Isotope effect on superconductivity in Josephson coupled stripes in underdoped cuprates

Inelastic neutron scattering data for YBaCuO as well as for LaSrCuO indicate incommensurate neutron scattering peaks with incommensuration $\delta(x)$ away from the $(\pi,\pi)$ point. $T_c(x)$ can be replotted as a linear function of the incommensuration for these materials. This linear relation implies that the constant that relates these two quantities, one being the incommensuration (momentum) and another being $T_c(x)$ (energy), has the dimension of velocity we denote $v^*$: $k_B T_c(x) = \hbar v^* \delta(x)$. We argue that this experimentally derived relation can be obtained in a simple model of Josephson coupled stripes. Within this framework we address the role of the $O^{16} \to O^{18}$ isotope effect on the $T_c(x)$. We assume that the incommensuration is set by the {\em doping} of the sample and is not sensitive to the oxygen isotope given the fixed doping. We find therefore that the only parameter that can change with O isotope substitution in the relation $T_c(x) \sim \delta(x)$ is the velocity $v^*$. We predict an oxygen isotope effect on $v^*$ and expect it to be $\simeq 5$.Comment: 4 pages latex file, 2 eps fig

The homotopy theory of dg-categories and derived Morita theory

The main purpose of this work is the study of the homotopy theory of dg-categories up to quasi-equivalences. Our main result provides a natural description of the mapping spaces between two dg-categories $C$ and $D$ in terms of the nerve of a certain category of $(C,D)$-bimodules. We also prove that the homotopy category $Ho(dg-Cat)$ is cartesian closed (i.e. possesses internal Hom's relative to the tensor product). We use these two results in order to prove a derived version of Morita theory, describing the morphisms between dg-categories of modules over two dg-categories $C$ and $D$ as the dg-category of $(C,D)$-bi-modules. Finally, we give three applications of our results. The first one expresses Hochschild cohomology as endomorphisms of the identity functor, as well as higher homotopy groups of the \emph{classifying space of dg-categories} (i.e. the nerve of the category of dg-categories and quasi-equivalences between them). The second application is the existence of a good theory of localization for dg-categories, defined in terms of a natural universal property. Our last application states that the dg-category of (continuous) morphisms between the dg-categories of quasi-coherent (resp. perfect) complexes on two schemes (resp. smooth and proper schemes) is quasi-equivalent to the dg-category of quasi-coherent complexes (resp. perfect) on their product.Comment: 50 pages. Few mistakes corrected, and some references added. Thm. 8.15 is new. Minor corrections. Final version, to appear in Inventione

Accumulation and thermalization of cold atoms in a finite-depth magnetic trap

We experimentally and theoretically study the continuous accumulation of cold atoms from a magneto-optical trap (MOT) into a finite depth trap, consisting in a magnetic quadrupole trap dressed by a radiofrequency (RF) field. Chromium atoms (52 isotope) in a MOT are continuously optically pumped by the MOT lasers to metastable dark states. In presence of a RF field, the temperature of the metastable atoms that remain magnetically trapped can be as low as 25 microK, with a density of 10^17 atoms.m-3, resulting in an increase of the phase-space density, still limited to 7.10^-6 by inelastic collisions. To investigate the thermalization issues in the truncated trap, we measure the free evaporation rate in the RF-truncated magnetic trap, and deduce the average elastic cross section for atoms in the 5D4 metastable states, equal to 7.0 10^-16m2.Comment: 9 pages, 10 Figure

On the feasibility to study inverse proximity effect in a single S/F bilayer by Polarized Neutron Reflectometry

Here we report on a feasibility study aiming to explore the potential of Polarized Neutron Reflectometry (PNR) for detecting the inverse proximity effect in a single superconducting/ferromagnetic bilayer. Experiments, conducted on the V(40nm)/Fe(1nm) S/F bilayer, have shown that experimental spin asymmetry measured at T = 0.5TC is shifted towards higher Q values compared to the curve measured at T = 1.5TC. Such a shift can be described by the appearance in superconducting vanadium of magnetic sub-layer with thickness of 7 nm and magnetization of +0.8 kG.Comment: Changes in the 2nd version: small mistypes are corrected. Manuscript submitted to JETP let. 4 pages, 2 figure

Influence of positional correlations on the propagation of waves in a complex medium with polydisperse resonant scatterers

We present experimental results on a model system for studying wave propagation in a complex medium exhibiting low frequency resonances. These experiments enable us to investigate a fundamental question that is relevant for many materials, such as metamaterials, where low-frequency scattering resonances strongly influence the effective medium properties. This question concerns the effect of correlations in the positions of the scatterers on the coupling between their resonances, and hence on wave transport through the medium. To examine this question experimentally, we measure the effective medium wave number of acoustic waves in a sample made of bubbles embedded in an elastic matrix over a frequency range that includes the resonance frequency of the bubbles. The effective medium is highly dispersive, showing peaks in the attenuation and the phase velocity as functions of the frequency, which cannot be accurately described using the Independent Scattering Approximation (ISA). This discrepancy may be explained by the effects of the positional correlations of the scatterers, which we show to be dependent on the size of the scatterers. We propose a self-consistent approach for taking this "polydisperse correlation" into account and show that our model better describes the experimental results than the ISA

Quantum Fluctuations in Josephson Junction Comparators

We have developed a method for calculation of quantum fluctuation effects, in particular of the uncertainty zone developing at the potential curvature sign inversion, for a damped harmonic oscillator with arbitrary time dependence of frequency and for arbitrary temperature, within the Caldeira-Leggett model. The method has been applied to the calculation of the gray zone width Delta Ix of Josephson-junction balanced comparators driven by a specially designed low-impedance RSFQ circuit. The calculated temperature dependence of Delta Ix in the range 1.5 to 4.2K is in a virtually perfect agreement with experimental data for Nb-trilayer comparators with critical current densities of 1.0 and 5.5 kA/cm^2, without any fitting parameters.Comment: 4 pages, 4 figures, submitted to Physical Review Letter