Current-current correlations in hybrid superconducting and normal metal multiterminal structures

We consider a hybrid system consisting of two normal metal leads weakly connected to a superconductor. Current-current correlations of the normal leads are studied in the tunneling limit at subgap voltages and temperatures. We find that only two processes contribute to the cross-correlation: the crossed Andreev reflection (emission of electrons in different leads) and the elastic cotunneling. Both processes are possible due to the finite size of the Cooper pair. Noise measurements can thus be used to probe directly the superconducting wave function without the drawbacks appearing in average current measurements where the current is dominated by direct Andreev reflection processes. By tuning the voltages it is possible to change the sign of the cross correlation. Quantitative predictions are presented both in the diffusive and ballistic regimes.Comment: 7 pages, 2 Figure

Geometric phase for mixed states: a differential geometric approach

A new definition and interpretation of geometric phase for mixed state cyclic unitary evolution in quantum mechanics are presented. The pure state case is formulated in a framework involving three selected Principal Fibre Bundles, and the well known Kostant-Kirillov-Souriau symplectic structure on (co) adjoint orbits associated with Lie groups. It is shown that this framework generalises in a natural and simple manner to the mixed state case. For simplicity, only the case of rank two mixed state density matrices is considered in detail. The extensions of the ideas of Null Phase Curves and Pancharatnam lifts from pure to mixed states are also presented.Comment: 22 pages, revtex

Leachate Analyses of volcanic ashes from the 2010 Eyjafjallaj\uf6kull eruption

Volcanic processes which lead to eruptions can be investigated by monitoring a variety of parameters, including the composition of ash leachates. Fine-grained tephra erupted from active vents, and transported through volcanic plumes, can adsorb, and therefore rapidly scavenge, volatile elements such as sulphur, halogens, and metal species in the form of soluble salts adhering to ash surfaces. Analysis of such water-soluble surface materials is a suitable complement for the remote sensing of volcanic gases at inaccessible volcanoes. The April 2010 Eyjafjallaj\uf6kull eruption has been characterised by several distinct phases, with an initial effusion of alkali basalt on the volcano's northeast flank since March 20th, followed (since April 14th) by a complex summit, sustained, explosive to mixed activity, characterised by trachyandesitic magma The first phase of the summit eruption (14 to 18 April) was initially characterised by interaction between glacial meltwater from the icecap and erupting magma, and by three main pulses during which dark ash plumes were dispersed to the SE and S. Following a decrease in the intensity in explosive activity associated to the emission of a lava flow (from 19 April to 4 May), activity renewed in intensity on 5 May, when an ash-laden plume, up to 10 km in height, was continuously dispersed until May 18. Activity progressively declined and eruption closed on 9 June [1]. Here, we report on the chemical composition of leachates from volcanic ash samples deposited during the Eyjafjallaj\uf6kull explosive phase (from 14 April to 8 May). Twenty-eight freshly fallen volcanic ash samples were collected at various distances from the eruptive vent, and their leached solutions were analyzed for major and trace elements. We show that ash leachate solutions from Eyjafjallaj\uf6kull are dominated - among cations - by Na and Ca, while they display nearly equal S:Cl:F abundances (mean S/Cl and S/F molar ratios of 1.04 and 0.76 respectively), as characteristic of divergent-plate and within-plate volcanism. The good correlations between Ca and F (r2=0.8), Ca and SO4 (r2=0.7), and Na and Cl (r2=0.9) in ash leachates suggest that fluorite, anhydrite, and halite were the most likely soluble surface minerals formed in the plume (and therefore leached during our experiments). These correlations in the extracted solutions also indicate that either the sources of cations and anions in ash leachates were the same (e.g. direct condensation of NaCl(g) and CaSO4(g) from the plume) or, more probably, that the highest the condensation of plume acidic compounds (e.g., SO2(g), HCl(g), HF(g)) on ash, the largest the leaching of cations from silicate fragments. Indeed, our data bring evidence for that the extent of gas-ash reaction (likely, a proxy for ash residence time in the plume) was a key casual factor in determining ash leachate composition. Samples from the 4- 8th May eruptive period, showing the most acid pH values (4.5-5.5), consistently have the highest abundances for all elements, and especially Mg, S and F. Large variations in S and halogens proportions are observed in our dataset, with samples from the 4-8th May eruptive period showing the highest S/Cl and lowest Cl/F ratios. To interpret these variations, and particularly to verify whether they reflect changes in plume gas composition, in gas-ash reaction dynamics and rates,2]will require in-depth comparison with direct (FTIR) measurement of the Eyjafjallaj\uf6kull gas plume[2] . [1] Hoskuldsson, A., et al., 2011. Geophysical Research Abstracts Vol. 13, EGU2011-14165, 2011; [2] Allard, P., et al., 2010. Abstract V53F-07 presented at Fall Meeting, AGU, San Francisco, Calif. 13-17 Dec.

Unusual condensates in quark and atomic systems

In these lectures we discuss condensates which are formed in quark matter when it is squeezed and in a gas of fermionic atoms when it is cooled. The behavior of these two seemingly very different systems reveals striking similarities. In particular, in both systems the Bose-Einstein condensate to Bardeen--Cooper-Schrieffer (BEC-BCS) crossover takes place.Comment: Lectures delivered at 8th Moscow school of Physics (33rd ITEP Winter School of Physics

Thermodynamics of Crossover from Weak- to Strong-Coupling Superconductivity

In this paper we study an evolution of low-temperature thermodynamical quantities for an electron gas with a $\delta$-function attraction as the system crosses over from weak-coupling (BCS-type) to strong-coupling (Bose-type) superconductivity in three and two dimensions.Comment: Replaced with journal version. Insignificant presentation changes. Links to related papers are also available at the author home page http://www.teorfys.uu.se/PEOPLE/egor

Topological Phases near a Triple Degeneracy

We study the pattern of three state topological phases that appear in systems with real Hamiltonians and wave functions. We give a simple geometric construction for representing these phases. We then apply our results to understand previous work on three state phases. We point out that the ``mirror symmetry'' of wave functions noticed in microwave experiments can be simply understood in our framework.Comment: 4 pages, 1 figure, to appear in Phys. Rev. Let

Off-Diagonal Geometric Phases

We investigate the adiabatic evolution of a set of non-degenerate eigenstates of a parameterized Hamiltonian. Their relative phase change can be related to geometric measurable quantities that extend the familiar concept of Berry phase to the evolution of more than one state. We present several physical systems where these concepts can be applied, including an experiment on microwave cavities for which off-diagonal phases can be determined from published data.Comment: 5 pages 2 figures - RevTeX. Revised version including geometrical interpretatio

Geometric Phases and Multiple Degeneracies in Harmonic Resonators

In a recent experiment Lauber et al. have deformed cyclically a microwave resonator and have measured the adiabatic normal-mode wavefunctions for each shape along the path of deformation. The nontrivial observed cyclic phases around a 3-fold degeneracy were accounted for by Manolopoulos and Child within an approximate theory. However, open-path geometrical phases disagree with experiment. By solving exactly the problem, we find unsuspected extra degeneracies around the multiple one that account for the measured phase changes throughout the path. It turns out that proliferation of additional degeneracies around a multiple one is a common feature of quantum mechanics.Comment: 4 pages, 4 figures. Accepted in Phys. Rev. Let

Dynamics of quantum systems

A relation between the eigenvalues of an effective Hamilton operator and the poles of the $S$ matrix is derived which holds for isolated as well as for overlapping resonance states. The system may be a many-particle quantum system with two-body forces between the constituents or it may be a quantum billiard without any two-body forces. Avoided crossings of discrete states as well as of resonance states are traced back to the existence of branch points in the complex plane. Under certain conditions, these branch points appear as double poles of the $S$ matrix. They influence the dynamics of open as well as of closed quantum systems. The dynamics of the two-level system is studied in detail analytically as well as numerically.Comment: 21 pages 7 figure

Observation of off-diagonal geometric phase in polarized neutron interferometer experiments

Off-diagonal geometric phases acquired in the evolution of a spin-1/2 system have been investigated by means of a polarized neutron interferometer. Final counts with and without polarization analysis enable us to observe simultaneously the off-diagonal and diagonal geometric phases in two detectors. We have quantitatively measured the off-diagonal geometric phase for noncyclic evolutions, confirming the theoretical predictions. We discuss the significance of our experiment in terms of geometric phases (both diagonal and off-diagonal) and in terms of the quantum erasing phenomenon.Comment: pdf, 22 pages + 8 figures (included in the pdf). In print on Phys. Rev.