There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations that are necessary for quantum computation are carried out by braiding quasiparticles and then measuring the multiquasiparticle states. The fault tolerance of a topological quantum computer arises from the nonlocal encoding of the quasiparticle states, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the $\ensuremath{\nu}=5∕2$ state, although several other prospective candidates have been proposed in systems as disparate as ultracold atoms in optical lattices and thin-film superconductors. In this review article, current research in this field is described, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. Both the mathematical underpinnings of topological quantum computation and the physics of the subject are addressed, using the $\ensuremath{\nu}=5∕2$ fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.

Non-Abelian Anyons and Topological Quantum Computation

Coherent preparation by laser light of quantum states of atoms and molecules can lead to quantum interference in the amplitudes of optical transitions. In this way the optical properties of a medium can be dramatically modified, leading to electromagnetically induced transparency and related effects, which have placed gas-phase systems at the center of recent advances in the development of media with radically new optical properties. This article reviews these advances and the new possibilities they offer for nonlinear optics and quantum information science. As a basis for the theory of electromagnetically induced transparency the authors consider the atomic dynamics and the optical response of the medium to a continuous-wave laser. They then discuss pulse propagation and the adiabatic evolution of field-coupled states and show how coherently prepared media can be used to improve frequency conversion in nonlinear optical mixing experiments. The extension of these concepts to very weak optical fields in the few-photon limit is then examined. The review concludes with a discussion of future prospects and potential new applications.

/pdf/electromagnetically-induced-transparency-optics-in-coherent-2dhges92td.pdf

Electromagnetically induced transparency : Optics in coherent media

The so-called Klein paradox—unimpeded penetration of relativistic particles through high and wide potential barriers—is one of the most exotic and counterintuitive consequences of quantum electrodynamics. The phenomenon is discussed in many contexts in particle, nuclear and astro-physics but direct tests of the Klein paradox using elementary particles have so far proved impossible. Here we show that the effect can be tested in a conceptually simple condensed-matter experiment using electrostatic barriers in single- and bi-layer graphene. Owing to the chiral nature of their quasiparticles, quantum tunnelling in these materials becomes highly anisotropic, qualitatively different from the case of normal, non-relativistic electrons. Massless Dirac fermions in graphene allow a close realization of Klein’s gedanken experiment, whereas massive chiral fermions in bilayer graphene offer an interesting complementary system that elucidates the basic physics involved.

/pdf/chiral-tunnelling-and-the-klein-paradox-in-graphene-5g1fsh0dta.pdf

Chiral tunnelling and the Klein paradox in graphene

Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as {it Non-Abelian anyons}, meaning that they obey {it non-Abelian braiding statistics}. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations which are necessary for quantum computation are carried out by braiding quasiparticles, and then measuring the multi-quasiparticle states. The fault-tolerance of a topological quantum computer arises from the non-local encoding of the states of the quasiparticles, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the nu=5/2 state, although several other prospective candidates have been proposed in systems as disparate as ultra-cold atoms in optical lattices and thin film superconductors. In this review article, we describe current research in this field, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. We address both the mathematical underpinnings of topological quantum computation and the physics of the subject using the nu=5/2 fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.

Optical trapping and manipulation of microcavity exciton polaritons rely on effective potentials induced by the interaction of polaritons with a reservoir of high energy excitonic particles injected by an off-resonant optical pump. Here, we experimentally investigate possible mechanisms responsible for reshaping of these effective potentials in the low-density exciton-polariton regime. We infer the spatial distribution of the reservoir from the spatially resolved energy of exciton-polariton emission measured at zero momentum (zero kinetic energy). Power-dependent shape analysis of the potential barrier induced by a focused continuous wave laser pump shows a monotonic decrease of the barrier width with increasing excitation power, which is attributed to the local heating of the sample at the pump spot. In addition, we observe the significant influence of the reservoir on the zero-momentum emission tens of micrometers away from the laser pump spot, which is in line with the previously reported enhanced transport of high-momentum excitonic polaritons from the bottleneck region. Our work presents evidence for a complex spatial reshaping of the reservoir with the pump power, contrary to the common assumption of a static reservoir distribution fixed by the intensity profile of the pump.

Spatial distribution of an optically induced excitonic reservoir below exciton-polariton condensation threshold

/pdf/gated-magnetotransport-in-a-very-high-mobility-gaas-algaas-1z98ttsmmv.pdf

Gated Magnetotransport in a Very-High Mobility GaAs/AlGaAs Quantum Well

Interaction Corrections to Conductivity of Ultra High Mobility Dilute Two-Dimensional Holes in the Ballistic Regime

http://www2.egr.uh.edu/~jbao/Publication/Bao-6.pdf

Impulsive excitation of cyclotron oscillations in a two-dimensional electron gas

The photoinduced microwave absorption in undoped bulk GaAs crystals is studied at low temperatures. It is observed that when the microwave power and exciting light intensity exceed certain threshold values, self-oscillations appear in the microwave absorption. The oscillation frequency is dependent on the light intensity and also on the external magnetic field. This phenomenon is qualitatively explained in terms of impact ionization of shallow donors that are neutralized by the photoexcitation.

L. N. Pfeiffer

Papers

Spatial distribution of an optically induced excitonic reservoir below exciton-polariton condensation threshold

Gated Magnetotransport in a Very-High Mobility GaAs/AlGaAs Quantum Well

Interaction Corrections to Conductivity of Ultra High Mobility Dilute Two-Dimensional Holes in the Ballistic Regime

Impulsive excitation of cyclotron oscillations in a two-dimensional electron gas

Microwave radiation induced instability in photoexcited undoped GaAs