Theory of microwave spectroscopy of Andreev bound states with a Josephson junction

We present a microscopic theory for the current through a tunnel Josephson junction coupled to a non-linear environment, which consists of an Andreev two-level system coupled to a harmonic oscillator. It models a recent experiment [Bretheau, Girit, Pothier, Esteve, and Urbina, Nature (London) 499, 312 (2013)] on photon spectroscopy of Andreev bound states in a superconducting atomic-size contact. We find the eigenenergies and eigenstates of the environment and derive the current through the junction due to inelastic Cooper pair tunneling. The current-voltage characteristic reveals the transitions between the Andreev bound states, the excitation of the harmonic mode that hybridizes with the Andreev bound states, as well as multi-photon processes. The calculated spectra are in fair agreement with the experimental data.Comment: 8 pages, 6 figure

Evidence for long-lived quasiparticles trapped in superconducting point contacts

We have observed that the supercurrent across phase-biased, highly transmitting atomic size contacts is strongly reduced within a broad phase interval around {\pi}. We attribute this effect to quasiparticle trapping in one of the discrete sub-gap Andreev bound states formed at the contact. Trapping occurs essentially when the Andreev energy is smaller than half the superconducting gap {\Delta}, a situation in which the lifetime of trapped quasiparticles is found to exceed 100 \mus. The origin of this sharp energy threshold is presently not understood.Comment: Article (5 pages) AND Supplemental material (14 pages). To be published in Physical Review Letter

FAIRE-seq data analysis of Chlamydomonas reinhardtii under carbon deprivation

For the genome-wide identification of nucleosome depleted regions under carbon deprivation, we analyze an available set of data from an assay of formaldehyde-assisted isolation of regulatory elements followed by sequencing (FAIRE-seq). Mapping to the sequenced nuclear genome of C.reinhardtii, followed by the identification of the enrichment-sequenced fragments was performed. We examined the location of these fragments relative to annotated genes. The related genes were associated to the corresponding Gene-Ontology (GO), for an evaluation of over-representate GO categories. Some genes, link with functions or locations, that have been previous described, indicating the success of the method finding carbon-metabolism related fragments

Superconducting atomic contacts under microwave irradiation

We have measured the effect of microwave irradiation on the dc current-voltage characteristics of superconducting atomic contacts. The interaction of the external field with the ac supercurrents leads to replicas of the supercurrent peak, the well known Shapiro resonances. The observation of supplementary fractional resonances for contacts containing highly transmitting conduction channels reveals their non-sinusoidal current-phase relation. The resonances sit on a background current which is itself deeply modified, as a result of photon assisted multiple Andreev reflections. The results provide firm support for the full quantum theory of transport between two superconductors based on the concept of Andreev bound states

Superconducting atomic contacts inductively coupled to a microwave resonator

We describe and characterize a microwave setup to probe the Andreev levels of a superconducting atomic contact. The contact is part of a superconducting loop inductively coupled to a superconducting coplanar resonator. By monitoring the resonator reflection coefficient close to its resonance frequency as a function of both flux through the loop and frequency of a second tone we perform spectroscopy of the transition between two Andreev levels of highly transmitting channels of the contact. The results indicate how to perform coherent manipulation of these states.Comment: 14 pages, 10 figures, to appear in special issue on break-junctions in JOPC

Singularidad centro-foco en R3

En este articulo se estudian las singularidades de campos vectoriales X en el origen de R3 (con coordenadas (x1, x2, x3)) tales que DX(0) = - bx2 --+ bx1 --+ AX3 --. ax1 ax2 . ax3 b, A f O. La conducta de estas singularidades corresponde alcentrojoco en R3 con un eje hiperbólico. El conjunto de gérmenes de tales campos vectoriales es un conjunto estratificado, cuyas estratas son conjuntos localmente cerrados y de codimensión creciente en el espacio de gérmenes de singularidades en R3. Además estas singularidades son localmente C° estables y se bifurcan a n-parámetros colapsando n-cilindros concéntricos invariantes, es decir. una bifurcación de Hopf cilindrar generalizada