Phase retrapping in aφJosephson junction: onset of the butterfly effect

We investigate experimentally the retrapping of the phase in a φ Josephson junction upon return of the junction to the zero-voltage state. Since the Josephson energy profile U 0 ( ψ ) in φ JJ is a 2 π periodic double-well potential with minima at ψ = ± φ mod 2 π , the question is at which of the two minima − φ or + φ the phase will be trapped upon return from a finite voltage state during quasistatic decrease of the bias current (tilt of the potential). By measuring the relative population of two peaks in escape histograms, we determine the probability of phase trapping in the ± φ wells for different temperatures. Our experimental results agree qualitatively with theoretical predictions. In particular, we observe an onset of the butterfly effect with an oscillating probability of trapping. Unexpectedly, this probability saturates at a value different from 50% at low temperatures

Analytical calculation of the excess current in the OTBK theory

We present an analytical derivation of the excess current in Josephson junctions within the Octavio-Tinkham-Blonder-Klapwijk theory for both symmetric and asymmetric barrier strengths. We confirm the result found numerically by Flensberg et al. for equal barriers [Phys. Rev. B 38, 8707 (1988)], including the prediction of negative excess current for low transparencies, and we generalize it for differing barriers. Our analytical formulae provide for convenient fitting of experimental data, also in the less studied, but practically relevant case of the barrier asymmetry.Comment: 13 pages, 3 figures, submitted to Superconductor Science and Technolog

Multi-Particle Universal Processes

We generalize bipartite universal processes to the subclass of multi-particle universal processes from one to N particles. We show how the general statement for a multi-particle universal process can be constructed. The one-parameter family of processes generating totally anti-symmetric states has been generalized to a multi-particle regime and its entanglement properties have been studied. A view is given on the complete positivity and the possible physical realization of universal processes.

Completely positive covariant two-qubit quantum processes and optimal quantum NOT operations for entangled qubit pairs

The structure of all completely positive quantum operations is investigated which transform pure two-qubit input states of a given degree of entanglement in a covariant way. Special cases thereof are quantum NOT operations which transform entangled pure two-qubit input states of a given degree of entanglement into orthogonal states in an optimal way. Based on our general analysis all covariant optimal two-qubit quantum NOT operations are determined. In particular, it is demonstrated that only in the case of maximally entangled input states these quantum NOT operations can be performed perfectly.Comment: 14 pages, 2 figure

Electron transport in single wall carbon nanotube weak links in the Fabry-Perot regime

We fabricated reproducible high transparency superconducting contacts consisting of superconducting Ti/Al/Ti trilayers to gated single-walled carbon nanotubes (SWCNTs). The reported semiconducting SWCNT have normal state differential conductance up to $3e^2/h$ and exhibit clear Fabry-Perot interference patterns in the bias spectroscopy plot. We observed subharmonic gap structure in the differential conductance and a distinct peak in the conductance at zero bias which is interpreted as a manifestation of a supercurrent. The gate dependence of this supercurrent as well as the excess current are examined and compared to a coherent theory of superconducting point contacts with good agreement.Comment: 10 pages, 4 figure

Optimal copying of entangled two-qubit states

We investigate the problem of copying pure two-qubit states of a given degree of entanglement in an optimal way. Completely positive covariant quantum operations are constructed which maximize the fidelity of the output states with respect to two separable copies. These optimal copying processes hint at the intricate relationship between fundamental laws of quantum theory and entanglement.Comment: 13 pages, 7 figure

On apparent breaking the second law of thermodynamics in quantum transport studies

We consider a model for stationary electronic transport through a one-dimensional chain of two leads attached to a perturbed central region (quantum dot) in the regime where the theory proposed recently by Capek for a similar model of phonon transport predicts the striking phenomenon of a permanent current between the leads. This result based on a rigorous but asymptotic Davies theory is at variance with the zero current yielded by direct transport calculations which can be carried out in the present model. We find the permanent current to be within the error of the asymptotic expansion for finite couplings, and identify cancelling terms of the same order.Comment: 5 pages, 3 figure

Defining rural areas of Visegrad countries

The article is focused on the introduction and categorization of various approaches to rurality, and the identification and delimitation of rural areas in Visegrad countries. Three substantively different groups of conceptualizations and definitions of rural and rurality are described as follows: functional definitions, rural as locality (political-economic approaches), and social representation. Latter, basic sorts of methods and appro - aches to the delimitation of rural areas in V4 countries are introduced emphasizing its historical development, differences in spatial level and criteria of delimitation in current research. Due to different nature of rural areas and even local administrative units (the basic units usually used for delimitation of rural areas), it is not possible to reach sufficient and reliable identification of rural areas for whole V4 area using any of criteria or definitions applied in the research at national levels. Therefore, the average population density of entire V4 area was used as a main criterion for distinguishing between urban and rural LAU 2 at the whole Visegrad area level. Such approach is also affected by generalization but it captures various conditions in each country relatively well and moreover, it is comparable with the OECD and European Union methods to some extent