Pointwise estimates for the Bergman kernel of the weighted Fock space

We prove upper pointwise estimates for the Bergman kernel of the weighted Fock space of entire functions in $L^2(e^{-2\phi})$ where $\phi$ is a subharmonic function with $\Delta \phi$ a doubling measure. We derive estimates for the canonical solution operator to the inhomogeneous Cauchy-Riemann equation and we characterize the compactness of this operator in terms of $\Delta \phi$

Observation of nonlinear self-trapping of broad beams in defocusing waveguide arrays

We demonstrate experimentally the localization of broad optical beams in periodic arrays of optical waveguides with defocusing nonlinearity. This observation in optics is linked to nonlinear self-trapping of Bose-Einstein-condensed atoms in stationary periodic potentials being associated with the generation of truncated nonlinear Bloch states, existing in the gaps of the linear transmission spectrum. We reveal that unlike gap solitons, these novel localized states can have an arbitrary width defined solely by the size of the input beam while independent of nonlinearity

On the growth of the Bergman kernel near an infinite-type point

We study diagonal estimates for the Bergman kernels of certain model domains in $\mathbb{C}^2$ near boundary points that are of infinite type. To do so, we need a mild structural condition on the defining functions of interest that facilitates optimal upper and lower bounds. This is a mild condition; unlike earlier studies of this sort, we are able to make estimates for non-convex pseudoconvex domains as well. This condition quantifies, in some sense, how flat a domain is at an infinite-type boundary point. In this scheme of quantification, the model domains considered below range -- roughly speaking -- from being ``mildly infinite-type'' to very flat at the infinite-type points.Comment: Significant revisions made; simpler estimates; very mild strengthening of the hypotheses on Theorem 1.2 to get much stronger conclusions than in ver.1. To appear in Math. An

Concept of an ionizing time-domain matter-wave interferometer

We discuss the concept of an all-optical and ionizing matter-wave interferometer in the time domain. The proposed setup aims at testing the wave nature of highly massive clusters and molecules, and it will enable new precision experiments with a broad class of atoms, using the same laser system. The propagating particles are illuminated by three pulses of a standing ultraviolet laser beam, which detaches an electron via efficient single photon-absorption. Optical gratings may have periods as small as 80 nm, leading to wide diffraction angles for cold atoms and to compact setups even for very massive clusters. Accounting for the coherent and the incoherent parts of the particle-light interaction, we show that the combined effect of phase and amplitude modulation of the matter waves gives rise to a Talbot-Lau-like interference effect with a characteristic dependence on the pulse delay time.Comment: 25 pages, 5 figure

Appraising Kirchhoff approximation theory for the scattering of elastic shear waves by randomly rough defects

Rapid and accurate methods, based on the Kirchhoff approximation (KA), are developed to evaluate the scattering of shear waves by rough defects and quantify the accuracy of this approximation. Defect roughness has a strong effect on the reflection of ultrasound, and every rough defect has a different surface, so standard methods of assessing the sensitivity of inspection based on smooth defects are necessarily limited. Accurately resolving rough cracks in non-destructive evaluation (NDE) inspections often requires shear waves since they have higher sensitivity to surface roughness than longitudinal waves. KA models are attractive, since they are rapid to deploy, however they are an approximation and it is important to determine the range of validity for the scattering of ultrasonic shear waves; this range is found here. Good agreement between KA and high fidelity finite element simulations is obtained for a range of incident/scattering angles, and the limits of validity for KA are found to be much stricter than for longitudinal wave incidence; as the correlation length of rough surfaces is reduced to the order of the incident shear wavelength, a combination of multiple scattering and surface wave mode conversion leads to KA predictions diverging from those of the true diffuse scattered fields

Elastic shear wave scattering by randomly rough surfaces

Characterizing cracks within elastic media forms an important aspect of ultrasonic non-destructive evaluation (NDE) where techniques such as time-of-flight diffraction and pulse-echo are often used with the presumption of scattering from smooth, straight cracks. However, cracks are rarely straight, or smooth, and recent attention has focussed upon rough surface scattering primarily by longitudinal wave excitations. We provide a comprehensive study of scattering by incident shear waves, thus far neglected in models of rough surface scattering despite their practical importance in the detection of surface-breaking defects, using modelling, simulation and supporting experiments. The scattering of incident shear waves introduces challenges, largely absent in the longitudinal case, related to surface wave mode-conversion, the reduced range of validity of the Kirchhoff approximation (KA) as compared with longitudinal incidence, and an increased importance of correlation length. The expected reflection from a rough defect is predicted using a statistical model from which, given the angle of incidence and two statistical parameters, the expected reflection amplitude is obtained instantaneously for any scattering angle and length of defect. If the ratio of correlation length to defect length exceeds a critical value, which we determine, there is an explicit dependence of the scattering results on correlation length, and we modify the modelling to find this dependence. The modelling is cross-correlated against Monte Carlo simulations of many different surface profiles, sharing the same statistical parameter values, using numerical simulation via ray models (KA) and finite element (FE) methods accelerated with a GPU implementation. Additionally we provide experimental validations that demonstrate the accuracy of our predictions

Colloquium: Quantum interference of clusters and molecules

We review recent progress and future prospects of matter wave interferometry with complex organic molecules and inorganic clusters. Three variants of a near-field interference effect, based on diffraction by material nanostructures, at optical phase gratings, and at ionizing laser fields are considered. We discuss the theoretical concepts underlying these experiments and the experimental challenges. This includes optimizing interferometer designs as well as understanding the role of decoherence. The high sensitivity of matter wave interference experiments to external perturbations is demonstrated to be useful for accurately measuring internal properties of delocalized nanoparticles. We conclude by investigating the prospects for probing the quantum superposition principle in the limit of high particle mass and complexity.Comment: 19 pages, 13 figures; v2: corresponds to published versio

Two-Particle Interference with Double Twin-Atom Beams

We demonstrate a source for correlated pairs of atoms characterized by two opposite momenta and two spatial modes forming a Bell state only involving external degrees of freedom. We characterize the state of the emitted atom beams by observing strong number squeezing up to -10 dB in the correlated two-particle modes of emission. We furthermore demonstrate genuine two-particle interference in the normalized second-order correlation function $g^{(2)}$ relative to the emitted atoms.Comment: 6 pages, 3 figure

First order superconducting transition near a ferromagnetic quantum critical point

We address the issue of how triplet superconductivity emerges in an electronic system near a ferromagnetic quantum critical point (FQCP). Previous studies found that the superconducting transition is of second order, and Tc is strongly reduced near the FQCP due to pair-breaking effects from thermal spin fluctuations. In contrast, we demonstrate that near the FQCP, the system avoids pair-breaking effects by undergoing a first order transition at a much larger Tc. A second order superconducting transition emerges only at some distance from the FQCP.Comment: 4 pages, 2 figure