Clock spectroscopy of interacting bosons in deep optical lattices

We report on high-resolution optical spectroscopy of interacting bosonic $^{174}$Yb atoms in deep optical lattices with negligible tunneling. We prepare Mott insulator phases with singly- and doubly-occupied isolated sites and probe the atoms using an ultra-narrow "clock" transition. Atoms in singly-occupied sites undergo long-lived Rabi oscillations. Atoms in doubly-occupied sites are strongly affected by interatomic interactions, and we measure their inelastic decay rates and energy shifts. We deduce from these measurements all relevant collisional parameters involving both clock states, in particular the intra- and inter-state scattering lengths

Relative Riemann-Zariski spaces

In this paper we study relative Riemann-Zariski spaces attached to a morphism of schemes and generalizing the classical Riemann-Zariski space of a field. We prove that similarly to the classical RZ spaces, the relative ones can be described either as projective limits of schemes in the category of locally ringed spaces or as certain spaces of valuations. We apply these spaces to prove the following two new results: a strong version of stable modification theorem for relative curves; a decomposition theorem which asserts that any separated morphism between quasi-compact and quasi-separated schemes factors as a composition of an affine morphism and a proper morphism. (In particular, we obtain a new proof of Nagata's compactification theorem.)Comment: 30 pages, the final version, to appear in Israel J. of Mat

Transport of ferrihydrite nanoparticles in saturated porous media: role of ionic strength and flow rate

The use of nanoscale ferrihydrite particles, which are known to effectively enhance microbial degradation of a wide range of contaminants, represents a promising technology for in situ remediation of contaminated aquifers. Thanks to their small size, ferrihydrite nanoparticles can be dispersed in water and directly injected into the subsurface to create reactive zones where contaminant biodegradation is promoted. Field applications would require a detailed knowledge of ferrihydrite transport mechanisms in the subsurface, but such studies are lacking in the literature. The present study is intended to fill this gap, focusing in particular on the influence of flow rate and ionic strength on particle mobility. Column tests were performed under constant or transient ionic strength, including injection of ferrihydrite colloidal dispersions, followed by flushing with particle-free electrolyte solutions. Particle mobility was greatly affected by the salt concentration, and particle retention was almost irreversible under typical salt content in groundwater. Experimental results indicate that, for usual ionic strength in European aquifers (2 to 5 mM), under natural flow condition ferrihydrite nanoparticles are likely to be transported for 5 to 30 m. For higher ionic strength, corresponding to contaminated aquifers, (e.g., 10 mM) the travel distance decreases to few meters. A simple relationship is proposed for the estimation of travel distance with changing flow rate and ionic strength. For future applications to aquifer remediation, ionic strength and injection rate can be used as tuning parameters to control ferrihydrite mobility in the subsurface and therefore the radius of influence during field injection

Non-linear Relaxation of Interacting Bosons Coherently Driven on a Narrow Optical Transition

We study the dynamics of a two-component Bose-Einstein condensate (BEC) of $^{174}$Yb atoms coherently driven on a narrow optical transition. The excitation transfers the BEC to a superposition of states with different internal and momentum quantum numbers. We observe a crossover with decreasing driving strength between a regime of damped oscillations, where coherent driving prevails, and an incoherent regime, where relaxation takes over. Several relaxation mechanisms are involved: inelastic losses involving two excited atoms, leading to a non-exponential decay of populations; Doppler broadening due to the finite momentum width of the BEC and inhomogeneous elastic interactions, both leading to dephasing and to damping of the oscillations. We compare our observations to a two-component Gross-Pitaevskii (GP) model that fully includes these effects. For small or moderate densities, the damping of the oscillations is mostly due to Doppler broadening. In this regime, we find excellent agreement between the model and the experimental results. For higher densities, the role of interactions increases and so does the damping rate of the oscillations. The damping in the GP model is less pronounced than in the experiment, possibly a hint for many-body effects not captured by the mean-field description.Comment: 7 pages, 4 figures; supplementary material available as ancillary fil

Evidence for a 3 x 10^8 solar mass black hole in NGC 7052 from HST observations of the nuclear gas disk

We present an HST study of the nuclear region of the E4 radio galaxy NGC 7052, which has a nuclear disk of dust and gas. The WFPC2 was used to obtain B, V and I broad-band images and an H_alpha+[NII] narrow-band image. The FOS was used to obtain H_alpha+[NII] spectra along the major axis, using a 0.26 arcsec diameter circular aperture. The observed rotation velocity of the ionized gas is V = 155 +/- 17 km/s at r = 0.2 arcsec from the nucleus. The Gaussian dispersion of the emission lines increases from sigma = 70 km/s at r=1 arcsec, to sigma = 400 km/s on the nucleus. To interpret the gas kinematics we construct axisymmetric models in which the gas and dust reside in a disk in the equatorial plane of the stellar body. It is assumed that the gas moves on circular orbits, with an intrinsic velocity dispersion due to turbulence. The circular velocity is calculated from the combined gravitational potential of the stars and a possible nuclear black hole (BH). Models without a BH predict a rotation curve that is shallower than observed (V_pred = 92 km/s at r = 0.2 arcsec), and are ruled out at > 99% confidence. Models with a BH of 3.3^{+2.3}_{-1.3} x 10^8 solar masses provide an acceptable fit. NGC 7052 can be added to the list of active galaxies for which HST spectra of a nuclear gas disk provide evidence for the presence of a central BH. The BH masses inferred for M87, M84, NGC 6251, NGC 4261 and NGC 7052 span a range of a factor 10, with NGC 7052 falling on the low end. By contrast, the luminosities of these galaxies are identical to within 25%. Any relation between BH mass and luminosity, as suggested by independent arguments, must therefore have a scatter of at least a factor 10.Comment: 39 pages, LaTeX, with 16 PostScript figures. Submitted to the Astronomical Journal. Postscript version with higher resolution figures available from http://sol.stsci.edu/~marel/abstracts/abs_R22.htm

Silent Springs: Why Are All the Frogs “Croaking”?

Amphibians are a fabulously successful group of animals; however, it is increasingly clear that they are experiencing extinction rates that far exceed those experienced by other classes of vertebrates. A new book examines the various reasons why amphibians are so threatened, and what can be done about it