Dual approach to circuit quantization using loop charges

The conventional approach to circuit quantization is based on node fluxes and traces the motion of node charges on the islands of the circuit. However, for some devices, the relevant physics can be best described by the motion of polarization charges over the branches of the circuit that are in general related to the node charges in a highly nonlocal way. Here, we present a method, dual to the conventional approach, for quantizing planar circuits in terms of loop charges. In this way, the polarization charges are directly obtained as the differences of the two loop charges on the neighboring loops. The loop charges trace the motion of fluxes through the circuit loops. We show that loop charges yield a simple description of the flux transport across phase-slip junctions. We outline a concrete construction of circuits based on phase-slip junctions that are electromagnetically dual to arbitrary planar Josephson junction circuits. We argue that loop charges also yield a simple description of the flux transport in conventional Josephson junctions shunted by large impedances. We show that a mixed circuit description in terms of node fluxes and loop charges yields an insight into the flux decompactification of a Josephson junction shunted by an inductor. As an application, we show that the fluxonium qubit is well approximated as a phase-slip junction for the experimentally relevant parameters. Moreover, we argue that the $0$-$\pi$ qubit is effectively the dual of a Majorana Josephson junction.Comment: 20 pages, 11 figures. Version accepted for publication in PRB. Changes: introduction has become less technical and an example for the inclusion of offset charges has been adde

Majorana-assisted nonlocal electron transport through a floating topological superconductor

The nonlocal nature of the fermionic mode spanned by a pair of Majorana bound states in a one-dimensional topological superconductor has inspired many proposals aiming at demonstrating this property in transport. In particular, transport through the mode from a lead attached to the left bound state to a lead attached to the right will result in current cross-correlations. For ideal zero modes on a grounded superconductor, the cross-correlations are however completely suppressed in favor of purely local Andreev reflection. In order to obtain a non-vanishing cross-correlation, previous studies have required the presence of an additional global charging energy. Adding nonlocal terms in the form of a global charging energy to the Hamiltonian when testing the intrinsic nonlocality of the Majorana modes seems to be conceptually troublesome. Here, we show that a floating superconductor allows to observe nonlocal current correlations in the absence of charging energy. We show that the non-interacting and the Coulomb-blockade regime have the same peak conductance $e^2/h$ but different shot-noise power; while the shot noise is sub-Poissonian in the Coulomb-blockade regime in the large bias limit, Poissonian shot noise is generically obtained in the non-interacting case

Supersymmetry in the Majorana Cooper-Pair Box

Over the years, supersymmetric quantum mechanics has evolved from a toy model of high energy physics to a field of its own. Although various examples of supersymmetric quantum mechanics have been found, systems that have a natural realization are scarce. Here, we show that the extension of the conventional Cooper-pair box by a 4pi-periodic Majorana-Josephson coupling realizes supersymmetry for certain values of the ratio between the conventional Josephson and the Majorana- Josephson coupling strength. The supersymmetry we find is a "hidden" minimally bosonized supersymmetry that provides a non-trivial generalization of the supersymmetry of the free particle and relies crucially on the presence of an anomalous Josephson junction in the system. We show that the resulting degeneracy of the energy levels can be probed directly in a tunneling experiment and discuss the various transport signatures. An observation of the predicted level degeneracy would provide clear evidence for the presence of the anomalous Josephson coupling.Comment: 10 pages, 5 figure

Universal power-law decay of electron-electron interactions due to nonlinear screening in a Josephson junction array

Josephson junctions are the most prominent nondissipative and at the same time nonlinear elements in superconducting circuits allowing Cooper pairs to tunnel coherently between two superconductors separated by a tunneling barrier. Due to this, physical systems involving Josephson junctions show highly complex behavior and interesting novel phenomena. Here, we consider an infinite one-dimensional chain of superconducting islands where neighboring islands are coupled by capacitances. We study the effect of Josephson junctions shunting each island to a common ground superconductor. We treat the system in the regime where the Josephson energy exceeds the capacitive coupling between the islands. For the case of two offset charges on two distinct islands, we calculate the interaction energy of these charges mediated by quantum phase slips due to the Josephson nonlinearities. We treat the phase slips in an instanton approximation and map the problem onto a classical partition function of interacting particles. Using the Mayer cluster expansion, we find that the interaction potential of the offset charges decays with an universal inverse-square power law behavior.Comment: 10 pages, 5 figure

Spectral Properties and Local Density of States of Disordered Quantum Hall Systems with Rashba Spin-Orbit Coupling

We theoretically investigate the spectral properties and the spatial dependence of the local density of states (LDoS) in disordered two-dimensional electron gases (2DEG) in the quantum Hall regime, taking into account the combined presence of electrostatic disorder, random Rashba spin-orbit in- teraction, and finite Zeeman coupling. To this purpose, we extend a coherent-state Green's function formalism previously proposed for spinless 2DEG in the presence of smooth arbitrary disorder, that here incorporates the nontrivial coupling between the orbital and spin degrees of freedom into the electronic drift states. The formalism allows us to obtain analytical and controlled nonperturbative expressions of the energy spectrum in arbitrary locally flat disorder potentials with both random electric fields and Rashba coupling. As an illustration of this theory, we derive analytical microscopic expressions for the LDoS in different temperature regimes which can be used as a starting point to interpret scanning tunneling spectroscopy data at high magnetic fields. In this context, we study the spatial dependence and linewidth of the LDoS peaks and explain an experimentally-noticed correlation between the spatial dispersion of the spin-orbit splitting and the local extrema of the potential landscape.Comment: 18 pages, 5 figures; typos corrected and Sec. IV A rewritten; published versio

Probing variations of the Rashba spin-orbit coupling at the nanometer scale

The Rashba effect as an electrically tunable spin-orbit interaction is the base for a multitude of possible applications such as spin filters, spin transistors, and quantum computing using Majorana states in nanowires. Moreover, this interaction can determine the spin dephasing and antilocalization phenomena in two dimensions. However, the real space pattern of the Rashba parameter has never been probed, albeit it critically influences, e.g., the more robust spin transistors using the spin helix state and the otherwise forbidden electron backscattering in topologically protected channels. Here, we map this pattern down to nanometer length scales by measuring the spin splitting of the lowest Landau level using scanning tunnelling spectroscopy. We reveal strong fluctuations correlated with the local electrostatic potential for an InSb inversion layer with a large Rashba coefficient (~1 eV{\AA}). The novel type of Rashba field mapping enables a more comprehensive understanding of the critical fluctuations, which might be decisive towards robust semiconductor-based spintronic devices.Comment: A modified version will be published in Nature Physic

The pyramid scheme of the Gestapo in its fight against the German resistance movement: A Cologne case study

At some moment sooner or later in any of the big investigations and persecutions against the resistance movement conducted by the Gestapo, the German secret police of the Third Reich, they found one suspected person ready not only to reveal his own contribution to the resistance movement but to accuse other participants for their part. From the first testimony on an entire pyramid scheme of mutual allegations by the accused resistants was generated. We tried to analyze this scheme by means of methods and software developed by Social Network Analysts and were able to show how much the Gestapo benefitted from rather ordinary criminological means.At some moment sooner or later in any of the big investigations and persecutions against the resistance movement conducted by the Gestapo, the German secret police of the Third Reich, they found one suspected person ready not only to reveal his own contribution to the resistance movement but to accuse other participants for their part. From the first testimony on an entire pyramid scheme of mutual allegations by the accused resistants was generated. We tried to analyze this scheme by means of methods and software developed by Social Network Analysts and were able to show how much the Gestapo benefitted from rather ordinary criminological means

Physics case for an LHCb Upgrade II - Opportunities in flavour physics, and beyond, in the HL-LHC era

The LHCb Upgrade II will fully exploit the flavour-physics opportunities of the HL-LHC, and study additional physics topics that take advantage of the forward acceptance of the LHCb spectrometer. The LHCb Upgrade I will begin operation in 2020. Consolidation will occur, and modest enhancements of the Upgrade I detector will be installed, in Long Shutdown 3 of the LHC (2025) and these are discussed here. The main Upgrade II detector will be installed in long shutdown 4 of the LHC (2030) and will build on the strengths of the current LHCb experiment and the Upgrade I. It will operate at a luminosity up to 2×1034 cm−2s−1, ten times that of the Upgrade I detector. New detector components will improve the intrinsic performance of the experiment in certain key areas. An Expression Of Interest proposing Upgrade II was submitted in February 2017. The physics case for the Upgrade II is presented here in more depth. CP-violating phases will be measured with precisions unattainable at any other envisaged facility. The experiment will probe b → sl+l−and b → dl+l− transitions in both muon and electron decays in modes not accessible at Upgrade I. Minimal flavour violation will be tested with a precision measurement of the ratio of B(B0 → μ+μ−)/B(Bs → μ+μ−). Probing charm CP violation at the 10−5 level may result in its long sought discovery. Major advances in hadron spectroscopy will be possible, which will be powerful probes of low energy QCD. Upgrade II potentially will have the highest sensitivity of all the LHC experiments on the Higgs to charm-quark couplings. Generically, the new physics mass scale probed, for fixed couplings, will almost double compared with the pre-HL-LHC era; this extended reach for flavour physics is similar to that which would be achieved by the HE-LHC proposal for the energy frontier

LHCb upgrade software and computing : technical design report

This document reports the Research and Development activities that are carried out in the software and computing domains in view of the upgrade of the LHCb experiment. The implementation of a full software trigger implies major changes in the core software framework, in the event data model, and in the reconstruction algorithms. The increase of the data volumes for both real and simulated datasets requires a corresponding scaling of the distributed computing infrastructure. An implementation plan in both domains is presented, together with a risk assessment analysis