered by our survey is well described by photoionization from the central cluster where the ionizing continuum is dominated by the most massive O stars. We show that if 30 Dor were viewed at a cosmological distance, its integrated light would be dominated by its extensive regions of lower surface-brightness rather than by the bright, eye-catching arcs.Comment: 42 pages, 16 figures, Accepted for publication in ApJ

Non-standard grain properties, dark gas reservoir, and extended submillimeter excess, probed by Herschel in the Large Magellanic Cloud

Context. Herschel provides crucial constraints on the IR SEDs of galaxies, allowing unprecedented accuracy on the dust mass estimates. However, these estimates rely on non-linear models and poorly-known optical properties. Aims. In this paper, we perform detailed modelling of the Spitzer and Herschel observations of the LMC, in order to: (i) systematically study the uncertainties and biases affecting dust mass estimates; and to (ii) explore the peculiar ISM properties of the LMC. Methods. To achieve these goals, we have modelled the spatially resolved SEDs with two alternate grain compositions, to study the impact of different submillimetre opacities on the dust mass. We have rigorously propagated the observational errors (noise and calibration) through the entire fitting process, in order to derive consistent parameter uncertainties. Results. First, we show that using the integrated SED leads to underestimating the dust mass by ≃50% compared to the value obtained with sufficient spatial resolution, for the region we studied. This might be the case, in general, for unresolved galaxies. Second, we show that Milky Way type grains produce higher gas-to-dust mass ratios than what seems possible according to the element abundances in the LMC. A spatial analysis shows that this dilemma is the result of an exceptional property: the grains of the LMC have on average a larger intrinsic submm opacity (emissivity index β ≃ 1.7 and opacity κ_(abs)(160 μm) = 1.6 m^2   kg^(-1)) than those of the Galaxy. By studying the spatial distribution of the gas-to-dust mass ratio, we are able to constrain the fraction of unseen gas mass between ≃10, and ≃100% and show that it is not sufficient to explain the gas-to-dust mass ratio obtained with Milky Way type grains. Finally, we confirm the detection of a 500 μm extended emission excess with an average relative amplitude of ≃15%, varying up to 40%. This excess anticorrelates well with the dust mass surface density. Although we do not know the origin of this excess, we show that it is unlikely the result of very cold dust, or CMB fluctuations

Dust in the bright supernova remnant N49 in the LMC

We investigate the dust associated with the supernova remnant (SNR) N49 in the Large Magellanic Cloud (LMC) as observed with the Herschel Space Observatory. N49 is unusually bright because of an interaction with a molecular cloud along its eastern edge. We have used PACS and SPIRE to measure the far IR flux densities of the entire SNR and of a bright region on the eastern edge of the SNR where the SNR shock is encountering the molecular cloud. Using these fluxes supplemented with archival data at shorter wavelengths, we estimate the dust mass associated with N49 to be about 10 Msun. The bulk of the dust in our simple two-component model has a temperature of 20-30 K, similar to that of nearby molecular clouds. Unfortunately, as a result of the limited angular resolution of Herschel at the wavelengths sampled with SPIRE, the uncertainties are fairly large. Assuming this estimate of the dust mass associated with the SNR is approximately correct, it is probable that most of the dust in the SNR arises from regions where the shock speed is too low to produce significant X-ray emission. The total amount of warm 50-60 K dust is ~0.1 or 0.4 Msun, depending on whether the dust is modeled in terms of carbonaceous or silicate grains. This provides a firm lower limit to the amount of shock heated dust in N49.Comment: accepted by the Astronomy & Astrophysics Lette

Solutions to Maxwell's Equations using Spheroidal Coordinates

Analytical solutions to the wave equation in spheroidal coordinates in the short wavelength limit are considered. The asymptotic solutions for the radial function are significantly simplified, allowing scalar spheroidal wave functions to be defined in a form which is directly reminiscent of the Laguerre-Gaussian solutions to the paraxial wave equation in optics. Expressions for the Cartesian derivatives of the scalar spheroidal wave functions are derived, leading to a new set of vector solutions to Maxwell's equations. The results are an ideal starting point for calculations of corrections to the paraxial approximation

An Extremely Bright Echo Associated With SN 2002hh

We present new, very late-time optical photometry and spectroscopy of the interesting Type II-P supernova, SN 2002hh, in NGC 6946. Gemini/GMOS-N has been used to acquire visible spectra at six epochs between 2004 August and 2006 July, following the evolution of the SN from age 661 to 1358 days. Few optical spectra of Type II supernovae with ages greater than one year exist. In addition, g'r'i' images were acquired at all six epochs. The spectral and photometric evolution of SN 2002hh has been very unusual. Measures of the brightness of this SN, both in the R and I bands as well as in the H-alpha emission flux, show no significant fading over an interval of nearly two years. The most straightforward explanation for this behavior is that the light being measured comes not only from the SN itself but also from an echo off of nearby dust. Echoes have been detected previously around several SNe but these echoes, at their brightest, were ~8 mag below the maximum brightness of the SN. At V~21 mag, the putative echo dominates the light of SN 2002hh and is only ~4 mag below the outburst's peak brightness. There is an estimated 6 magnitudes of total extinction in V towards SN 2002hh. The proposed explanation of a differential echo/SN absorption is inconsistent with the observed BVRI colors.Comment: 24 pages, 6 figures. Accepted for publication in the Ap