The Saito-Kurokawa lifting and Darmon points

Let E_{/_\Q} be an elliptic curve of conductor $Np$ with $p\nmid N$ and let $f$ be its associated newform of weight 2. Denote by $f_\infty$ the $p$-adic Hida family passing though $f$, and by $F_\infty$ its $\Lambda$-adic Saito-Kurokawa lift. The $p$-adic family $F_\infty$ of Siegel modular forms admits a formal Fourier expansion, from which we can define a family of normalized Fourier coefficients $\{\widetilde A_T(k)\}_T$ indexed by positive definite symmetric half-integral matrices $T$ of size $2\times 2$. We relate explicitly certain global points on $E$ (coming from the theory of Stark-Heegner points) with the values of these Fourier coefficients and of their $p$-adic derivatives, evaluated at weight $k=2$.Comment: 14 pages. Title change

Minimally-destructive detection of magnetically-trapped atoms using frequency-synthesised light

We present a technique for atomic density measurements by the off-resonant phase-shift induced on a two-frequency, coherently-synthesised light beam. We have used this scheme to measure the column density of a magnetically trapped atom cloud and to monitor oscillations of the cloud in real time by making over a hundred non-destructive local density measurments. For measurements using pulses of 10,000-100,000 photons lasting ~10 microsecond, the precision is limited by statistics of the photons and the photodiode avalanche. We explore the relationship between measurement precision and the unwanted loss of atoms from the trap and introduce a figure of merit that characterises it. This method can be used to probe the density of a BEC with minimal disturbance of its phase.Comment: Submitted to New Journal of Physic

A single atom detector integrated on an atom chip: fabrication, characterization and application

We describe a robust and reliable fluorescence detector for single atoms that is fully integrated into an atom chip. The detector allows spectrally and spatially selective detection of atoms, reaching a single atom detection efficiency of 66%. It consists of a tapered lensed single-mode fiber for precise delivery of excitation light and a multi-mode fiber to collect the fluorescence. The fibers are mounted in lithographically defined holding structures on the atom chip. Neutral 87Rb atoms propagating freely in a magnetic guide are detected and the noise of their fluorescence emission is analyzed. The variance of the photon distribution allows to determine the number of detected photons / atom and from there the atom detection efficiency. The second order intensity correlation function of the fluorescence shows near-perfect photon anti-bunching and signs of damped Rabi-oscillations. With simple improvements one can boost the detection efficiency to > 95%.Comment: 24 pages, 11 figure

Averages of Fourier coefficients of Siegel modular forms and representation of binary quadratic forms by quadratic forms in four variables

Let $-d$ be a a negative discriminant and let $T$ vary over a set of representatives of the integral equivalence classes of integral binary quadratic forms of discriminant $-d$. We prove an asymptotic formula for $d \to \infty$ for the average over $T$ of the number of representations of $T$ by an integral positive definite quaternary quadratic form and obtain results on averages of Fourier coefficients of linear combinations of Siegel theta series. We also find an asymptotic bound from below on the number of binary forms of fixed discriminant $-d$ which are represented by a given quaternary form. In particular, we can show that for growing $d$ a positive proportion of the binary quadratic forms of discriminant $-d$ is represented by the given quaternary quadratic form.Comment: v5: Some typos correcte

Experiments on a videotape atom chip: fragmentation and transport studies

This paper reports on experiments with ultra-cold rubidium atoms confined in microscopic magnetic traps created using a piece of periodically-magnetized videotape mounted on an atom chip. The roughness of the confining potential is studied with atomic clouds at temperatures of a few microKelvin and at distances between 30 and 80 microns from the videotape-chip surface. The inhomogeneities in the magnetic field created by the magnetized videotape close to the central region of the chip are characterized in this way. In addition, we demonstrate a novel transport mechanism whereby we convey cold atoms confined in arrays of videotape magnetic micro-traps over distances as large as ~ 1 cm parallel to the chip surface. This conveying mechanism enables us to survey the surface of the chip and observe potential-roughness effects across different regions.Comment: 29 pages, 22 figures

Phytochrome interacting factors 4 and 5 control seedling growth in changing light conditions by directly controlling auxin signaling.

Plant growth is strongly influenced by the presence of neighbors that compete for light resources. In response to vegetational shading shade-intolerant plants such as Arabidopsis display a suite of developmental responses known as the shade-avoidance syndrome (SAS). The phytochrome B (phyB) photoreceptor is the major light sensor to mediate this adaptive response. Control of the SAS occurs in part with phyB, which controls protein abundance of phytochrome-interacting factors 4 and 5 (PIF4 and PIF5) directly. The shade-avoidance response also requires rapid biosynthesis of auxin and its transport to promote elongation growth. The identification of genome-wide PIF5-binding sites during shade avoidance revealed that this bHLH transcription factor regulates the expression of a subset of previously identified SAS genes. Moreover our study suggests that PIF4 and PIF5 regulate elongation growth by controlling directly the expression of genes that code for auxin biosynthesis and auxin signaling components

An integrated atom-photon junction

Photonic chips that integrate guides, switches, gratings and other components, process vast amounts of information rapidly on a single device. A new branch of this technology becomes possible if the light is coupled to cold atoms in a junction of small enough cross section, so that small numbers of photons interact appreciably with the atoms. Cold atoms are among the most sensitive of metrological tools and their quantum nature also provides a basis for new information processing methods. Here we demonstrate a photonic chip which provides multiple microscopic junctions between atoms and photons. We use the absorption of light at a junction to reveal the presence of one atom on average. Conversely, we use the atoms to probe the intensity and polarisation of the light. Our device paves the way for a new type of chip with interconnected circuits of atoms and photons.Comment: 5 pages, 4 figure. Submitted to Nature Photonic