Solid-state Majorana fermions are generating intensive interest because of their unique properties and possible applications in fault tolerant quantum memory devices. Here we propose a method to detect signatures of Majorana fermions in hybrid devices by employing the sensitive apparatus of the superconducting charge-qubit architecture and its efficient coupling to microwave photons. In the charge and transmon regimes of this device, we find robust signatures of the underlying Majorana fermions that are, remarkably, not washed out by the smallness of the Majorana contribution to the Josephson current. It is predicted that at special gate bias points the photon-qubit coupling can be switched off via quantum interference, and in other points it is exponentially dependent on the control parameter E J /E C . We propose that this device could be used to manipulate the quantum state of the Majorana fermion and realize a tunable high coherence four-level system in the superconducting-circuit architecture.

The Moore-Read Pfaffian =5/2 quantum Hall state is a p-wave superconductor of composite fermions. Small deviations from =5/2 result in the formation of an array of vortices within this superconductor, each supporting a Majorana zero mode near its core. We consider how tunneling between these cores is reflected in the electronic response to an electric field of a nonzero wave-vector q and frequency . We find a mechanism for dissipative transport at frequencies below the =5/2 gap, and calculate the q , dependence of the dissipative conductivity. The contributions we find depend exponentially on ͉ −5/2͉ −1/2 .

In recent years there has been an intensive search for Majorana fermion states in condensed matter systems. Predicted to be localized on cores of vortices in certain nonconventional superconductors, their presence is known to render the exchange statistics of bulk vortices non-abelian. Here we study the equations governing the dynamics of phase solitons (fluxons) in a Josephson junction in a topological superconductor. We show that the fluxon will bind a localized zero energy Majorana mode and will consequently behave as a non-abelian anyon. The low mass of the fluxon, as well as its experimentally observed quantum mechanical wave-like nature, will make it a suitable candidate for vortex interferometry experiments demonstrating non-abelian statistics. We suggest two experiments that may reveal the presence of the zero mode carried by the fluxon. Specific experimental realizations will be discussed as well.

We consider a quantum dot in the regime of the quantum Hall effect, particularly in Laughlin states and non-Abelian Read-Rezayi states. We find the location of the Coulomb blockade peaks in the conductance as a function of the area of the dot and the magnetic field. When the magnetic field is fixed and the area of the dot is varied, the peaks are equally spaced for the Laughlin states. In contrast, non-Abelian statistics is reflected in modulations of the spacing which depend on the magnetic field.

The ν=5/2 anti-Pfaffian state and the ν=2/3 state are believed to have an edge composed of counterpropagating charge and neutral modes. This situation allows the generation of a pure thermal bias between two composite edge states across a quantum point contact as was experimentally established by Bid et al. [Nature 466, 585 (2010)]. We show that replacing the quantum point contact by a quantum dot provides a natural way for detecting the neutral modes via the dc current generated by the thermoelectric response of the dot. We also show that the degeneracies of the dot spectrum, dictated by the conformal field theories describing these states, induce asymmetries in the thermoelectric current peaks. This in turn provides a direct fingerprint of the corresponding conformal field theory.

We examine the growth of entanglement under a quantum quench at point contacts of simple fractional quantum Hall fluids and its relation with the measurement of local observables. Recently Klich and Levitov proposed that the noise generated from a local quantum quench provides a measure of the entanglement entropy. Their methods were specific to non-interacting electrons and the generalization to interacting systems was left as an open question. In this work, we generalize their result to the Laughlin states. We investigate the noise generated in the current along the edge of a fractional quantum Hall state at filling factors $\nu=1/m$, when a quantum point contact, initially closed, is fully opened at some initial time $t_0=0$. We find that local quenching in these systems gives time dependent correlation functions that have universal behavior on sufficiently long time and length scales. We calculate the noise and full counting statistics for $\nu=1/m$ and find that in general, the entanglement entropy and noise generated are unrelated quantities. We also discuss a generalization of this problem to the critical quantum Ising spin chain.Comment: 15 pages, 3 figures. v2, minor typos corrected and clarification adde

Combining superconducting qubits with mesoscopic devices that carry topological states of matter may lead to compact and improved qubit devices with properties useful for fault-tolerant quantum computation. Recently, a charge qubit device based on a topological superconductor circuit has been introduced where signatures of Majorana fermions could be detected spectroscopically in the transmon regime. This device stores quantum information in coherent superpositions of fermion parity states originating from the Majorana fermions, generating a highly isolated qubit whose coherence time could be greatly enhanced. We extended the conventional semi-classical method and obtained analytical derivations for strong transmon-photon coupling. The analytical challenge is rendered tractable via a formalism based on the WKB method that allows to extract the energy eigenstates of the qubit and its dipole matrix elements. Using this formalism, we study the effect of the Majorana fermions on the quantum electrodynamics of the device embedded within an optical cavity and develop protocols to initialise, 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

Experimental signatures of non-Abelian statistics in clustered quantum Hall statesIlan, R.; Grosfeld, E.; Schoutens, C.J.M.; Stern, A. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. We discuss transport experiments for various non-Abelian quantum Hall states, including the Read-Rezayi series and a paired spin-singlet state. We analyze the signatures of the unique characters of these states on Coulomb blockaded transport through large quantum dots. We show that the non-Abelian nature of the states manifests itself through modulations in the spacings between Coulomb blockade peaks as a function of the area of the dot. Even though the current flows only along the edge, these modulations vary with the number of quasiholes that are localized in the bulk of the dot. We discuss the effect of relaxation of edge states on the predicted Coulomb blockade patterns, and show that it may suppress the dependence on the number of bulk quasiholes. We predict the form of the lowest-order interference term in a Fabry-Pérot interferometer for the spin-singlet state. The result indicates that this interference term is suppressed for certain values of the quantum numbers of the collective state of the bulk quasiholes, in agreement with previous findings for other clustered states belonging to the Read-Rezayi series.