Creating exotic condensates via quantum-phase-revival dynamics in engineered lattice potentials

In the field of ultracold atoms in optical lattices a plethora of phenomena governed by the hopping energy $J$ and the interaction energy $U$ have been studied in recent years. However, the trapping potential typically present in these systems sets another energy scale and the effects of the corresponding time scale on the quantum dynamics have rarely been considered. Here we study the quantum collapse and revival of a lattice Bose-Einstein condensate (BEC) in an arbitrary spatial potential, focusing on the special case of harmonic confinement. Analyzing the time evolution of the single-particle density matrix, we show that the physics arising at the (temporally) recurrent quantum phase revivals is essentially captured by an effective single particle theory. This opens the possibility to prepare exotic non-equilibrium condensate states with a large degree of freedom by engineering the underlying spatial lattice potential.Comment: 9 pages, 6 figure

Random sequential adsorption of shrinking or spreading particles

We present a model of one-dimensional irreversible adsorption in which particles once adsorbed immediately shrink to a smaller size or expand to a larger size. Exact solutions for the fill factor and the particle number variance as a function of the size change are obtained. Results are compared with approximate analytical solutions.Comment: 9 pages, 8 figure

A causal look into the quantum Talbot effect

A well-known phenomenon in both optics and quantum mechanics is the so-called Talbot effect. This near field interference effect arises when infinitely periodic diffracting structures or gratings are illuminated by highly coherent light or particle beams. Typical diffraction patterns known as quantum carpets are then observed. Here the authors provide an insightful picture of this nonlocal phenomenon as well as its classical limit in terms of Bohmian mechanics, also showing the causal reasons and conditions that explain its appearance. As an illustration, theoretical results obtained from diffraction of thermal He atoms by both N-slit arrays and weak corrugated surfaces are analyzed and discussed. Moreover, the authors also explain in terms of what they call the Talbot-Beeby effect how realistic interaction potentials induce shifts and distortions in the corresponding quantum carpets.Comment: 12 pages, 6 figure

Electron interferometry with nano-gratings

We present an electron interferometer based on near-field diffraction from two nanostructure gratings. Lau fringes are observed with an imaging detector, and revivals in the fringe visibility occur as the separation between gratings is increased from 0 to 3 mm. This verifies that electron beams diffracted by nanostructures remain coherent after propagating farther than the Talbot length $z_T = 2d^2/\lambda$ = 1.2 mm, and hence is a proof of principle for the function of a Talbot-Lau interferometer for electrons. Distorted fringes due to a phase object demonstrates an application for this new type of electron interferometer.Comment: 4 pgs, 6 figure

PT-Symmetric Talbot Effects

We show that complex PT-symmetric photonic lattices can lead to a new class of self-imaging Talbot effects. For this to occur, we find that the input field pattern, has to respect specific periodicities which are dictated by the symmetries of the system. While at the spontaneous PT-symmetry breaking point, the image revivals occur at Talbot lengths governed by the characteristics of the passive lattice, at the exact phase it depends on the gain and loss parameter thus allowing one to control the imaging process.Comment: 5 pages, 3 figure

An electron Talbot interferometer

The Talbot effect, in which a wave imprinted with transverse periodicity reconstructs itself at regular intervals, is a diffraction phenomenon that occurs in many physical systems. Here we present the first observation of the Talbot effect for electron de Broglie waves behind a nanofabricated transmission grating. This was thought to be difficult because of Coulomb interactions between electrons and nanostructure gratings, yet we were able to map out the entire near-field interference pattern, the "Talbot carpet", behind a grating. We did this using a Talbot interferometer, in which Talbot interference fringes from one grating are moire'-filtered by a 2nd grating. This arrangement has served for optical, X-ray, and atom interferometry, but never before for electrons. Talbot interferometers are particularly sensitive to distortions of the incident wavefronts, and to illustrate this we used our Talbot interferometer to measure the wavefront curvature of a weakly focused electron beam. Here we report how this wavefront curvature demagnified the Talbot revivals, and we discuss applications for electron Talbot interferometers.Comment: 5 pages, 5 figures, updated version with abstrac

Electromagnetically induced Talbot effect

By modulating transmission function of a weak probe field via a strong control standing wave, an electromagnetically induced grating can be created in the probe channel. Such a nonmaterial grating may lead to self-imaging of ultra-cold atoms or molecules in the Fresnel near-field regime. This work may offer a nondestructive and lensless way to image ultra-cold atoms or molecules.Comment: submitte

Factorization of Numbers with the temporal Talbot effect: Optical implementation by a sequence of shaped ultrashort pulses

We report on the successful operation of an analogue computer designed to factor numbers. Our device relies solely on the interference of classical light and brings together the field of ultrashort laser pulses with number theory. Indeed, the frequency component of the electric field corresponding to a sequence of appropriately shaped femtosecond pulses is determined by a Gauss sum which allows us to find the factors of a number

The homeobox gene CDX2 in colorectal carcinoma: a genetic analysis

Accumulation of mutations in tumour suppressor genes and oncogenes has been proposed to underlie the initiation and progression of sporadic colorectal cancer (CRC). Evidence is accumulating to suggest that the caudal homeobox gene CDX2 is implicated in the pathogenesis of CRC. The CDX2 transcription factor is expressed in intestinal epithelium and is markedly down-regulated in colon tumours. Furthermore, Cdx2 heterozygous null mice develop multiple intestinal tumours. In this present study, we have investigated CDX2 as a potential candidate gene for sporadic CRC by a thorough search of all exons and exon/intron boundaries for DNA polymorphisms and rare variants in a panel of CRC tumours. 6 polymorphisms were identified and the haplotypes determined. In addition two rare variants were found, one of which was only identified in DNA from a CRC case. Loss of heterozygosity was observed in 3 out of 28 informative CRC cases. A possible association between particular haplotypes and tumour progression was also suggested by the data. In addition a preliminary analysis of the relative expression of CDX2 alleles in tumour/normal tissue suggested some variation in the levels, however further analysis is required before any conclusions can be drawn. While CDX2 mutations predisposing to sporadic CRC have not been identified, this study has established that loss of CDX2 contributes towards the progression of some sporadic CRC tumours. © 2001 Cancer Research Campaign http://www.bjcancer.co

EFFICIENT MODULAR IMPLEMENTATION OF BRANCH-AND-BOUND ALGORITHMS *

This paper demonstrates how branch-and-bound algorithms can be modularized to obtain implementation efficiencies. For the manager, this advantage can be used to obtain faster implementation of algorithm results; for the scientist, it allows efficiencies in the construction of similar algorithms with different search and addressing structures for the purpose of testing to find a preferred algorithm. The demonstration in part is achieved by showing how the computer code of a central module of logic can be transported between different algorithms that have the same search strategy. Modularizations of three common searches (the best-bound search and two variants of the last-in-first-out search) with two addressing methods are detailed and contrasted. Using four assembly line balancing algorithms as examples, modularization is demonstrated and the search and addressing methods are contrasted. The application potential of modularization is broad and includes linear programming-based integer programming. Benefits and disadvantages of modularization are discussed. Computational results demonstrate the viability of the method.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75538/1/j.1540-5915.1988.tb00251.x.pd