Cooper pair splitting in a nanoSQUID geometry at high transparency

We describe a Josephson device composed of two superconductors separated by two interacting quantum dots in parallel, as a probe for Cooper pair splitting. In addition to sequential tunneling of electrons through each dot, an additional transport channel exists in this system: crossed Andreev reflection, where a Cooper pair from the source is split between the two dots and recombined in the drain superconductor. Unlike non-equilibrium scenarios for Cooper pair splitting which involves superconducting/normal metal "forks", our proposal relies on an Aharonov-Bohm measurement of the DC Josephson current when a flux is inserted between the two dots. We provide a path integral approach to treat arbitrary transparencies, and we explore all contributions for the individual phases ($0$ or $\pi$) of the quantum dots. We propose a definition of the Cooper pair splitting efficiency for arbitrary transparencies, which allows us to find the phase associations which favor the crossed Andreev process. Possible applications to experiments using nanowires as quantum dots are discussed.Comment: 12 pages, 13 figure

Hanbury Brown and Twiss noise correlations in a topological superconductor beam splitter

We study Hanbury-Brown and Twiss current cross-correlations in a three-terminal junction where a central topological superconductor (TS) nanowire, bearing Majorana bound states at its ends, is connected to two normal leads. Relying on a non-perturbative Green function formalism, our calculations allow us to provide analytical expressions for the currents and their correlations at subgap voltages, while also giving exact numerical results valid for arbitrary external bias. We show that when the normal leads are biased at voltages $V_1$ and $V_2$ smaller than the gap, the sign of the current cross-correlations is given by -\mbox{sgn}(V_1 \, V_2). In particular, this leads to positive cross-correlations for opposite voltages, a behavior in stark contrast with the one of a standard superconductor, which provides a direct evidence of the presence of the Majorana zero-mode at the edge of the TS. We further extend our results, varying the length of the TS (leading to an overlap of the Majorana bound states) as well as its chemical potential (driving it away from half-filling), generalizing the boundary TS Green function to those cases. In the case of opposite bias voltages, \mbox{sgn}(V_1 \, V_2)=-1, driving the TS wire through the topological transition leads to a sign change of the current cross-correlations, providing yet another signature of the physics of the Majorana bound state.Comment: 14 pages, 8 figure

Giant shot noise from Majorana zero modes in topological trijunctions

The clear-cut experimental identification of Majorana bound states in transport measurements still poses experimental challenges. We here show that the zero-energy Majorana state formed at a junction of three topological superconductor wires is directly responsible for giant shot noise amplitudes, in particular at low voltages and for small contact transparency. The only intrinsic noise limitation comes from the current-induced dephasing rate due to multiple Andreev reflection processes

Observation of coherent backscattering of light by cold atoms

Coherent backscattering (CBS) of light waves by a random medium is a signature of interference effects in multiple scattering. This effect has been studied in many systems ranging from white paint to biological tissues. Recently, we have observed CBS from a sample of laser-cooled atoms, a scattering medium with interesting new properties. In this paper we discuss various effects, which have to be taken into account for a quantitative study of coherent backscattering of light by cold atoms.Comment: 25 pages LaTex2e, 17 figures, submitted to J. Opt. B: Quant. Semicl. Op

Euclidean versus hyperbolic congestion in idealized versus experimental networks

This paper proposes a mathematical justification of the phenomenon of extreme congestion at a very limited number of nodes in very large networks. It is argued that this phenomenon occurs as a combination of the negative curvature property of the network together with minimum length routing. More specifically, it is shown that, in a large n-dimensional hyperbolic ball B of radius R viewed as a roughly similar model of a Gromov hyperbolic network, the proportion of traffic paths transiting through a small ball near the center is independent of the radius R whereas, in a Euclidean ball, the same proportion scales as 1/R^{n-1}. This discrepancy persists for the traffic load, which at the center of the hyperbolic ball scales as the square of the volume, whereas the same traffic load scales as the volume to the power (n+1)/n in the Euclidean ball. This provides a theoretical justification of the experimental exponent discrepancy observed by Narayan and Saniee between traffic loads in Gromov-hyperbolic networks from the Rocketfuel data base and synthetic Euclidean lattice networks. It is further conjectured that for networks that do not enjoy the obvious symmetry of hyperbolic and Euclidean balls, the point of maximum traffic is near the center of mass of the network.Comment: 23 pages, 4 figure

Unified scattering approach to Josephson current and thermal noise in BCS and topological superconducting junctions

We present a unified description of a junction between $s$-wave (BCS) superconductors and a junction between $p$-wave superconductors in a topologically nontrivial phase, which relies on a scattering state expansion. We compute Josephson current and thermal noise in the two kinds of junction and exhibit some characteristic features for a junction of two topological superconductors hosting Majorana zero-energy modes.Comment: 12 pages, 13 figure

Andreev quantum dot with several conducting channels

We study an Andreev quantum dot, that is a quantum dot inserted in a superconducting ring, with several levels or conducting channels. We analyze the degeneracy of the ground state as a function of the phase difference and of the gate voltage and find its dependence on the Coulomb interaction within and between channels. We compute a (non integer) charge of the dot region and Josephson current. The charge-to-phase and current-to-gate voltage sensitivities are studied. We find that, even in the presence of Coulomb interaction between the channels, the sensitivity increases with the number of channels, although it does not scale linearly as in the case with no interactions. The Andreev quantum dot may therefore be used as a sensitive detector of magnetic flux or as a Josephson transistor.Comment: 13 pages, 10 figures, minor correction

Needle age-related and seasonal photosynthetic capacity variation is negligible for modelling yearly gas exchange of a sparse temperate Scots pine forest

In this study, we quantified the predictive accuracy loss involved with omitting photosynthetic capacity variation for a Scots pine (<i>Pinus sylvestris</i> L.) stand in Flanders, Belgium. Over the course of one phenological year, we measured the maximum carboxylation capacity at 25 &deg;C (<i>V</i>_m25), the maximum electron transport capacity at 25 &deg;C (<i>J</i>_m25), and the leaf area index (LAI) of different-aged needle cohorts in the upper and lower canopy. We used these measurements as input for a process-based multi-layer canopy model with the objective to quantify the difference in yearly gross ecosystem productivity (GEP) and canopy transpiration (<i>E</i>_can) simulated under scenarios in which the observed needle age-related and/or seasonal variation of <i>V</i>_m25 and <i>J</i>_m25 was omitted. We compared simulated GEP with estimations obtained from eddy covariance measurements. Additionally, we measured summer needle N content to investigate the relationship between photosynthetic capacity parameters and needle N content along different needle ages. <br><br> Results show that <i>V</i>_m25 and <i>J</i>_m25 were, respectively, 27% and 13% higher in current-year than in one-year old needles. A significant seasonality effect was found on <i>V</i>_m25, but not on <i>J</i>_m25. Summer needle N content was considerably lower in current-year than in one-year-old needles. As a result, the correlations between <i>V</i>_m25 and needle N content and <i>J</i>_m25 and needle N content were negative and non-significant, respectively. Some explanations for these unexpected correlations were brought forward. Yearly GEP was overestimated by the canopy model by &plusmn;15% under all scenarios. The inclusion and omission of the observed needle age-related <i>V</i>_m25 and <i>J</i>_m25 variation in the model simulations led to statistically significant but ecologically irrelevant differences in simulated yearly GEP and <i>E</i>_can. Omitting seasonal variation did not yield significant simulation differences. Our results indicate that intensive photosynthetic capacity measurements over the full growing season and separate simulation of needle age classes were no prerequisites for accurate simulations of yearly canopy gas exchange. This is true, at least, for the studied stand, which has a very sparse canopy and is exposed to high N deposition and, hence, is not fully representative for temperate Scots pine stands. Nevertheless, we believe well-parameterized process-based canopy models – as applied in this study – are a useful tool to quantify losses of predictive accuracy involved with canopy simplification in modelling

Nonreciprocal charge transport and subharmonic structure in voltage-biased Josephson diodes

We study charge transport in voltage-biased single-channel junctions involving helical superconductors with finite Cooper pair momentum. For a Josephson junction, the equilibrium current-phase relation shows a superconducting diode effect: the critical current depends on the propagation direction. We formulate a scattering theory for voltage-biased Josephson diodes and show that multiple Andreev reflection processes cause a rich subharmonic structure in the DC current-voltage curve at low temperatures and small voltages which can be understood by accounting for Doppler shifts of the spectral gap. We study Josephson diodes both in and out of equilibrium, in particular the dependence of the nonlinear conductance (which determines the rectification efficiency) on the contact transparency and on the Cooper pair momentum. We also discuss charge transport for NS junctions between a normal metal and a helical superconductor and comment on related models with spin-orbit interactions and magnetic Zeeman fields.Comment: 18 pages, 6 figure

Theory of non-equilibrium noise in general multi-terminal superconducting hydrid devices: application to multiple Cooper pair resonances

We consider the out-of-equilibrium behavior of a general class of mesoscopic devices composed of several superconducting or/and normal metal leads separated by quantum dots. Starting from a microscopic Hamiltonian description, we provide a non-perturbative approach to quantum electronic transport in the tunneling amplitudes between dots and leads: using the equivalent of a path integral formulation, the lead degrees of freedom are integrated out in order to compute both the current and the current correlations (noise) in this class of systems, in terms of the dressed Green's function matrix of the quantum dots. In order to illustrate the efficiency of this formalism, we apply our results to the "all superconducting Cooper pair beam splitter", a device composed of three superconducting leads connected via two quantum dots, where crossed Andreev reflection operates Cooper pair splitting. Commensurate voltage differences between the three leads allow to obtain expressions for the current and noise as a function of the Keldysh Nambu Floquet dressed Green's function of the dot system. This voltage configuration allows the occurrence of non-local processes involving multiple Cooper pairs which ultimately lead to the presence of non-zero DC currents in an out-of-equilibrium situation. We investigate in details the results for the noise obtained numerically in the specific case of opposite voltages, where the transport properties are dominated by the so called "quartet processes", involving the coherent exchange of two Cooper pairs among all three superconducting terminals. We show that these processes are noiseless in the non-resonant case, and that this property is also observed for other voltage configurations. When the dots are in a resonant regime, the noise characteristics change qualitatively, with the appearance of giant Fano factors.Comment: 18 pages, 12 figure