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.

Tunable antenna-coupled intersubband terahertz (TACIT) mixers are a new type of THz heterodyne detectors based on intersubband transitions in single GaAs/AlGaAs quantum wells. TACIT mixers have been predicted to have low single-sideband (SSB) noise temperature (∼2,000 K) at 20–60 K with a wide IF bandwidth (∼10 GHz) and a small required local-oscillator (LO) power (< 1 µW). In addition, the detection frequency of TACIT mixers can be tuned in-situ in a wide frequency range (2–5 THz). In TACIT mixers, THz signal (RF) channel is separated from GHz intermediate-frequency (IF) read-out channel, allowing individual optimization of the RF and IF channels for efficient impedance matching. We present simple equivalent-circuit models for the RF and IF channels of TACIT mixers and demonstrate that the RF and IF impedances calculated from the models are in good agreement with their indirect or direct experimental characterizations in prototype TACIT mixers. We show that the separately optimized RF and IF channels in practical TACIT mixers can yield high impedance matching efficiencies.

Impedance models for tunable antenna-coupled intersubband terahertz (TACIT) mixers

We report an anti-levitation behavior of Landau levels in vanishing magnetic fields in a high quality hetero-junction insulated-gated field-effect transistor. We found, in the Landau fan diagram of electron density versus magnetic field, the positions of the magneto-resistance minima at Landau level fillings \\nu=4, 5, 6 move below the 'traditional' Landau level line to lower electron densities. Moreover, the even and odd filling factors show quantitatively different behaviors in anti-levitation, suggesting that the exchange interactions may be important.

Anti-levitation of Landau levels in vanishing magnetic fields

The spin polarization of the obscure even-denominator FQHE state at ν= 5 2 remains an open, but important question to answer. One method to address this question is to measure the angular dependence of its energy gap. Since the energy gap at ν= 5 2 is rather small, this kind of experiments is technically extraordinary challenging, due to the requirement of in situ rotation of the sample at ultra-low temperatures. We constructed a rotator, made from polycarbonate and operated hydraulically using liquid 3 He . A sequence of experiments at ν= 5 2 clearly demonstrated the possibility of performing angular-dependent measurements at temperatures below 10 mK .

Angular dependent measurements of the fractional quantum Hall effect state at ultra-low temperatures

We measured absorption spectrum of a single T-shaped quantum wire at 5K by waveguide-transmission spectroscopy. The absolute value of absorption at one-dimensional-ground-state exciton peak is 84 cm/sup -1/ despite a single wire.

Strong photo-absorption by a single quantum wire in waveguide-transmission measurement

: A new type of log-periodic antenna, the wire log-spiral, has been designed and implemented on low temperature grown GaAs substrates. The new antenna is compared to two traditional antenna designs (log-periodic and dipole) for the detection of pulsed THz radiation.

L. N. Pfeiffer

Papers

Impedance models for tunable antenna-coupled intersubband terahertz (TACIT) mixers

Anti-levitation of Landau levels in vanishing magnetic fields

Angular dependent measurements of the fractional quantum Hall effect state at ultra-low temperatures

Strong photo-absorption by a single quantum wire in waveguide-transmission measurement

Broadband Periodic Antennas for Detecting Picosecond Terahertz Radiation