Fermion parity measurement and control in Majorana circuit quantum electrodynamics

We investigate the quantum electrodynamics of a device based on a topological superconducting circuit embedded in a microwave resonator. The device stores its quantum information in coherent superpositions of fermion parity states originating from Majorana fermion hybridization. This generates a highly isolated qubit whose coherence time could be greatly enhanced. We extend the conventional semiclassical method and obtain analytical derivations for strong transmon-photon coupling. Using this formalism, we develop protocols to initialize, control, and measure the parity states. We show that, remarkably, the parity eigenvalue can be detected via dispersive shifts of the optical cavity in the strong-coupling regime and its state can be coherently manipulated via a second-order sideband transition.Comment: 7 pages, 3 figures (published version

Parity switching and decoherence by quasiparticles in single-junction transmons

The transmon superconducting qubit is being intensely investigated as a promising approach for the physical implementation of quantum information processing, and high quality factors of order $10^6$ have been achieved both in two- and three-dimensional architectures. These high quality factors enable detailed investigations of decoherence mechanisms. An intrinsic decoherence process originates from the coupling between the qubit degree of freedom and the quasiparticles that tunnel across Josephson junctions. In a transmon, tunneling of a single quasiparticle is associated with a change in parity. Here we present the theory of the parity-switching rates in single-junction transmons and compare it with recent measurements. We also show that parity switching can have an important role in limiting the coherence time.Comment: 10 pages, 4 figure

Interoperability between central counterparties

In reaction to recent requests for interoperability between central counterparties of European stock markets, regulators have issued new guidelines to contain systemic risk. Our analysis confirms that the currently applied cross-CCP risk management model can be a source of contagion, particularly if applied in multilateral frameworks. While regulators' new guidelines eliminate systemic risk, this comes at the cost of an inefficiently overcollateralised clearing system. We discuss further approaches that contain systemic risk while reducing or eliminating overcollateralisation. Interoperability is of economic importance as it may contribute to the efficiency and safety of a worldwide fragmented clearing infrastructure.interoperability between central counterparties, financial network, systemic risk, netting efficiency

Time scales for Majorana manipulation using Coulomb blockade in gate-controlled superconducting nanowires

We numerically compute the low-energy spectrum of a gate-controlled superconducting topological nanowire segmented into two islands, each Josephson-coupled to a bulk superconductor. This device may host two pairs of Majorana bound states and could provide a platform for testing Majorana fusion rules. We analyze the crossover between (i) a charge-dominated regime utilizable for initialization and readout of Majorana bound states, (ii) a single-island regime for dominating inter-island Majorana coupling, (iii) a Josephson-plasmon regime for large coupling to the bulk superconductors, and (iv) a regime of four Majorana bound states allowing for topologically protected Majorana manipulations. From the energy spectrum, we derive conservative estimates for the time scales of a fusion-rule testing protocol proposed recently [arXiv:1511.05153]. We also analyze the steps needed for basic Majorana braiding operations in branched nanowire structures

Superconductor-insulator duality for the array of Josephson wires

We propose novel model system for the studies of superconductor-insulator transitions, which is a regular lattice, whose each link consists of Josephson-junction chain of $N \gg 1$ junctions in sequence. The theory of such an array is developed for the case of semiclassical junctions with the Josephson energy $E_J$ large compared to the junctions's Coulomb energy $E_C$. Exact duality transformation is derived, which transforms the Hamiltonian of the proposed model into a standard Hamiltonian of JJ array. The nature of the ground state is controlled (in the absence of random offset charges) by the parameter $q \approx N^2 \exp(-\sqrt{8E_J/E_C})$, with superconductive state corresponding to small $q < q_c$. The values of $q_c$ are calculated for magnetic frustrations $f= 0$ and $f= \frac12$. Temperature of superconductive transition $T_c(q)$ and $q < q_c$ is estimated for the same values of $f$. In presence of strong random offset charges, the T=0 phase diagram is controlled by the parameter $\bar{q} = q/\sqrt{N}$; we estimated critical value $\bar{q}_c$.Comment: 5 pages, 2 figure

IceCube Constraints on Fast-Spinning Pulsars as High-Energy Neutrino Sources

Relativistic winds of fast-spinning pulsars have been proposed as a potential site for cosmic-ray acceleration from very high energies (VHE) to ultrahigh energies (UHE). We re-examine conditions for high-energy neutrino production, considering the interaction of accelerated particles with baryons of the expanding supernova ejecta and the radiation fields in the wind nebula. We make use of the current IceCube sensitivity in diffusive high-energy neutrino background, in order to constrain the parameter space of the most extreme neutron stars as sources of VHE and UHE cosmic rays. We demonstrate that the current non-observation of $10^{18}$ eV neutrinos put stringent constraints on the pulsar scenario. For a given model, birthrates, ejecta mass and acceleration efficiency of the magnetar sources can be constrained. When we assume a proton cosmic ray composition and spherical supernovae ejecta, we find that the IceCube limits almost exclude their significant contribution to the observed UHE cosmic-ray flux. Furthermore, we consider scenarios where a fraction of cosmic rays can escape from jet-like structures piercing the ejecta, without significant interactions. Such scenarios would enable the production of UHE cosmic rays and help remove the tension between their EeV neutrino production and the observational data.Comment: 23 pages, 8 figures; published in JCAP04(2016)01

Energy band structure and intrinsic coherent properties in two weakly linked Bose Einstein Condensates

The energy band structure and energy splitting due to quantum tunneling in two weakly linked Bose-Einstein condensates were calculated by using the instanton method. The intrinsic coherent properties of Bose Josephson junction were investigated in terms of energy splitting. For $E_{C}/E_{J}\ll 1$, the energy splitting is small and the system is globally phase coherent. In the opposite limit, $E_{C}/E_{J}\gg 1$, the energy splitting is large and the system becomes a phase dissipation. Our reslults suggest that one should investigate the coherence phenomna of BJJ in proper condition such as $E_{C}/E_{J}\sim 1$.Comment: to appear in Phys. Rev. A, 2 figure

Observation of transition from escape dynamics to underdamped phase diffusion in a Josephson junction

We have investigated the dynamics of underdamped Josephson junctions. In addition to the usual crossover between macroscopic quantum tunnelling and thermally activated (TA) behaviour we observe in our samples with relatively small Josephson coupling E_J, for the first time, the transition from TA behaviour to underdamped phase diffusion. Above the crossover temperature the threshold for switching into the finite voltage state becomes extremely sharp. We propose a (T,E_J) phase-diagram with various regimes and show that for a proper description of it dissipation and level quantization in a metastable well are crucial.Comment: 4 pages, 3 figure

Effect of disorder on coherent quantum phase slips in Josephson junction chains

We study coherent quantum phase-slips in a Josephson junction chain, including two types of quenched disorder: random spatial modulation of the junction areas and random induced background charges. Usually, the quantum phase-slip amplitude is sensitive to the normal mode structure of superconducting phase oscillations in the ring (Mooij-Sch\"on modes, which are all localized by the area disorder). However, we show that the modes' contribution to the disorder-induced phase-slip action fluctuations is small, and the fluctuations of the action on different junctions are mainly determined by the local junction parameters. We study the statistics of the total QPS amplitude on the chain and show that it can be non-Gaussian for not sufficiently long chains