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

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

Manipulating the Quantum State of an Electrical Circuit

We have designed and operated a superconducting tunnel junction circuit that behaves as a two-level atom: the ``quantronium''. An arbitrary evolution of its quantum state can be programmed with a series of microwave pulses, and a projective measurement of the state can be performed by a pulsed readout sub-circuit. The measured quality factor of quantum coherence Qphi=25000 is sufficiently high that a solid-state quantum processor based on this type of circuit can be envisioned.Comment: 4 figures include

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

Measurement of the current-phase relation of superconducting atomic contacts

We have probed the current-phase relation of an atomic contact placed with a tunnel junction in a small superconducting loop. The measurements are in quantitative agreement with the predictions of a resistively shunted SQUID model in which the Josephson coupling of the contact is calculated using the independently determined transmissions of its conduction channels.Comment: to be published in Physical Review Letter

On the succinctness of query rewriting over shallow ontologies

We investigate the succinctness problem for conjunctive query rewritings over OWL2QL ontologies of depth 1 and 2 by means of hypergraph programs computing Boolean functions. Both positive and negative results are obtained. We show that, over ontologies of depth 1, conjunctive queries have polynomial-size nonrecursive datalog rewritings; tree-shaped queries have polynomial positive existential rewritings; however, in the worst case, positive existential rewritings can be superpolynomial. Over ontologies of depth 2, positive existential and nonrecursive datalog rewritings of conjunctive queries can suffer an exponential blowup, while first-order rewritings can be superpolynomial unless NP �is included in P/poly. We also analyse rewritings of tree-shaped queries over arbitrary ontologies and note that query entailment for such queries is fixed-parameter tractable

Computing FO-Rewritings in EL in Practice: from Atomic to Conjunctive Queries

A prominent approach to implementing ontology-mediated queries (OMQs) is to rewrite into a first-order query, which is then executed using a conventional SQL database system. We consider the case where the ontology is formulated in the description logic EL and the actual query is a conjunctive query and show that rewritings of such OMQs can be efficiently computed in practice, in a sound and complete way. Our approach combines a reduction with a decomposed backwards chaining algorithm for OMQs that are based on the simpler atomic queries, also illuminating the relationship between first-order rewritings of OMQs based on conjunctive and on atomic queries. Experiments with real-world ontologies show promising results

Obstinate memory: working class politics and neoliberal forgetting in the UK and Chile

In the forty years since Chile and the UK became the crucibles of neoliberalization, working class agency has been transformed, its institutions systematically dismantled, and its politics, after the continuity neoliberalism of both the UK Blair government and the Chilean Concertaçion, in a crisis of legitimacy. In the process, memories of struggle have been captured within narratives of ‘capitalist realism’ (Fisher) – the present, past and future collapsed into Walter Benjamin’s ‘empty homogenous time’. This paper explores ways in which two traumatic moments of working-class struggle have been narrativized by the media in the service of this “presentism”: the 1973 coup in Chile, and the 1984-85 Miners’ Strike in the UK. We argue that the use of “living history” or bottom-up approaches to memory provides an urgently needed recovery of disruptive narratives of class identity, and offers a way of reclaiming alternative futures from the grip of reductive economic nationalism