Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.

/pdf/topological-insulators-and-superconductors-2nf6p2217g.pdf

Topological insulators and superconductors

The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.

Reaction-rate theory: fifty years after Kramers

We review the field of cavity optomechanics, which explores the interaction between electromagnetic radiation and nano- or micromechanical motion This review covers the basics of optical cavities and mechanical resonators, their mutual optomechanical interaction mediated by the radiation pressure force, the large variety of experimental systems which exhibit this interaction, optical measurements of mechanical motion, dynamical backaction amplification and cooling, nonlinear dynamics, multimode optomechanics, and proposals for future cavity quantum optomechanics experiments In addition, we describe the perspectives for fundamental quantum physics and for possible applications of optomechanical devices

Cavity Optomechanics

Recent interest in aspects common to quantum information and condensed matter has prompted a flurry of activity at the border of these disciplines that were far distant until a few years ago. Numerous interesting questions have been addressed so far. Here an important part of this field, the properties of the entanglement in many-body systems, are reviewed. The zero and finite temperature properties of entanglement in interacting spin, fermion, and boson model systems are discussed. Both bipartite and multipartite entanglement will be considered. In equilibrium entanglement is shown tightly connected to the characteristics of the phase diagram. The behavior of entanglement can be related, via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an experimental test. Out of equilibrium entangled states are generated and manipulated by means of many-body Hamiltonians.

/pdf/entanglement-in-many-body-systems-sqpatuxt14.pdf

Entanglement in many-body systems

Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.

Topological Photonics

Periodic and solitary states of the driven sine-Gordon chain

Transmission probabilities and the quantum Hall effect

When a photon beam from a light source is split in two, with one part transmitted and the other reflected at a half-silvered mirror, it is found that the intensities of these beams are correlated: the photons exhibit "bunching," that is, they tend to come in clusters of identical particles occupying the same state. In contrast, electrons are expected to exhibit "antibunching" and therefore a negative intensity correlation. BA¼ttiker (page [275][1]) discusses two successful measurements of such antibunching of fermions in mesoscopic conductors (Henny et al. , page [296][2], and Oliver et al. , page [299][3]) and explains why their approach is important for investigating a range of subjects from superconductivity to noise suppression in quantum computing.

 [1]: http://www.sciencemag.org/cgi/content/short/284/5412/275
 [2]: http://www.sciencemag.org/cgi/content/short/284/5412/296
 [3]: http://www.sciencemag.org/cgi/content/short/284/5412/299

/pdf/bunches-of-photons-antibunches-of-electrons-1kxv0zsxae.pdf

Bunches of Photons--Antibunches of Electrons

Electronic Hanbury Brown Twiss correlations are discussed for geometries in which transport is along adiabatically guided edge channels. We briefly discuss partition noise experiments and discuss the effect of inelastic scattering and dephasing on current correlations. We then consider a two-source Hanbury Brown Twiss experiment which demonstrates strikingly that even in geometries without an Aharonov–Bohm effect in the conductance matrix (second-order interference), correlation functions can (due to fourth-order interference) be sensitive to a flux. Interestingly, we find that this fourth-order interference effect is closely related to orbital entanglement. The entanglement can be detected via violation of a Bell Inequality in this geometry even so particles emanate from uncorrelated sources.

/pdf/entangled-hanbury-brown-twiss-effects-with-edge-states-2zczi53hgz.pdf

Entangled Hanbury Brown Twiss effects with edge states

In many conduction problems quantum coherent carrier transport competes with incoherent conduction. We review and extend an approach which introduces phase randomizing events via side branches leading away from the conductor to an electron reservoir. This discussion allows to treat the entire transition with increasing phase-randomization from the completely coherent limit to the completely incoherent limit. Transmission through opaque barriers is enhanced by phase randomizing events whereas resonant transmission is reduced by phase-randomizing events. The effect of a wide incident carrier distribution due to elevated temperatures or due to a large applied bias is considered. In all cases we find that phase randomization reduces the peak to valley ratio. In addition to double harriers we also discuss phase randomization in periodic lattices.

Markus Büttiker

Papers

Periodic and solitary states of the driven sine-Gordon chain

Transmission probabilities and the quantum Hall effect

Bunches of Photons--Antibunches of Electrons

Entangled Hanbury Brown Twiss effects with edge states

Quantum Coherence and Phase Randomization in Series Resistors