Braiding of non-Abelian anyons using pairwise interactions

The common approach to topological quantum computation is to implement quantum gates by adiabatically moving non-Abelian anyons around each other. Here we present an alternative perspective based on the possibility of realizing the exchange (braiding) operators of anyons by adiabatically varying pairwise interactions between them rather than their positions. We analyze a system composed by four anyons whose couplings define a T-junction and we show that the braiding operator of two of them can be obtained through a particular adiabatic cycle in the space of the coupling parameters. We also discuss how to couple this scheme with anyonic chains in order to recover the topological protection.Comment: 8 pages, 7 figures. Errors corrected, clarifications and comments adde

Thermal conductance as a probe of the non-local order parameter for a topological superconductor with gauge fluctuations

We investigate the effect of quantum phase slips on a helical quantum wire coupled to a superconductor by proximity. The effective low-energy description of the wire is that of a Majorana chain minimally coupled to a dynamical $\mathbb{Z}_2$ gauge field. Hence the wire emulates a matter-coupled gauge theory, with fermion parity playing the role of the gauged global symmetry. Quantum phase slips lift the ground state degeneracy associated with unpaired Majorana edge modes at the ends of the chain, a change that can be understood as a transition between the confined and the Higgs-mechanism regimes of the gauge theory. We identify the quantization of thermal conductance at the transition as a robust experimental feature separating the two regimes. We explain this result by establishing a relation between thermal conductance and the Fredenhagen-Marcu string order-parameter for confinement in gauge theories. Our work indicates that thermal transport could serve as a measure of non-local order parameters for emergent or simulated topological quantum order.Comment: 5 pages, 2 figures; v2: different introduction, added references, updated figure 2; published version to appear in PR

Minimal circuit for a flux-controlled Majorana qubit in a quantum spin-Hall insulator

We construct a minimal circuit, based on the top-transmon design, to rotate a qubit formed out of four Majorana zero-modes at the edge of a two-dimensional topological insulator. Unlike braiding operations, generic rotations have no topological protection, but they do allow for a full characterization of the coherence times of the Majorana qubit. The rotation is controlled by variation of the flux through a pair of split Josephson junctions in a Cooper pair box, without any need to adjust gate voltages. The Rabi oscillations of the Majorana qubit can be monitored via oscillations in the resonance frequency of the microwave cavity that encloses the Cooper pair box.Comment: Contribution for the proceedings of the Nobel Symposium on topological insulators. 8 pages, 6 figure

Large Surveys in Cosmology: The Changing Sociology

Galaxy redshift surveys and Cosmic Microwave Background experiments are undertaken with larger and larger teams, in a fashion reminiscent of particle physics experiments and the human genome projects. We discuss the role of young researchers, the issue of multiple authorship, and ways to communicate effectively in teams of tens to hundreds of collaborators.Comment: Invited article for "Organizations and Strategies in Astronomy II", ed. A. Heck, Kluwer Acad. Publ., in press (7 pages, no figures

Zeeman and spin-orbit effects in the Andreev spectra of nanowire junctions

We study the energy spectrum and the electromagnetic response of Andreev bound states in short Josephson junctions made of semiconducting nanowires. We focus on the joint effect of Zeeman and spin-orbit coupling on the Andreev level spectra. Our model incorporates the penetration of the magnetic field in the proximitized wires, which substantially modifies the spectra. We pay special attention to the occurrence of fermion parity switches at increasing values of the field and to the magnetic field dependence of the absorption strength of microwave-induced transitions. Our calculations can be used to extract quantitative information from microwave and tunneling spectroscopy experiments, such as the recently reported measurements in Van Woerkom et al., arXiv:1609.00333.Comment: 22 pages, 12 figures. v2: a few edits in text and figures, references added. Published versio

Conductance of a proximitized nanowire in the Coulomb blockade regime

We identify the leading processes of electron transport across finite-length segments of proximitized nanowires and build a quantitative theory of their two-terminal conductance. In the presence of spin-orbit interaction, a nanowire can be tuned across the topological transition point by an applied magnetic field. Due to a finite segment length, electron transport is controlled by the Coulomb blockade. Upon increasing of the field, the shape and magnitude of the Coulomb blockade peaks in the linear conductance is defined, respectively, by Andreev reflection, single-electron tunneling, and resonant tunneling through the Majorana modes emerging after the topological transition. Our theory provides the framework for the analysis of experiments with proximitized nanowires, such as reported in Albrecht et al., Nature 531, 206-209 (2016), and identifies the signatures of the topological transition in the two-terminal conductance.Comment: 19 pages, 7 figures. v2: minor corrections. v3: a few typos fixed. Published in PRB, Editors' Suggestio

The Performance of CRTNT Fluorescence Light Detector for Sub-EeV Cosmic Ray Observation

Cosmic Ray Tau Neutrino Telescopes (CRTNT) using for sub-EeV cosmic ray measurement is discussed. Performances of a stereoscope configuration with a tower of those telescopes plus two side-triggers are studied. This is done by using a detailed detector simulation driven by Corsika. Detector aperture as a function of shower energy above 10^17 eV is calculated. Event rate of about 20k per year for the second knee measurement is estimated. Event rate for cross calibration with detectors working on higher energy range is also estimated. Different configurations of the detectors are tried for optimization.Comment: 5 pages, 4 figures, submitted to HEP & N

Single fermion manipulation via superconducting phase differences in multiterminal Josephson junctions

We show how the superconducting phase difference in a Josephson junction may be used to split the Kramers degeneracy of its energy levels and to remove all the properties associated with time reversal symmetry. The superconducting phase difference is known to be ineffective in two-terminal short Josephson junctions, where irrespective of the junction structure the induced Kramers degeneracy splitting is suppressed and the ground state fermion parity must stay even, so that a protected zero-energy Andreev level crossing may never appear. Our main result is that these limitations can be completely avoided by using multi-terminal Josephson junctions. There the Kramers degeneracy breaking becomes comparable to the superconducting gap, and applying phase differences may cause the change of the ground state fermion parity from even to odd. We prove that the necessary condition for the appearance of a fermion parity switch is the presence of a "discrete vortex" in the junction: the situation when the phases of the superconducting leads wind by $2\pi$. Our approach offers new strategies for creation of Majorana bound states as well as spin manipulation. Our proposal can be implemented using any low density, high spin-orbit material such as InAs quantum wells, and can be detected using standard tools.Comment: Source code available as ancillary files. 10 pages, 7 figures. v2: minor changes, published versio

Topologically protected charge transfer along the edge of a chiral p\textit{p}-wave superconductor

The Majorana fermions propagating along the edge of a topological superconductor with $p_x+ip_y$ pairing deliver a shot noise power of $\frac{1}{2}\times e^2/h$ per eV of voltage bias. We calculate the full counting statistics of the transferred charge and find that it becomes trinomial in the low-temperature limit, distinct from the binomial statistics of charge-$e$ transfer in a single-mode nanowire or charge-$2e$ transfer through a normal-superconductor interface. All even-order correlators of current fluctuations have a universal quantized value, insensitive to disorder and decoherence. These electrical signatures are experimentally accessible, because they persist for temperatures and voltages large compared to the Thouless energy.Comment: 5 pages, 4 figures. v3 [post-publication]: added an appendix on the effect of a tunnel barrier at the normal-superconductor contac

Quantum Criticality in Resonant Andreev Conduction

Motivated by recent experiments with proximitized nanowires, we study a mesoscopic s-wave superconductor connected via point contacts to normal-state leads. We demonstrate that at energies below the charging energy the system is described by the two-channel Kondo model, which can be brought to the quantum critical regime by varying the gate potential and conductances of the contacts