Electronic structure of superposition states in flux qubits

Flux qubits, small superconducting loops interrupted by Josephson junctions, are successful realizations of quantum coherence for macroscopic variables. Superconductivity in these loops is carried by $\sim 10^6$ -- $10^{10}$ electrons, which has been interpreted as suggesting that coherent superpositions of such current states are macroscopic superpositions analogous to Schr\"odinger's cat. We provide a full microscopic analysis of such qubits, from which the macroscopic quantum description can be derived. This reveals that the number of microscopic constituents participating in superposition states for experimentally accessible flux qubits is surprisingly but not trivially small. The combination of this relatively small size with large differences between macroscopic observables in the two branches is seen to result from the Fermi statistics of the electrons and the large disparity between the values of superfluid and Fermi velocity in these systems.Comment: Minor cosmetic changes. Published version

Two-channel Kondo effect and renormalization flow with macroscopic quantum charge states

Many-body correlations and macroscopic quantum behaviors are fascinating condensed matter problems. A powerful test-bed for the many-body concepts and methods is the Kondo model which entails the coupling of a quantum impurity to a continuum of states. It is central in highly correlated systems and can be explored with tunable nanostructures. Although Kondo physics is usually associated with the hybridization of itinerant electrons with microscopic magnetic moments, theory predicts that it can arise whenever degenerate quantum states are coupled to a continuum. Here we demonstrate the previously elusive `charge' Kondo effect in a hybrid metal-semiconductor implementation of a single-electron transistor, with a quantum pseudospin-1/2 constituted by two degenerate macroscopic charge states of a metallic island. In contrast to other Kondo nanostructures, each conduction channel connecting the island to an electrode constitutes a distinct and fully tunable Kondo channel, thereby providing an unprecedented access to the two-channel Kondo effect and a clear path to multi-channel Kondo physics. Using a weakly coupled probe, we reveal the renormalization flow, as temperature is reduced, of two Kondo channels competing to screen the charge pseudospin. This provides a direct view of how the predicted quantum phase transition develops across the symmetric quantum critical point. Detuning the pseudospin away from degeneracy, we demonstrate, on a fully characterized device, quantitative agreement with the predictions for the finite-temperature crossover from quantum criticality.Comment: Letter (5 pages, 4 figures) and Methods (10 pages, 6 figures

The Kondo Effect in Non-Equilibrium Quantum Dots: Perturbative Renormalization Group

While the properties of the Kondo model in equilibrium are very well understood, much less is known for Kondo systems out of equilibrium. We study the properties of a quantum dot in the Kondo regime, when a large bias voltage V and/or a large magnetic field B is applied. Using the perturbative renormalization group generalized to stationary nonequilibrium situations, we calculate renormalized couplings, keeping their important energy dependence. We show that in a magnetic field the spin occupation of the quantum dot is non-thermal, being controlled by V and B in a complex way to be calculated by solving a quantum Boltzmann equation. We find that the well-known suppression of the Kondo effect at finite V>>T_K (Kondo temperature) is caused by inelastic dephasing processes induced by the current through the dot. We calculate the corresponding decoherence rate, which serves to cut off the RG flow usually well inside the perturbative regime (with possible exceptions). As a consequence, the differential conductance, the local magnetization, the spin relaxation rates and the local spectral function may be calculated for large V,B >> T_K in a controlled way.Comment: 9 pages, invited paper for a special edition of JPSJ "Kondo Effect -- 40 Years after the Discovery", some typos correcte

Kondo Effect on Mesoscopic Scale (Review)

Following the discovery of the Kondo effect the bulk transport and magnetic behavior of the dilute magnetic alloys have been successfully described. In the last fifteen years new directions have been developed as the study of the systems of reduced dimensions and the artificial atoms so called quantum dots. In this review the first subject is reviewed starting with the scanning tunneling microscope (STM) study of a single magnetic impurity. The next subject is the reduction of the amplitude of the Kondo effect in samples of reduced dimension which was explained by the surface magnetic anisotropy which blocks the motion of the integer spin nearby the surface. The electron dephasing and energy relaxation experiments are discussed with the possible explanation including the surface anisotropy, where the situation in cases of integer and half-integer spins is very different. Finally, the present situation of the theory of dynamical structural defects is briefly presented which may lead to two-channel Kondo behavior.Comment: 8 pages, submitted to the JPSJ Special Issue "Kondo effect -- 40 years after the Discovery

Precise measurement of particle-wall hydrodynamic interactions at low Reynolds number using laser interferometry

International audienceThe motion of a spherical particle (with radius 1 to 6 mm) in a viscous fluid is measured using laser interferometry. The typical sensitivity on the measured displacement of the sphere is of the order of 50 nm. The particle is moving on the axis of a closed cylinder. The hydrodynamic interactions between the particle and the walls of the cylinder are compared with the theoretical result of Sano [J. Phys. Soc. Jpn. 56, 2713 (1987)] valid for a very small sphere. The agreement is excellent for the smallest sphere used in the experiment. The experiment also agrees with the result from the theory of lubrication when the sphere is close to a plane end wall. The effect of the particle roughness appears at small distances. Laser interferometry appears as a useful tool to study particle–wall hydrodynamic interactions when the geometry is cumbersome

Activation of N−O σ Bonds with Transition Metals: A Versatile Platform for Organic Synthesis and C−N Bonds Formation

Abstract N−O σ bonds containing compounds are versatile substrates for organic synthesis under transition metal catalysis. Their ability to react through both polar (oxidative addition, formation of metallanitrene, nucleophilic substitution) and radical pathways (single electron transfer, homolytic bond scission) have triggered the development of various synthetic methodologies, particularly toward synthesizing nitrogen‐containing compounds. In this review, we discuss the different modes of activation of N−O bonds in the presence of transition metal catalysts, emphasizing the experimental and computational mechanistic proofs in the literature to help to design new synthetic pathways toward the synthesis of C−N bonds

X-RAY AND MAGNETIZATION STUDIES OF THE GEOMETRICAL PARAMETERS OF THE GRAINS OF A FERROFLUID

On présente une étude par microscopie électronique, par diffusion centrale des rayons X et par aimantation, de la distribution en taille, de la structure et des corrélations magnétiques entre les grains de colloïdes magnétiques. Pour les colloïdes à base d'eau (Fe3O4 dans l'eau), les grains se comportent comme des sphères dures dispersées dans un fluide porteur. Pour les colloïdes à base de toluène (grains de cobalt) on propose un modèle où le grain est constitué d'un noyau de cobalt pur entouré d'une couche non magnétique. Dans les colloïdes de cobalt, des corrélations ont été observées qui mettent en évidence une périodicité dans la distance entre grains. Une forte anisotropie magnétique est observée pour les deux types de colloïdes.The size distribution, structure and magnetic correlations between the grains of magnetic colloids are studied by electron microscopy, small angle scattering of X-rays and magnetic measurements. For water-base colloids (Fe3O4 in water) the grains behave as hard spheres dispersed in a carrier liquid. For toluene-base colloids (Co grains) a model of a grain constituted by a core of pure cobalt and a non magnetic sheath surrounding it is proposed. In toluene-base colloids, correlations have been observed which reveal a periodicity in the intergrain spacing. Strong magnetic anisotropy is reported for both colloids

Interaction between a laser beam and some liquid media

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Lubricating motion of a sphere in a conical vessel

International audienceThe final stage of sedimentation of a spherical particle moving along the axis of a conical vessel containing a viscous incompressible fluid is studied both theoretically by lubrication analysis and experimentally by laser interferometry. The particle settling velocity varies like d5/2, where d is the gap. There is an excellent agreement between this result from lubrication theory and experiment, the upper bound being for a gap of about 1/30 radius and the lower practical bound being at the size of the particle roughness