Potential Harmonics Expansion Method for Trapped Interacting Bosons : Inclusion of Two-Body Correlation

We study a system of $A$ identical interacting bosons trapped by an external field by solving ab initio the many-body Schroedinger equation. A complete solution by using, for example, the traditional hyperspherical harmonics (HH) basis develops serious problems due to the large degeneracy of HH basis, symmetrization of the wave function, calculation of the matrix elements, etc. for large $A$. Instead of the HH basis, here we use the "potential harmonics" (PH) basis, which is a subset of HH basis. We assume that the contribution to the orbital and grand orbital [in $3(A-1)$-dimensional space of the reduced motion] quantum numbers comes only from the interacting pair. This implies inclusion of two-body correlations only and disregard of all higher-body correlations. Such an assumption is ideally suited for the Bose-Einstein condensate (BEC), which is extremely dilute. Unlike the $(3A-4)$ hyperspherical variables in HH basis, the PH basis involves only three {\it{active}} variables. It drastically reduces the number of coupled equations and calculation of the potential matrix becomes tremendously simplified, as it involves integrals over only three variables for any $A$. One can easily incorporate realistic atom-atom interactions in a straight forward manner. We study the ground and excited state properties of the condensate for both attractive and repulsive interactions for various particle number.Comment: 36 pages, 7 included figures, plain late

Condenser-free contrast methods for transmitted-light microscopy

Phase contrast microscopy allows the study of highly transparent yet detail-rich specimens by producing intensity contrast from phase objects within the sample. Presented here is a generalized phase contrast illumination schema in which condenser optics are entirely abrogated, yielding a condenser- free yet highly effective method of obtaining phase contrast in transmitted-light microscopy. A ring of light emitting diodes (LEDs) is positioned within the light-path such that observation of the objective back focal plane places the il- luminating ring in appropriate conjunction with the phase ring. It is demonstrated that true Zernike phase contrast is obtained, whose geometry can be flexibly manipulated to provide an arbitrary working distance between illuminator and sample. Condenser-free phase contrast is demonstrated across a range of magnifications (4–100×), numerical apertures (0.13–1.65NA) and conventional phase positions. Also demonstrated is condenser-free darkfield microscopy as well as combinatorial contrast including Rheinberg illumination and simultaneous, colour-contrasted, brightfield, darkfield and Zernike phase contrast. By providing enhanced and arbitrary working space above the preparation, a range of concurrent imaging and electrophysiological techniques will be technically facilitated. Condenser-free phase contrast is demonstrated in conjunction with scanning ion conductance microscopy (SICM), using a notched ring to admit the scanned probe. The compact, versatile LED illumination schema will further lend itself to novel next-generation transmitted-light microscopy designs. The condenser-free illumination method, using rings of independent or radially-scanned emitters, may be exploited in future in other electromagnetic wavebands, including X-rays or the infrared

A comparative evaluation of interest point detectors and local descriptors for visual SLAM

Abstract In this paper we compare the behavior of different interest points detectors and descriptors under the conditions needed to be used as landmarks in vision-based simultaneous localization and mapping (SLAM). We evaluate the repeatability of the detectors, as well as the invariance and distinctiveness of the descriptors, under different perceptual conditions using sequences of images representing planar objects as well as 3D scenes. We believe that this information will be useful when selecting an appropriat

Remarkable enhancement in crystalline perfection, second harmonic generation efficiency, optical transparency, and laser damage threshold in potassium dihydrogen phosphate crystals by L-threonine doping

Effect of L-threonine (LT) doping on crystalline perfection, second harmonic generation (SHG) efficiency, optical transparency, and laser damage threshold (LDT) in potassium dihydrogen phosphate (KDP) crystals grown by slow evaporation solution technique (SEST) has been investigated. The influence of doping on growth rate and morphology of the grown crystals has also been studied. Powder x-ray diffraction data confirms the crystal structure of KDP and shows a systematic variation in intensity of diffraction peaks in correlation with morphology due to varying LT concentration. No extra phase formation was observed which is further confirmed by Fourier transform Raman (FT-Raman) studies. High-resolution x-ray diffraction curves indicate that crystalline perfection has been improved to a great extent at low concentrations with a maximum perfection at 1 mol % doping. At higher concentrations (5 to 10 mol %), it is slightly reduced due to excess incorporation of dopants at the interstitial sites of the crystalline matrix. LDT has been increased considerably with increase in doping concentration, whereas SHG efficiency was found to be maximum at 1 mol % in correlation with crystalline. The optical transparency for doped crystals has been increased as compared to that of pure KDP with a maximum value at 1 mol % doping

Effect of a Physical Phase Plate on Contrast Transfer in an Aberration-Corrected Transmission Electron Microscope

In this theoretical study we analyze contrast transfer of weak-phase objects in a transmission electron microscope, which is equipped with an aberration corrector (Cs-corrector) in the imaging lens system and a physical phase plate in the back focal plane of the objective lens. For a phase shift of pi/2 between scattered and unscattered electrons induced by a physical phase plate, the sine-type phase contrast transfer function is converted into a cosine-type function. Optimal imaging conditions could theoretically be achieved if the phase shifts caused by the objective lens defocus and lens aberrations would be equal zero. In reality this situation is difficult to realize because of residual aberrations and varying, non-zero local defocus values, which in general result from an uneven sample surface topography. We explore the conditions - i.e. range of Cs-values and defocus - for most favourable contrast transfer as a function of the information limit, which is only limited by the effect of partial coherence of the electron wave in Cs-corrected transmission electron microscopes. Under high-resolution operation conditions we find that a physical phase plate improves strongly low- and medium-resolution object contrast, while improving tolerance to defocus and Cs-variations, compared to a microscope without a phase plate

Proton-3^{3}He elastic scattering at low energies

We present new accurate measurements of the differential cross section $\sigma(\theta)$ and the proton analyzing power $A_{y}$ for proton-$^{3}$He elastic scattering at various energies. A supersonic gas jet target has been employed to obtain these low energy cross section measurements. The $\sigma(\theta)$ distributions have been measured at $E_{p}$ = 0.99, 1.59, 2.24, 3.11, and 4.02 MeV. Full angular distributions of $A_{y}$ have been measured at $E_{p}$ = 1.60, 2.25, 3.13, and 4.05 MeV. This set of high-precision data is compared to four-body variational calculations employing realistic nucleon-nucleon (NN) and three-nucleon (3N) interactions. For the unpolarized cross section the agreement between the theoretical calculation and data is good when a $3N$ potential is used. The comparison between the calculated and measured proton analyzing powers reveals discrepancies of approximately 50% at the maximum of each distribution. This is analogous to the existing ``$A_{y}$ Puzzle'' known for the past 20 years in nucleon-deuteron elastic scattering.Comment: 22 pages, 9 figures, to be published in Physical Review C, corrected reference 4

Wideband THz time domain spectroscopy based on optical rectification and electro-optic sampling

We present an analytical model describing the full electromagnetic propagation in a THz time-domain spectroscopy (THz-TDS) system, from the THz pulses via Optical Rectification to the detection via Electro Optic-Sampling. While several investigations deal singularly with the many elements that constitute a THz-TDS, in our work we pay particular attention to the modelling of the time-frequency behaviour of all the stages which compose the experimental set-up. Therefore, our model considers the following main aspects: (i) pump beam focusing into the generation crystal; (ii) phase-matching inside both the generation and detection crystals; (iii) chromatic dispersion and absorption inside the crystals; (iv) Fabry-Perot effect; (v) diffraction outside, i.e. along the propagation, (vi) focalization and overlapping between THz and probe beams, (vii) electro-optic sampling. In order to validate our model, we report on the comparison between the simulations and the experimental data obtained from the same set-up, showing their good agreement

Watching a superfluid untwist itself: Recurrence of Rabi oscillations in a Bose-Einstein condensate

The order parameter of a condensate with two internal states can continuously distort in such a way as to remove twists that have been imposed along its length. We observe this effect experimentally in the collapse and recurrence of Rabi oscillations in a magnetically trapped, two-component Bose-Einstein condensate of ^87Rb

Soft X-Ray Projection Lithography Using a 1-1 Ring Field Optical-System

An iridium-coated Offner 1:1 ring field camera has been used to carry out projection lithography using 42 nm light from an undulator in the vacuum ultra violet storage ring at Brookhaven National Laboratory. Near-diffraction-limited resolution has been obtained showing features as small as 0.2-mu-m within a 2 mm x 0.25 mm image field. Images of both transmission and reflection masks have been obtained. The impact of source coherence on imagery has been investigated. Hydrocarbon contamination problems experienced in this photon energy range have been investigated and possible solutions are suggested