The quantum acousto-optic effect in Bose-Einstein condensate

We investigate the interaction between a single mode light field and an elongated cigar shaped Bose-Einstein condensate (BEC), subject to a temporal modulation of the trap frequency in the tight confinement direction. Under appropriate conditions, the longitudinal sound like waves (Faraday waves) in the direction of weak confinement acts as a dynamic diffraction grating for the incident light field analogous to the acousto-optic effect in classical optics. The change in the refractive index due to the periodic modulation of the BEC density is responsible for the acousto-optic effect. The dynamics is characterised by Bragg scattering of light from the matter wave Faraday grating and simultaneous Bragg scattering of the condensate atoms from the optical grating formed due to the interference between the incident light and the diffracted light fields. Varying the intensity of the incident laser beam we observe the transition from the acousto-optic effect regime to the atomic Bragg scattering regime, where Rabi oscillations between two momentum levels of the atoms are observed. We show that the acousto-optic effect is reduced as the atomic interaction is increased.     

Diffuse scattering from dodecagonal quasicrystals

General formulae for thermal diffuse scattering from quasicrystals are applied to the case of dodecagonal quasicrystals from corresponding elasticity theory. Contours of constant diffuse scattering intensity are illustrated. Unlike ordinary crystals, shapes of isointensity contours are much more complicated and vary even among the collinear Bragg spots. Diffuse scattering patterns in the plane perpendicular to a given zone axis are associated with corresponding specific elastic constants. Information about elastic constants can be extracted from quantitative analysis of diffuse scattering patterns. Received 7 December 1998 and Received in final form 12 March 1999     

Uncovering flux line correlations in superconductors by reverse monte carlo refinement of neutron scattering data

We describe the use of reverse Monte Carlo refinement to extract structural information from angle-resolved data of a Bragg peak. Starting with small-angle neutron scattering data, the positional order of an ensemble of flux lines in superconducting Nb is revealed. We discuss the uncovered correlation functions in the light of topical theories, in particular, the "Bragg glass" paradigm.     

Acoustic scattering from a thermally driven buoyant plume revisited

Far-field weak scattering theory is applied to the case of high-frequency broad-bandwidth acoustic scattering from a thermally generated buoyant plume in a controlled laboratory environment. To first order, the dominant scattering mechanism is thermally driven sound-speed variations that are related to temperature deviations from ambient. As a result, the received complex acoustic scattering is a measure of the one-component three-dimensional Fourier transform of the temperature difference field measured at the Bragg wave number. The Bragg wave number vector is the difference between the scattered and incident wave vectors. Solving for its magnitude yields the Bragg scattering condition; this is the Fourier component of the plume variability that produces scattering. Results are presented for multistatic scattering from unstable and turbulent plumes using a parallel scattering geometry. The data justify application of the far-field weak scattering theory to the present case of a thermal plume. As a consequence, quantitative results on medium variability can be inferred using high-frequency broad-bandwidth acoustic scattering. Particular attention is given to the role of anisotropy of the variability of the scattering field in determining the validity of far-field Bragg scattering.     

Phase-sensitive detection of bragg scattering at 1D optical lattices

We report on the observation of Bragg scattering at 1D atomic lattices. Cold atoms are confined by optical dipole forces at the antinodes of a standing wave generated by the two counterpropagating modes of a laser-driven high-finesse ring cavity. By heterodyning the Bragg-scattered light with a reference beam, we obtain detailed information on phase shifts imparted by the Bragg scattering process. Being deep in the Lamb-Dicke regime, the scattered light is not broadened by the motion of individual atoms.     

Second-order grazing-angle scattering in uniform wide holographic gratings

Grazing-angle scattering (GAS) is a type of Bragg scattering in slanted wide periodic gratings. It occurs when the diffracted order satisfying the Bragg condition (scattered wave) propagates at a grazing angle to the grating boundaries. Previous research has been concerned only with first-order GAS, which has been shown to be a highly unusual type of scattering characterised by a strong resonant increase of amplitudes of the scattered and incident waves in the grating. In this paper, a rigorous numerical study of second-order GAS is presented for the case of bulk TE electromagnetic waves in planar holographic gratings. A highly unusual pattern of strong resonances in the grating, which is strongly different from that for first-order GAS, is predicted, described, and discussed. Physical interpretations of the predicted results are presented. In particular, a special new type of eigenmodes in a slanted wide periodic grating with large amplitude is predicted. These eigenmodes are shown to be guided by the grating alone without any conventional guiding effect in the structure. The typical field structure in such eigenmodes is investigated and discussed. Received: 16 September 2002 / Revised version: 4 November 2002 / Published online: 22 January 2003 RID="*" ID="*"Corresponding author. Fax: +61-7/3864-9079, E-mail: d.pile@osa.org     

Bragg scattering of cooper pairs in an ultracold Fermi gas

We present a theoretical treatment of Bragg scattering of a degenerate Fermi gas in the weakly interacting BCS regime. Our numerical calculations predict correlated scattering of Cooper pairs into a spherical shell in momentum space. The scattered shell of correlated atoms is centered at half the usual Bragg momentum transfer, and can be clearly distinguished from atoms scattered by the usual single-particle Bragg mechanism. We develop an analytic model that explains key features of the correlated-pair Bragg scattering, and determine the dependence of that scattering on the initial pair correlations in the gas.     

One-dimensional bulk ferromagnets: NdAl2 and hcp cobalt

It is shown experimentally that NdAl₂ and hcp cobalt are one-dimensional (1D) bulk ferromagnets. For hcp cobalt this is only under the condition that the sample is magnetically saturated, i.e. that all moments are aligned parallel to the hexagonal c-axis. In 1D magnets the transverse interactions need not to be zero but must be sufficiently weak such that the transverse correlation length does not diverge at the critical temperature. The transverse interactions are then not relevant and the phase transition is driven by the longitudinal interactions. On the other hand, magnetic Bragg scattering relies on finite transverse correlations. For NdAl₂ no conventional magnetic Bragg scattering is observed if all moments are aligned vertical to the scattering plane by a magnetic field. For hcp cobalt the scattering intensity is considerably reduced in this geometry instead of having its maximum. From this observation it can be concluded that the transverse correlation length is practically zero in NdAl₂ but has a finite value in hcp cobalt. The macroscopic magnetization shows normal ferromagnetic saturation.     

Lyotropic bicontinuous cubic phase single crystals investigated using high-resolved X-ray scattering

Single crystals of an Ia d bicontinuous direct cubic phase formed by a non-ionic surfactant in water are investigated using high-resolved X-ray diffraction. The shape of the Bragg peaks confirms the existence of a 3D long-range order inside the cubic phase. A weak diffuse scattered intensity signal is measured very near the Bragg peaks. We attribute this signal to thermal diffuse scattering (TDS) and we give an estimation of the contribution of elastic waves to this TDS. Received 4 May 2000     

Quasi-wavelet calculations of sound scattering behind barriers

Quasi-wavelets (QWs) are a representation of turbulence consisting of self-similar, eddy-like structures with random orientations and positions in space. They are used in this paper to calculate the scattering, due to turbulent velocity fluctuations, of sound behind noise barriers as a function of the size and spatial location of the eddies. The sound scattering cross-section for QWs of an individual size class (eddy size) is derived and shown to reproduce results for the von Kármán spectrum when the scattered energies from a continuous distribution of QW sizes are combined. A Bragg resonance condition is derived for the eddy size that scatters most strongly for a given acoustic wavenumber and scattering angle. Results for scattering over barriers show that, for typical barrier conditions, most of the scattered energy originates from eddies in the size range of approximately one-half to twice the size of the eddies responsible for maximum scattering. The results also suggest that scattering over the barrier due to eddies with a line of sight to both the source and receiver is generally significant only for frequencies above several kilohertz, for sources and receivers no more than a few meters below the top of the barrier, and for very turbulent atmospheric conditions.     

Dynamics of modulated and composite aperiodic crystals

We compare within an unifying formalism the dynamical properties of modulated and composite aperiodic (incommensurate) crystals. We discuss the concept of inner polarization and we define an inner polarization parameter β that distinguishes between different acoustic modes of aperiodic crystals. Although this concept has its limitations, we show that it can be used to extract valuable information from neutron coherent inelastic scattering experiments. Within certain conditions, the ratio between the dynamic and the static structure factors at various Bragg peaks depends only on β. We show how the knowledge of β for modes of an unknown structure can be used to decide whether the structure is composite or modulated. The same information can be used to predict scattered intensity within unexplored regions of the reciprocal space, being thus a guide for experiments. Received 9 June 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: Ovidiu.Radulescu@univ-rennes1.fr     

Angular dependence of electronically allowed nuclear bragg reflection of Mössbauer radiation

A typical angular integrated Mössbauer reflection spectrum of an electronically allowed nuclear Bragg reflection was analysed. Mössbauer reflection spectra were measured with high angular resolution. They reveal almost pure nuclear scattering far off Bragg and strong nuclear-electronic interference in the scattering near and at Bragg. The spectra show a pronounced asymmetry with respect to the Bragg position, which is caused by refraction and by interference of nuclear and electronic scattering.     

Compton scattering of photons from standing wave fields in the Bragg case of X-ray diffraction

Within the limits of the impulse approximation the double differential cross section for inelastic X-ray scattering of photons from standing wave fields in the Bragg case of diffraction can provide information about projections of non-diagonal elements of the one-particle density matrix in momentum space on definite crystal directions.     

Disordered surface sheets in solid matter near bulk instabilities

In this article, I review surface-sensitive X-ray scattering experiments using evanescent X-ray scattering and asymptotic Bragg scattering techniques which have been carried out in order to investigate the thermodynamic behaviour of the surface and the subsurface layers when the bulk of the system approaches a phase transition. I discuss the surface structures of the binary alloys Fe₃Al and Cu₃Au close to the order-disorder transition, the surface of the molecular crystal NH₄Br near the critical temperature and ice single-crystal surfaces close the bulk melting point. The observed surface phenomena range from surface disorder and surface-induced new universal critical behaviour to surface melting and surface segregation. They all have in common that they are not bound to the outermost layers, but rather occur within a surface sheet whose thickness can grow to a mesoscopic or even macroscopic size.     

Bragg rods and multiple X-ray scattering in random-stacking colloidal crystals

Synchrotron small-angle x-ray diffraction images of random-stacking-induced Bragg scattering rods are obtained in a wide range of wave vectors from a single colloidal crystal. The results reveal a strong multiple scattering effect, which leads to new features in the diffraction pattern-secondary Bragg rods. We argue that dynamic x-ray diffraction is rather common for high-quality colloidal photonic crystals and should be taken into account.     

Annular dark field imaging in a TEM

Annular objective apertures are fabricated for a CM300 transmission electron microscope using a focused ion beam system. A central beam stop in the back focal plane of the objective lens of the microscope blocks all electrons scattered up to a semi-angle of approximately 20 mrad. In this manner, contributions to the image from Bragg scattering are largely reduced and the image contrast is sensitive to the atomic number Z. Experimentally, we find that single atom scattering cross sections measured with this technique are close to Rutherford scattering values. A comparison between this new method and STEM-HAADF shows that both techniques result in qualitatively similar images although the resolution of ADF-TEM is limited by contrast delocalization caused by the spherical aberration of the objective lens. This problem can be overcome by using an aberration corrected microscope.     

Complementary use of neutron and synchrotron X-ray scattering for problems of interest in condensed matter physics

We discuss the relative advantages and disadvantages of neutron and synchrotron X-ray scattering for studying problems in magnetism, highly correlated systems and superconductors, and problems where both techniques can be applied to obtain complementary information.     

Small-angle X-ray scattering investigation of deformation-induced nanovoids in AA6063 aluminium alloy

Abstract

Small-angle X-ray scattering studies of microstructure in metallic systems are prone to contamination by double Bragg scattering from the crystalline matrix. This is particularly problematic to the study of fracture in ductile metals via the nucleation and growth of nanovoids in response to plastic deformation. We show clear evidence of the presence of these scattering artefacts in the scattering data from representative Al systems and describe a simple method of numerically isolating and removing potentially misleading information to reveal the true small angle scattering response of the sample. This data correction process is used to obtain quantitative measurements of the nanovoid volume fraction in deformed AA6063. The SAXS results yield values comparable to existing predictions of the total vacancy volume fraction obtained from the mechanical stress–strain data.     

X-ray point- and line-projection microscopy and diffraction

A theoretical framework is presented to treat both imaging and diffraction experiments performed with point-focus and line-focus X-ray sources, with particular emphasis on two-dimensional and planar X-ray waveguides. In particular, point-projection and line-projection microscopy has been approached within the Huygens-Fresnel formalism; point-projection and line-projection diffraction, such as spatially-resolved Bragg/Laue diffraction of crystalline samples in a regime of dynamical scattering, has been treated both by means of the Huygens-Fresnel formalism and of the Takagi-Taupin dynamical theory. Both in point- and line- projection geometry, simply rotating the investigated crystalline samples, it is possible to switch from Fresnel self-imaging to Bragg/Laue diffraction conditions. This means to image, within the same experiment, either morphological features, with a sub-micrometric resolution, out of the exact diffraction condition, or the structure order on an atomic scale if placing the sample in diffraction.