Tunneling current noise in the fractional quantum Hall effect: when the effective charge is not what it appears to be

Fractional quantum Hall quasiparticles are famous for having fractional electric charge. Recent experiments report that the quasiparticles' effective electric charge determined through tunneling current noise measurements can depend on the system parameters such as temperature or bias voltage. Several works proposed to understand this as a signature for edge theory properties changing with energy scale. I consider two of such experiments and show that in one of them the apparent dependence of the electric charge on a system parameter is likely to be an artefact of experimental data analysis. Conversely, in the second experiment the dependence cannot be explained in such a way.Comment: 10 pages, 6 figure

New methods of observation and characterization of fractional quantum Hall states

In this work we study new ways to observe and characterize specific fractional quantum Hall (FQH) states. In the first chapter we investigate the possibility to realize specific FQH states in bilayer graphene (BLG). BLG is a novel material in which the electron-electron interaction can be tuned with the help of external parameters. This allows one to make one or another FQH state favourable. We develop a framework for theoretical investigation of the stability of FQH states in BLG. We apply our framework to investigate the stability of the Pfaffian state. We find that the region in which our framework allows for making reliable predictions is quite restricted because of Landau level mixing effects. However, within that region we find the conditions under which the Pfaffian is more stable than in the conventional "non-relativistic" systems. These conditions can, in principle, be realized experimentally. In the second chapter we focus on characterizing the FQH states with the help of measurements of the noise of the electric current tunnelling between two FQH edges. We develop a theoretical framework allowing for analysing such data, and test it by successfully applying it to describe the results of the experiment [Bid et al., Nature 466, 585 (2010)]. We further develop our framework and show that it is possible to determine the tunnelling quasiparticle scaling dimension from such measurements. We also investigate experimental conditions necessary for this

Bounds on nonlocal correlations in the presence of signaling and their application to topological zero modes

Bell's theorem renders quantum correlations distinct from those of any local-realistic model. Although being stronger than classical correlations, quantum correlations are limited by the Tsirelson bound. This bound, however, applies for Hermitian, commutative operators corresponding to non-signaling observables in Alice's and Bob's spacelike-separated labs. As an attempt to explore theories beyond quantum mechanics and analyze the uniqueness of the latter, we examine in this work the extent of non-local correlations when relaxing these fundamental assumptions, which allows for theories with non-local signaling. We prove that, somewhat surprisingly, the Tsirelson bound in the Bell-Clauser-Horne-Shimony-Holt scenario, and similarly other related bounds on non-local correlations, remain effective as long as we maintain the Hilbert space structure of the theory. Furthermore, in the case of Hermitian observables we find novel relations between non-locality, local correlations, and signaling. We demonstrate that such non-local signaling theories are naturally simulated by quantum systems of parafermionic zero modes. We numerically study the derived bounds in parafermionic systems, confirming the bounds' validity yet finding a drastic difference between correlations of 'signaling' and 'non-signaling' sets of observables. We also propose an experimental procedure for measuring the relevant correlations.Comment: Accepted versio

Quantum Zeno effect appears in stages

In the quantum Zeno effect, quantum measurements can block the coherent oscillation of a two level system by freezing its state to one of the measurement eigenstates. The effect is conventionally controlled by the measurement frequency. Here we study the development of the Zeno regime as a function of the measurement strength for a continuous partial measurement. We show that the onset of the Zeno regime is marked by a $\textit{cascade of transitions}$ in the system dynamics as the measurement strength is increased. Some of these transitions are only apparent in the collective behavior of individual quantum trajectories and are invisible to the average dynamics. They include the appearance of a region of dynamically inaccessible states and of singularities in the steady-state probability distribution of states. These newly predicted dynamical features, which can be readily observed in current experiments, show the coexistence of fundamentally unpredictable quantum jumps with those continuously monitored and reverted in recent experiments.Comment: 6+8 pages, 3+0 figure

Extracting the scaling dimension of quantum Hall quasiparticles from current correlations

Fractional quantum Hall quasiparticles are generally characterized by two quantum numbers: electric charge $Q$ and scaling dimension $\Delta$. For the simplest states (such as the Laughlin series) the scaling dimension determines the quasiparticle's anyonic statistics (the statistical phase $\theta=2\pi\Delta$). For more complicated states (featuring counterpropagating modes or non-Abelian statistics) knowing the scaling dimension is not enough to extract the quasiparticle statistics. Nevertheless, even in those cases knowing the scaling dimension facilitates distinguishing different candidate theories for describing the quantum Hall state at a particular filling (such as PH-Pfaffian and anti-Pfaffian at $\nu=5/2$). Here we propose a scheme for extracting the scaling dimension of quantum Hall quasiparticles from thermal tunneling noise produced at a quantum point contact. Our scheme makes only minimal assumptions about the edge structure and features the level of robustness, simplicity, and model independence comparable to extracting the quasiparticle charge from tunneling shot noise.Comment: 8 pages, 6 figures + appendices. User-friendly explanation of the results in the first 3.5 page