Evidence of Raleigh-Hertz surface waves and shear stiffness anomaly in granular media

Due to the non-linearity of Hertzian contacts, the speed of sound in granular matter increases with pressure. Under gravity, the non-linear elastic description predicts that acoustic propagation is only possible through surface modes, called Rayleigh-Hertz modes and guided by the index gradient. Here we directly evidence these modes in a controlled laboratory experiment and use them to probe the elastic properties of a granular packing under vanishing confining pressure. The shape and the dispersion relation of both transverse and sagittal modes are compared to the prediction of non-linear elasticity that includes finite size effects. This allows to test the existence of a shear stiffness anomaly close to the jamming transition.Comment: 4 pages 4 figure

An acoustic analog to the dynamical Casimir effect in a Bose-Einstein condensate

We have realized an acoustic analog to the Dynamical Casimir effect. The density of a trapped Bose-Einstein condensate is modulated by changing the trap stiffness. We observe the creation of correlated excitations with equal and opposite momenta, and show that for a well defined modulation frequency, the frequency of the excitations is half that of the trap modulation frequency.Comment: Includes supplemental informatio

Spontaneous Four-Wave Mixing of de Broglie Waves: Beyond Optics

We investigate the atom-optical analog of degenerate four-wave mixing of photons by colliding two Bose-Einstein condensates (BECs) of metastable helium and measuring the resulting momentum distribution of the scattered atoms with a time and space resolved detector. For the case of photons, phase matching conditions completely define the final state of the system, and in the case of two colliding BECs, simple analogy implies a spherical momentum distribution of scattered atoms. We find, however, that the final momenta of the scattered atoms instead lie on an ellipsoid whose radii are smaller than the initial collision momentum. Numerical and analytical calculations agree well with the measurements, and reveal the interplay between many-body effects, mean-field interaction, and the anisotropy of the source condensate

Charon's radius and density from the combined data sets of the 2005 July 11 occultation

The 2005 July 11 C313.2 stellar occultation by Charon was observed by three separate research groups, including our own, at observatories throughout South America. Here, the published timings from the three data sets have been combined to more accurately determine the mean radius of Charon: 606.0 +/- 1.5 km. Our analysis indicates that a slight oblateness in the body (0.006 +/- 0.003) best matches the data, with a confidence level of 86%. The oblateness has a pole position angle of 71.4 deg +/- 10.4 deg and is consistent with Charon's pole position angle of 67 deg. Charon's mean radius corresponds to a bulk density of 1.63 +/- 0.07 g/cm3, which is significantly less than Pluto's (1.92 +/- 0.12 g/cm3). This density differential favors an impact formation scenario for the system in which at least one of the impactors was differentiated. Finally, unexplained differences between chord timings measured at Cerro Pachon and the rest of the data set could be indicative of a depression as deep as 7 km on Charon's limb.Comment: 25 pages including 4 tables and 2 figures. Submitted to the Astronomical Journal on 2006 Feb 0

Closedness of star products and cohomologies

We first review the introduction of star products in connection with deformations of Poisson brackets and the various cohomologies that are related to them. Then we concentrate on what we have called ``closed star products" and their relations with cyclic cohomology and index theorems. Finally we shall explain how quantum groups, especially in their recent topological form, are in essence examples of star products.Comment: 16 page

Sub-Poissonian number differences in four-wave mixing of matter waves

We demonstrate sub-Poissonian number differences in four-wave mixing of Bose-Einstein condensates of metastable helium. The collision between two Bose-Einstein condensates produces a scattering halo populated by pairs of atoms of opposing velocities, which we divide into several symmetric zones. We show that the atom number difference for opposing zones has sub-Poissonian noise fluctuations whereas that of nonopposing zones is well described by shot noise. The atom pairs produced in a dual number state are well adapted to sub shot-noise interferometry and studies of Einstein-Podolsky-Rosen-type nonlocality tests.Comment: 4 pages, 3 figure

Violation of the Cauchy-Schwarz inequality with matter waves

The Cauchy-Schwarz (CS) inequality -- one of the most widely used and important inequalities in mathematics -- can be formulated as an upper bound to the strength of correlations between classically fluctuating quantities. Quantum mechanical correlations can, however, exceed classical bounds.Here we realize four-wave mixing of atomic matter waves using colliding Bose-Einstein condensates, and demonstrate the violation of a multimode CS inequality for atom number correlations in opposite zones of the collision halo. The correlated atoms have large spatial separations and therefore open new opportunities for extending fundamental quantum-nonlocality tests to ensembles of massive particles.Comment: Final published version (with minor changes). 5 pages, 3 figures, plus Supplementary Materia