Inducing odd-frequency triplet superconducting correlations in a normal metal

This work discusses theoretically the interplay between the superconducting and ferromagnetic proximity effects, in a diffusive normal metal strip in contact with a superconductor and a non-uniformly magnetized ferromagnetic insulator. The quasiparticle density of states of the normal metal shows clear qualitative signatures of triplet correlations with spin one (TCS1). When one goes away from the superconduting contact, TCS1 focus at zero energy under the form of a peak surrounded by dips, which show a typical spatial scaling behavior. This behavior can coexist with a focusing of singlet correlations and triplet correlations with spin zero at finite but subgap energies. The simultaneous observation of both effects would enable an unambigous characterization of TCS1.Comment: To appear in Physical Review Letter

Probing coherent Cooper pair splitting with cavity photons

This work discusses theoretically the behavior of a microwave cavity and a Cooper pair beam splitter (CPS) coupled non-resonantly. The cavity frequency pull is modified when the CPS is resonant with a microwave excitation. This provides a direct way to probe the coherence of the Cooper pair splitting process. More precisely, the cavity frequency pull displays an anticrossing whose specificities can be attributed unambiguously to coherent Cooper pair injection. This work illustrates that microwave cavities represent a powerful tool to investigate current transport in complex nanocircuits.Comment: 7 pages, 4 figure

Conductance and current noise of a superconductor/ferromagnet quantum point contact

We study the conductance and current noise of a superconductor/ferromagnet (S/F) single channel Quantum Point Contact (QPC) as a function of the QPC bias voltage, using a scattering approach. We show that the Spin-Dependence of Interfacial Phase Shifts (SDIPS) acquired by electrons upon scattering by the QPC can strongly modify these signals. For a weakly transparent contact, the SDIPS induces sub-gap resonances in the conductance and differential Fano factor curves of the QPC. For high transparencies, these resonances are smoothed, but the shape of the signals remain extremely sensitive to the SDIPS. We show that noise measurements could help to gain more information on the device, e.g. in cases where the SDIPS modifies qualitatively the differential Fano factor of the QPC but not the conductance.Comment: 9 pages, 4 figure

A spin quantum bit with ferromagnetic contacts for circuit QED

We theoretically propose a scheme for a spin quantum bit based on a double quantum dot contacted to ferromagnetic elements. Interface exchange effects enable an all electric manipulation of the spin and a switchable strong coupling to a superconducting coplanar waveguide cavity. Our setup does not rely on any specific band structure and can in principle be realized with many different types of nanoconductors. This allows to envision on-chip single spin manipulation and read-out using cavity QED techniques

Divide and conquer in ABC: Expectation-Progagation algorithms for likelihood-free inference

ABC algorithms are notoriously expensive in computing time, as they require simulating many complete artificial datasets from the model. We advocate in this paper a "divide and conquer" approach to ABC, where we split the likelihood into n factors, and combine in some way n "local" ABC approximations of each factor. This has two advantages: (a) such an approach is typically much faster than standard ABC and (b) it makes it possible to use local summary statistics (i.e. summary statistics that depend only on the data-points that correspond to a single factor), rather than global summary statistics (that depend on the complete dataset). This greatly alleviates the bias introduced by summary statistics, and even removes it entirely in situations where local summary statistics are simply the identity function. We focus on EP (Expectation-Propagation), a convenient and powerful way to combine n local approximations into a global approximation. Compared to the EP- ABC approach of Barthelm\'e and Chopin (2014), we present two variations, one based on the parallel EP algorithm of Cseke and Heskes (2011), which has the advantage of being implementable on a parallel architecture, and one version which bridges the gap between standard EP and parallel EP. We illustrate our approach with an expensive application of ABC, namely inference on spatial extremes.Comment: To appear in the forthcoming Handbook of Approximate Bayesian Computation (ABC), edited by S. Sisson, L. Fan, and M. Beaumon

Mesoscopic admittance of a double quantum dot

We calculate the mesoscopic admittance $G(\omega)$ of a double quantum dot (DQD),which can be measured directly using microwave techniques. This quantity reveals spectroscopic information on the DQD and is also directly sensitive to a Pauli spin blockade effect. We then discuss the problem of a DQD coupled to a high quality photonic resonator. When the photon correlation functions can be developed along a random-phase-approximation-like scheme, the response of the resonator gives an access to $G(\omega)$

Squeezing light with Majorana fermions

Coupling a semiconducting nanowire to a microwave cavity provides a powerfull means to assess the presence or absence of isolated Majorana fermions in the nanowire. These exotic bound states can cause a significant cavity frequency shift but also a strong cavity nonlinearity leading for instance to light squeezing. The dependence of these effects on the nanowire gate voltages gives direct signatures of the unique properties of Majorana fermions, such as their self-adjoint character and their exponential confinement.Comment: long version: 11 pages, 5 figure

Subradiant split Cooper pairs

We suggest a way to characterize the coherence of the split Cooper pairs emitted by a double-quantum-dot based Cooper pair splitter (CPS), by studying the radiative response of such a CPS inside a microwave cavity. The coherence of the split pairs manifests in a strongly nonmonotonic variation of the emitted radiation as a function of the parameters controlling the coupling of the CPS to the cavity. The idea to probe the coherence of the electronic states using the tools of Cavity Quantum Electrodynamics could be generalized to many other nanoscale circuits.Comment: Main text + Supplemental material file (15 pages, 5 figures), to appear in Physical Review Letter

Numerical analysis of a penalization method for the three-dimensional motion of a rigid body in an incompressible viscous fluid

We present and analyze a penalization method wich extends the the method of [1] to the case of a rigid body moving freely in an incompressible fluid. The fluid-solid system is viewed as a single variable density flow with an interface captured by a level set method. The solid velocity is computed by averaging at avery time the flow velocity in the solid phase. This velocity is used to penalize the flow velocity at the fluid-solid interface and to move the interface. Numerical illustrations are provided to illustrate our convergence result. A discussion of our result in the light of existing existence results is also given. [1] Ph. Angot, C.-H. Bruneau and P. Fabrie, A penalization method to take into account obstacles in incompressible viscous flows, Numer. Math. 81: 497--520 (1999)Comment: 23 page