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

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

Proposal for the observation of nonlocal multipair production: the biSQUID

We propose an all-superconducting three-terminal setup consisting in a carbon nanotube (or semiconducting nanowire) contacted to three superconducting leads. The resulting device, referred to as a "biSQUID", is made of four quantum dots arranged in two loops of different surface area. We show how this biSQUID can prove a useful tool to probe nonlocal quantum phenomena in an interferometry setup. We study the measured critical current as a function of the applied magnetic field, which shows peaks in its Fourier spectrum, providing clear signatures of multipair Josephson processes. The device does not require any specific fine-tuning as these features are observed for a wide range of microscopic parameters -- albeit with a non-trivial dependence. Competing effects which may play a significant role in actual experimental realizations are also explored.Comment: 13 pages, 9 figure

Multipair DC-Josephson Resonances in a biased all-superconducting Bijunction

An all-superconducting bijunction consists of a central superconductor contacted to two lateral superconductors, such that non-local crossed Andreev reflection is operating. Then new correlated transport channels for the Cooper pairs appear in addition to those of separated conventional Joseph- son junctions. We study this system in a configuration where the superconductors are connected through gate-controllable quantum dots. Multipair phase-coherent resonances and phase-dependent multiple Andreev reflections are both obtained when the voltages of the lateral superconductors are commensurate, and they add to the usual local dissipative transport due to quasiparticles. The two-pair resonance (quartets) as well as some other higher order multipair resonances are {\pi}-shifted at low voltage. Dot control can be used to dramatically enhance the multipair current when the voltages are resonant with the dot levels.Comment: 6 page

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

Greenhouse gas emissions mitigation in more sustainable agroecosystems in Cerrado.

In this work, we show that the transition to more sustainable rural production can mitigate greenhouse gas (GHG) emissions by agroecosystems without compromising revenues, particularly in the Cerrado region.(Embrapa Gado de Corte. Documentos, 216). Coordenador Roberto Giolo de Almeida. II SIGEE. Disponível em: . Acesso em: 30 nov. 2016

Gaseous fluxes in oxisol soil surfaces at integrated plant-livestock systems.

The experiment consisted of additionally applying swine effluent of biodigester as an organic fertilizer with known doses (measured, not shown) in sites with arrangements of forestry mixed with agriculture (soya/corn rotation).(Embrapa Gado de Corte. Documentos, 216). Coordenador Roberto Giolo de Almeida. II SIGEE. Disponível em: . Acesso em: 30 nov. 2016

A Continued Fraction-Hyperbola based Attack on RSA cryptosystem

In this paper we present new arithmetical and algebraic results following the work of Babindamana and al. on hyperbolas and describe from the new results an approach to attacking a RSA-type modulus based on continued fractions, independent and not bounded by the size of the private key $d$ nor public exponent $e$ compared to Wiener's attack. When successful, this attack is bounded by $\displaystyle\mathcal{O}\left( b\log{\alpha_{j4}}\log{(\alpha_{i3}+\alpha_{j3})}\right)$ with $b=10^{y}$, $\alpha_{i3}+\alpha_{j3}$ a non trivial factor of $n$ and $\alpha_{j4}$ such that $(n+1)/(n-1)=\alpha_{i4}/\alpha_{j4}$. The primary goal of this attack is to find a point $\displaystyle X_{\alpha}=\left(-\alpha_{3}, \ \alpha_{3}+1 \right) \in \mathbb{Z}^{2}_{\star}$ that satisfies $\displaystyle\left\langle X_{\alpha_{3}}, \ P_{3} \right\rangle =0$ from a convergent of $\displaystyle\frac{\alpha_{i4}}{\alpha_{j4}}+\delta$, with $P_{3}\in \mathcal{B}_{n}(x, y)_{\mid_{x\geq 4n}}$. We finally present some experimental examples. We believe these results constitute a new direction in RSA Cryptanalysis using continued fractions