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.

We present a new family of more efficient terahertz (THz) radiation emitters and detectors enhanced by electric field singularities near sharp electrode features. The structures are fabricated on low temperature GaAs and with small dipole gaps (<10μm). The THz emission is maximal when fringing fields are enhanced by laterally offset sharp electrodes. We also find that the asymmetric THz emission near the anode gradually disappears as the dipole gap shrinks. The THz polarization properties of these new emitters will also be discussed.

Singular Electric Field Terahertz Emitters and Detectors.

We report on a detailed study of the electron-exciton scattering in a GaAs quantum well (QW) with a variable density two-dimensional electron gas. Both a bare QW and a QW embedded in a GaAs/AlGaAs microcavity are studied by measuring the reflection linewidths of the bare excitons and the cavity polaritons as a function of photoexcitation intensity, temperature, and a perpendicularly applied magnetic field. This field induces the formation of charged polaritons at temperatures higher than the range of the charged exciton binding energy. The bare exciton linewidth dependence on electron density shows a transition when the electron gas transforms from classical to degenerate state. The lowest polariton linewidth dependence on electron gas and detuning energy is explained by the overlap of the cavity mode with the asymmetric exciton lineshape.

Electron–Exciton Scattering in a GaAs/AlAs Bare Quantum Well and in a Microcavity

Real-time probing of electrons can uncover intricate relaxation mechanisms and many-body interactions hidden in strongly correlated materials. While experimenters have used ultrafast optical pump-probe methods in bulk materials, laser heating and insensitivity below the surface prevent their application to encapsulated low-dimensional electron systems at millikelvin temperatures, home to numerous intriguing electronic phases. Here, we introduce time, momentum, and energy resolved pump-probe tunneling spectroscopy (Tr-MERTS). The method allows the injection of electrons at particular energies and observation of their subsequent decay in energy-momentum space. Using Tr-MERTS, we visualize electronic decay processes in Landau levels with lifetimes up to tens of microseconds. Although most observed features agree with simple energy-relaxation, we discover an unexpected splitting in the nonequilibrium energy spectrum in the vicinity of a ferromagnetic state. An exact diagonalization study of the system suggests that the splitting arises from a maximally spin-polarized higher energy state, distinct from a conventional equilibrium skyrmion. Furthermore, we observe time-dependent relaxation of the splitting, which we attribute to single-flipped spins forming topological spin textures. These results establish Tr-MERTS as a powerful tool for studying the dynamics and properties of a two-dimensional electronic system beyond equilibrium.

Time, momentum, and energy resolved pump-probe tunneling spectroscopy of two-dimensional electron systems

In a high-mobility two-dimensional hole gas 2DHG in C-doped 001 GaAs/Al0.4Ga0.6As quantum wells, we observe sharp features in the differential magnetoresistance, which we interpret as the Zener-tunneling peak and valley associated with the commensuration transition of Landau orbits. Comparison of data with that in GaAs/Al0.3Ga0.7As 2D electron gas suggests that the amplitude of Zener oscillations in a 2DHG is strongly damped. The data indicate the significant role of band structures in nonlinear transport in 2D electronic systems.

http://manfragroup.org/wp-content/uploads/2014/12/Magnetotransport-in-Zener-tunneling-regime-in-a-high-mobility-two-dimensional-hole-gas.pdf

Magnetotransport in Zener Tunneling Regime in a High-Mobility Two-Dimensional Hole System

This corrects the article DOI: 10.1103/PhysRevLett.120.256601.

L. N. Pfeiffer

Papers

Singular Electric Field Terahertz Emitters and Detectors.

Electron–Exciton Scattering in a GaAs/AlAs Bare Quantum Well and in a Microcavity

Time, momentum, and energy resolved pump-probe tunneling spectroscopy of two-dimensional electron systems

Magnetotransport in Zener Tunneling Regime in a High-Mobility Two-Dimensional Hole System

Erratum: Direct observation of composite fermions and their fully-spin-polarized Fermi sea near ν=5/2 [Phys. Rev. Lett. 120, 256601 (2018)].