Density correlations and analog dynamical Casimir emission of Bogoliubov phonons in modulated atomic Bose-Einstein condensates

We present a theory of the density correlations that appear in an atomic Bose-Einstein condensate as a consequence of the emission of correlated pairs of Bogoliubov phonons by a time-dependent atom-atom scattering length. This effect can be considered as a condensed matter analog of the dynamical Casimir effect of quantum field theory. Different regimes as a function of the temporal shape of the modulation are identified and a simple physical picture of the phenomenon is discussed. Analytical expressions for the density correlation function are provided for the most significant limiting cases. This theory is able to explain some unexpected features recently observed in numerical studies of analog Hawking radiation from acoustic black holes.     

Intensity fluctuations of spherical acoustic waves propagating through thermal turbulence*

The intensity fluctuations of acoustic waves that propagate through thermal turbulence are investigated under well controlled laboratory conditions. Two heated grids in air are placed horizontally in a large anechoic room and the mixing of the free convection plumes above them generates a homogeneous isotropic random thermal field. The spectrum of refractive index fluctuations is accurately described by a modified von Karman model which takes into account the entire spectrum of turbulence. Experimental data are obtained by varying both the frequency of the spherical wave and the distance of propagation. In this paper we concentrate on the variance of the normalized intensity fluctuations and on their probability distributions. These measurements cover all the regimes from weak scattering to strong scattering including the peak of the intensity variance. Experimental values of the scintillation index are compared with classical theoretical predictions and also with the results of recent numerical simulations. The classical probability density functions (log-normal, exponential, I-K) are tested against the measured probability distributions. The generalized gamma distribution, which varies smoothly from log-normal to exponential as a function of two parameters, appears m represent the experimental data for a very large range of scattering conditions.     

Modeling of neutral-atom scattering at the surface of a crystal for the case of grazing incidence

The features of the angular distributions of accelerated neutral atoms at grazing angles of incidence on the Al(001) surface are studied using the mathematical modeling method. The interaction of accelerated atoms with crystal-lattice atoms and the electronic properties and atomic structure of the Al(001) surface are calculated using the electron-density-functional method. The angular distributions of scattered atoms are modeled by taking into account their interaction with several atomic layers in the crystal lattice and atomic displacements during thermal oscillations. The influence of crystal surface-layer relaxation on rainbow scattering, i.e., the difference between the distances of planes on the surface and in the volume, is established. The possibilities of using the effect of rainbow scattering to study the structural features of a crystal surface are discussed.     

Hilbert Space Methods in Quantum Mechanics,by Werner O. Amrein

This article, which is in two parts, surveys the wide application of scattering experiments to studies of the structures of solids and liquids. Part 1 outlines the general principles, and shows how the angular distribution of a scattered radiation is related by Fourier transform to correlations in the distributions of electrons and nuclei in the scattering target, citing the use of X-rays and of neutrons in determining time-averaged density distributions. Part 2 (to appear in the next issue) discusses the time-dependent aspects of the distributions for solids and liquids, including superfluid helium, and also of dynamical distributions of magnetization (or angular momentum) density, and examines the present limitations and future possibilities of scattering experiments.     

The specular component of light scattering and the charac- terization of the height distribution for random surfaces

The relations between the specular reflection component of the intensity scattered by random surfaces and the height distributions of the surfaces are analyzed theoretically. In the extraction of the height distribution, both the phase and the amplitude of the specular wave are required. The measured specular intensity data versus the perpendicular component of the wave vector are used for the retrieval of the phase distribution of the specular wave, in which the Ger-chberg-Saxton iterative algorithm is employed, and the characterization of the height distribution of random surfaces is accomplished. In the experiment, two samples with Gaussian and quasi-two level height distributions, respectively, are practically measured and the results of the height probability density function obtained by light scattering method are in good accordance with those by atomic force microscopy. The method of this paper is of important significance for the characterizations and studies of random surfaces.     

Identification of statistical regimes and crossovers in coherent random laser emission

We measure intensity statistics and identify statistical regimes and crossovers in random lasers based on nonresonant feedback. A single parameter extracted from an α-stable Levy fit is used to characterize the intensity distributions in all regimes. Measurements made over a range of scattering strengths, excitation energies, and sample sizes enable us to demarcate three regimes of intensity statistics and the corresponding crossovers. An initial subthreshold Gaussian regime abruptly transits into a Levy regime at the random lasing threshold, which is followed by a continuous gradual crossover toward a second Gaussian regime. We find that the prominence of the Levy regime depends upon the sample size.     

Measurement of one-particle correlations and momentum distributions for trapped 1D gases

Van Hove's theory of scattering of probe particles by a macroscopic target is generalized so as to relate the differential cross section for atomic ejection via stimulated Raman transitions to one-particle momentum-time correlations and momentum distributions of 1D trapped gases. This method is well suited to probing the longitudinal momentum distributions of 1D gases in situ, and examples are given for bosonic and fermionic atoms.     

Experimental determination of distributions of soot particle diameter and number density by emission and scattering techniques

A diagnostics method was presented that uses emission and scattering techniques to simultaneously determine the distributions of soot particle diameter and number density in hydrocarbon flames. Two manta G-504 C cameras were utilized for the scattering measurement, with consideration of the attenuation effect in the flames according to corresponding absorption coefficients. Distributions of soot particle diameter and number density were simultaneously determined using the measured scattering coefficients and absorption coefficients under multiple wavelengths already measured with a SOC701 V hyper-spectral imaging device, according to the Mie scattering theory. A flame was produced using an axisymmetric laminar diffusion flame burner with 194 mL/min ethylene and 284 L/min air, and distributions of particle diameter and number density for the flame were presented. Consequently, the distributions of soot volume fraction were calculated using these two parameters as well, which were in good agreement with the results calculated according to the Rayleigh approximation,demonstrating that the proposed diagnostic method is capable of simultaneous determination of the distributions of soot particle diameter and number density.     

Modulation and thermal stability of hydrogen in amorphous silicon

Hydrogenated amorphous silicon can be obtained by reactive evaporation of silicon under a flow of hydrogen atoms. By modulating the pressure of hydrogen, it is possible to prepare multilayers of type Si/Si:H/Si/Si:H/ … with thicknesses of bilayers less than 90 Å. Low-angle X-ray scattering shows diffraction peaks corresponding only to the modulation of atomic density, but low-angle neutron scattering permits to see the modulation of the isotopes hydrogen and deuterium. The thermal stability of the silicon atomic density modulation and of the hydrogen modulation is discussed.     

Barrier-wave-internal-wave interference and airy minima in 16O16+O elastic scattering

Taking 16O+16O elastic scattering at 124 MeV as an example, we show that a barrier-wave-internal-wave decomposition of the elastic scattering amplitude provides valuable information on the light heavy-ion interaction and complements the more conventional nearside-farside decomposition. In particular, we show that the Airy minima present in the angular distributions are due to a barrier-wave-internal-wave interference mechanism, which sheds additional light on the exceptional transparency displayed by some light heavy-ion scattering systems. Extension of these ideas to other fields, like atomic and molecular collision physics, could prove rewarding.     

Wave mixing of optical pulses and bose-einstein condensates

We investigate theoretically the four-wave mixing of optical and matter waves resulting from the scattering of a short light pulse off an atomic Bose-Einstein condensate, as recently demonstrated by D. Schneble et al. [Science 300, 475 (2003)]]. We show that atomic "pair production" from the condensate results in the generation of both forward- and backward-propagating matter waves. These waves are characterized by different phase-matching conditions, resulting in different angular distributions and temporal evolutions.     

The bases of authority for our symbols and units

This article, which is in two parts, surveys the wide application of scattering experiments to studies of the structures of solids and liquids. Part 1 showed how the angular distribution of a scattered beam of photons or neutrons is related by Fourier transform to the space and time-dependent distribution of electrons and nuclei in the scattering target. The use of X-rays and of neutrons in determining time-averaged density distributions was examined. Part 2 discusses the time-dependent aspects of the distributions for solids and liquids, including superfluid helium, and also of dynamical distributions of magnetism (or angular momentum) density, and examines the present limitations and future possibilities of scattering experiments.     

Optimization of measurement angles for soot aggregate sizing by elastic light scattering,through design-of-experiment theory

In multiangle elastic light scattering (MAELS) experiments, the morphology of aerosolized particles is inferred by shining collimated radiation through the aerosol and then measuring the scattered light intensity over a set of angles. In the case of soot-laden-aerosols MAELS can, in principle, be used to recover the size distribution of soot aggregates, although this involves solving an ill-posed inverse problem. This paper presents a design-of-experiment methodology for identifying the set of angles that maximizes the information content of the angular scattering measurements, thereby minimizing the ill-posedness of the underlying inverse problem. While the optimized angles highlight the physical significance of the scattering regimes, they do not improve the accuracy of size distributions reconstructed from simulated experimental data.     

Variational calculation of the angular width of the multiple scattering distribution in foil transmission

A simple formula is derived for calculating the angular width of multiple scattering distributions for atomic particles traversing thin foils. The universal result is obtained by applying the variational method on standard multiple scattering theory. This procedure can be carried through in a straight-forward way, thus saving lengthy series expansions and Fourier transforms. In the case of power cross sections exact analytical expressions can be obtained. A remarkably good agreement is found between our calculation and previous theories, as well as with results from our computer simulations.     

Die kinetischen Eigenschaften der Elektronen des anisothermen homogenen stationären Neon-Plasmas im Ionisierungsgradbereich von 10−9 bis 10−2

The time dependence of the spectral and spatial energy density of the fluorescence radiation of an atomic system generated by the resonance scattering of an intense laser pulse was calculated. Particularly the influence of the duration and the intensity of the incident laser pulse and of the atomic relaxation constants upon the fluorescence radiation has been studied.     

Interferometric determination of the s and d-wave scattering amplitudes in 87Rb

We demonstrate an interference method to determine the low-energy elastic scattering amplitudes of a quantum gas. We linearly accelerate two ultracold atomic clouds up to energies of 1.2 mK and observe the collision halo by direct imaging in free space. From the interference between s- and d- partial waves in the differential scattering pattern we extract the corresponding phase shifts. The method does not require knowledge of the atomic density. This allows us to infer accurate values for the s- and d-wave scattering amplitudes from the zero-energy limit up to the first Ramsauer minimum using only the van der Waals C6 coefficient as theoretical input. For the 87Rb triplet potential, the method reproduces the scattering length with an accuracy of 6%.     

Multiple scattering and neutralization aspects of low energy noble gas ions incident on a Cu (110) crystal

Experiments have been done with 1 keV Ne⁺ ions bombarding a Cu (110) single crystal in a (111) plane. From the measured energy spectra of the scattered ions the minimum and maximum scattering angles for multiple scattering on the surface are determined. These minimum and maximum scattering angles were also calculated using a computer model. The parameters for an interatomic potential function between ion and metal atom are determined by comparison of the experimental and calculated scattering angles. A neutralization model for an energetic ion at an atomic surface is given. The reliability of this model is tested by comparison of the results of computer calculations and the measured peak intensity distributions as a function of the scattering angle.