Supercurrent Spectroscopy of Andreev States

We measure the excitation spectrum of a superconducting atomic contact. In addition to the usual continuum above the superconducting gap, the single particle excitation spectrum contains discrete, spin-degenerate Andreev levels inside the gap. Quasiparticle excitations are induced by a broadband on-chip microwave source and detected by measuring changes in the supercurrent flowing through the atomic contact. Since microwave photons excite quasiparticles in pairs, two types of transitions are observed: Andreev transitions, which consists of putting two quasiparticles in an Andreev level, and transitions to odd states with a single quasiparticle in an Andreev level and the other one in the continuum. In contrast to absorption spectroscopy, supercurrent spectroscopy allows detection of long-lived odd states.Comment: typos correcte

Matematik öğretmen adaylarının örüntü genellemesi bilgilerini kullanarak yaptıkları etkinlik değişiklikleri

The purpose of the study is to evaluate how prospective mathematics teachers (PMTs) modify tasks to facilitate students’ learning of pattern generalization through the use of their mathematical knowledge for teaching. Case study, which is a type of qualitative research method, was used to determine the mathematical characteristics that PMTs use when modifying a mathematical task. The knowledge from which PMTs draw to modify the task has also been outlined. Accordingly, data were collected from PMTs’ task modifications and reflection reports. When PMTs worked on two or more forms of modification, as compared to just using one type of modification, they modified tasks more effectively and comprehensively. The PMTs who make condition modifications need to utilize specialized content knowledge through the use of models or tables. They aimed to help middle school students understand using these modifications, and thus they also utilized their knowledge of content and students. They also used their knowledge of content and teaching, especially while making modifications to questions and context. Task modification activities can be used to help prospective teachers notice the mathematical and pedagogical affordances and limitations offered by tasks.Bu çalışmanın amacı, öğrencilerin örüntü genellemelerine yardımcı olmak için matematik öğretmen adaylarının matematik öğretimi bilgilerini kullanarak yaptıkları etkinlik değişikliklerini değerlendirmektir. Öğretmen adaylarının matematiksel bir etkinliği değiştirirken kullandıkları matematiksel özellikleri belirlemek için nitel araştırma yöntemlerinden durum çalışması kullanılmıştır. Ayrıca öğretmen adaylarının etkinliği değiştirirken kullandıkları bilgileri belirlenmiştir. Veriler, öğretmen adaylarının değiştirdiği etkinliklerden ve yansıtma raporlarından toplanmıştır. Öğretmen adayları, etkinlik üzerinde yalnızca bir tür değişiklik yapmaya kıyasla iki veya daha fazla değişiklik türünü birlikte yaptıklarında, etkinliklerini daha anlamlı ve kapsamlı bir şekilde değiştirmişlerdir. Koşul değişiklikleri yapanlar, model veya tablo ekleyerek uzmanlık alan bilgilerini kullanmıştır. Bu değişiklikleri öğrencilerin anlamasına yardımcı olmak amacıyla da yapmışlar ve böylece öğrenci ve alan bilgilerini de kullanmışlardır. Ayrıca öğretmen adayları, alan ve öğretme bilgilerinden özellikle soru ve bağlam değişikliği yaparken yararlanmıştır. Etkinlik değiştirme çalışmaları, öğretmen adaylarının etkinliklerin sunduğu matematiksel ve pedagojik olanakları ve sınırlılıkları fark etmelerine yardımcı olmak için kullanılabilir

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

Exciting Andreev pairs in a superconducting atomic contact

The Josephson effect describes the flow of supercurrent in a weak link, such as a tunnel junction, nanowire, or molecule, between two superconductors. It is the basis for a variety of circuits and devices, with applications ranging from medicine to quantum information. Currently, experiments using Josephson circuits that behave like artificial atoms are revolutionizing the way we probe and exploit the laws of quantum physics. Microscopically, the supercurrent is carried by Andreev pair states, which are localized at the weak link. These states come in doublets and have energies inside the superconducting gap. Existing Josephson circuits are based on properties of just the ground state of each doublet and so far the excited states have not been directly detected. Here we establish their existence through spectroscopic measurements of superconducting atomic contacts. The spectra, which depend on the atomic configuration and on the phase difference between the superconductors, are in complete agreement with theory. Andreev doublets could be exploited to encode information in novel types of superconducting qubits.Comment: Submitted to Natur

Examining Two Middle School Mathematics Teachers’ Knowledge for Teaching Manipulation of Algebraic Expressions during Lesson Planning and Instruction

Teachers use their content and pedagogical content knowledge for teaching algebra. For this reason, the examination of how teachers use this knowledge may help shed light on how students learn algebra, especially in determining why they usually have difficulties. The aim of the current study is to reveal what teachers know, and propose what they actually need to know for teaching the simplification and equivalence of algebraic expressions. The multiple-case study design was used for this study to compare and contrast the two middle school teachers‟ lesson planning and instruction. The data corpus included lesson plans, actual instruction records, and post-observation interviews. Data analysis was conducted using the Mathematical Knowledge for Teaching (MKT) model. The findings indicated that both teachers had a lack of specialized content knowledge about mathematical representations such as algebra tiles. They did not use algebra tiles effectively and could not link algebraic and geometric representations that underlie the idea of multiplication. It was observed that both teachers generally used unknowns and variables interchangeably indicating the inadequacy of their common content knowledge. In the planning process, the two teachers were able to state the common misconceptions that the students generally had and the ways of addressing them. Through the cases of these two teachers, it was observed that teachers need to have a good conceptual mathematical understanding and also knowledge of students‟ thinking in order to design effective lessons. Based on the findings, the types of knowledge that the teachers need to have are outlined and the theoretical and practical implications of the study are discussed

Tunable Superconducting Phase Transition in Metal-Decorated Graphene Sheets

Using typical experimental techniques it is difficult to separate the effects of carrier density and disorder on the superconducting transition in two dimensions. Using a simple fabrication procedure based on metal layer dewetting, we have produced graphene sheets decorated with a non-percolating network of nanoscale tin clusters. These metal clusters both efficiently dope the graphene substrate and induce long-range superconducting correlations. This allows us to study the superconducting transition at fixed disorder and variable carrier concentration. We find that despite structural inhomogeneity on mesoscopic length scales (10-100 nm), this material behaves electronically as a homogenous dirty superconductor. Our simple self-assembly method establishes graphene as an ideal tunable substrate for studying induced two-dimensional electronic systems at fixed disorder and our technique can readily be extended to other order parameters such as magnetism

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

Dynamics of quasiparticle trapping in Andreev levels

We present a theory describing the trapping and untrapping of quasiparticles in the Andreev bound level of a single-channel weak link between two superconductors. We calculate the rates of the transitions between even and odd occupations of the Andreev level induced by absorption and emission of both photons and phonons. We apply the theory to a recent experiment [Phys. Rev. Lett. 106, 257003 (2011)] in which the dynamics of the trapping of quasiparticles in the Andreev levels of superconducting atomic contacts coupled to a Josephson junction was measured. We show that the plasma energy $h\nu_p$ of the Josephson junction defines a rather abrupt transition between a fast relaxation regime dominated by coupling to photons and a slow relaxation regime dominated by coupling to phonons. With realistic parameters the theory provides a semi-quantitative description of the experimental results.Comment: 11 pages, 9 figures. Accepted for publication in Physical Review

On the Precision of Search Engines: Results from a Controlled Experiment

Handling the growing amount of digital information is one of the major challenges when dealing with the World Wide Web (WWW). In particular, users crave for an effective and efficient retrieval of needed information. In this context, search engines adopt a key role. Besides conventional search engines such as Google, semantic search engines have emerged as an alternative approach in recent years. The quality of search results delivered by search engines is in influenced by many criteria. This paper picks up one specific issue, the precision, and investigates and compares the precision of current both conventional (i.e., non-semantic) and semantic search engines based on a controlled experiment with 77 participants. Specifically, Google, AltaVista, MetaGer, Hakia, Kngine, and WolframAlpha are investigated and compared