Linear optics with photon counting is a prominent candidate for practical quantum computing. The protocol by Knill, Laflamme, and Milburn [2001, Nature (London) 409, 46] explicitly demonstrates that efficient scalable quantum computing with single photons, linear optical elements, and projective measurements is possible. Subsequently, several improvements on this protocol have started to bridge the gap between theoretical scalability and practical implementation. The original theory and its improvements are reviewed, and a few examples of experimental two-qubit gates are given. The use of realistic components, the errors they induce in the computation, and how these errors can be corrected is discussed.

The available atomic data used for interpreting and modeling x-ray observations are reviewed. The applications for these data can be divided into several levels of detail, ranging from compilations which can be used with direct inspection of raw data, such as line finding lists, to synthetic spectra which attempt to fit to an entire observed dataset simultaneously. This review covers cosmic sources driven by both electron ionization and photoionization and touches briefly on planetary surfaces and atmospheres. The applications to x-ray astronomy, the available data, and recommendations for astronomical users are all reviewed, and an attempt to point out the applications where the shortcomings are greatest is also given.

The merging of coherent control (CC) and adiabatic passage (AP) and the type of problems that can be solved using the resulting coherently controlled adiabatic passage (CCAP) method are discussed. The discussion starts with the essence of CC as the guiding of a quantum system to arrive at a given final state via a number of different quantum pathways. The guiding is done by “tailor-made” external laser fields. Selectivity in a host of physical and chemical processes is shown to be achieved by controlling the interference between such quantum pathways. The AP process is then discussed, in which a system is navigated adiabatically along a single quantum pathway, resulting in a complete population transfer between two energy eigenstates. The merging of the two techniques (CCAP) is shown to achieve both selectivity and completeness. Application of CCAP to the solution of the nondegenerate quantum control problem is first discussed and shown that it is possible to completely transfer population from an initial wave packet of arbitrary shape, composed of a set of nondegenerate energy eigenstates, to a final arbitrary wave packet, also composed of nondegenerate states. The treatment is then extended to systems with degenerate states and shown how to induce isomerization between the broken-symmetry local minima of a Jahn-Teller ${\mathrm{Al}}_3\mathrm{O}$ molecule. These approaches can be further generalized to situations with many initial, intermediate, and final states and applied to quantum coding and decoding problems. CCAP is then applied to cyclic population transfer (CPT), induced by coupling three states of a chiral molecule in a cyclic fashion, $\mid 1⟩\leftrightarrow \mid 2⟩\leftrightarrow \mid 3⟩\leftrightarrow \mid 1⟩$. Interference between two adiabatic pathways in CPT allows for a complete population transfer, coupled with multichannel selectivity, by virtue of its phase sensitivity. CPT can be used to show the purification of mixtures of right-handed and left-handed chiral molecules. Finally, quantum-field coherent control is introduced, where CCAP is extended to the use of nonclassical light. This emerging field may be used to generate new types of entangled radiation-matter states.

This review provides an overview of the progress in using the low-gravity environment of space to explore critical phenomena and test modern theoretical predictions. Gravity-induced variations in the hydrostatic pressure and the resulting density gradients adversely affect ground-based measurements near fluid critical points. Performing measurements in a low-gravity environment can significantly reduce these difficulties. A number of significant experiments have been performed in low-Earth orbit. Experiments near the lambda transition in liquid helium explored the regime of large correlation lengths and tested the theoretical predictions to a level of precision that could not be obtained on Earth. Other studies have validated theoretical predictions for the divergence in the viscosity as well as the unexpected critical speeding up of the thermal equilibrium process in pure fluids near the liquid-gas critical point. We describe the scientific content of previously flown low-gravity investigations of critical phenomena as well as those in the development stage, and associated ground-based work.

Magnetically tunable Feshbach resonances were employed to associate cold diatomic molecules in a series of experiments involving both atomic Bose and two-spin-component Fermi gases. This review illustrates theoretical concepts of both the particular nature of the highly excited Feshbach molecules produced and the techniques for their association from unbound atom pairs. Coupled-channels theory provides a rigorous formulation of the microscopic physics of Feshbach resonances in cold gases. Concepts of dressed versus bare energy states, universal properties of Feshbach molecules, and the classification in terms of entrance- and closed-channel-dominated resonances are introduced on the basis of practical two-channel approaches. Their significance is illustrated for several experimental observations, such as binding energies and lifetimes with respect to collisional relaxation. Molecular association and dissociation are discussed in the context of techniques involving linear magnetic-field sweeps in cold Bose and Fermi gases and pulse sequences leading to Ramsey-type interference fringes. Their descriptions in terms of Landau-Zener, two-level mean-field, as well as beyond mean-field approaches are reviewed in detail, including the associated ranges of validity.

Four long-running currents in laser technology met and merged in 1999–2000. Two of these were the quest toward a stable repetitive sequence of ever-shorter optical pulses and, on the other hand, the quest for the most time-stable, unvarying optical frequency possible. The marriage of UltraFast and UltraStable lasers was brokered mainly by two international teams and became exciting when a special “designer” microstructure optical fiber was shown to be nonlinear enough to produce “white light” from the femtosecond laser pulses, such that the output spectrum embraced a full optical octave. Then, for the first time, one could realize an optical frequency interval equal to the comb’s lowest frequency, and count out this interval as a multiple of the repetition rate of the femtosecond pulse laser. This “gear-box” connection between the radio frequency standard and any/all optical frequency standards came just as Sensitivity-Enhancing ideas were maturing. The four-way Union empowered an explosion of accurate frequency measurement results in the standards field and prepares the way for refined tests of some of our cherished physical principles, such as the time-stability of some of the basic numbers in physics (e.g., the “fine-structure” constant, the speed of light, certain atomic mass ratios etc.), and the equivalence of time-keeping by clocks based on different physics. The stable laser technology also allows time-synchronization between two independent femtosecond lasers so exact they can be made to appear as if the source were a single laser. By improving pump/probe experiments, one important application will be in bond-specific spatial scanning of biological samples. This next decade in optical physics should be a blast.

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?

Application of the field-effect transistor principle to novel materials to achieve electrostatic doping is a relatively new research area. It may provide the opportunity to bring about modifications of the electronic and magnetic properties of materials through controlled and reversible changes of the carrier concentration without modifying the level of disorder, as occurs when chemical composition is altered. As well as providing a basis for new devices, electrostatic doping can in principle serve as a tool for studying quantum critical behavior, by permitting the ground state of a system to be tuned in a controlled fashion. In this paper progress in electrostatic doping of a number of materials systems is reviewed. These include structures containing complex oxides, such as cuprate superconductors and colossal magnetoresistive compounds, organic semiconductors, in the form of both single crystals and thin films, inorganic layered compounds, single molecules, and magnetic semiconductors. Recent progress in the field is discussed, including enabling experiments and technologies, open scientific issues and challenges, and future research opportunities. For many of the materials considered, some of the results can be anticipated by combining knowledge of macroscopic or bulk properties and the understanding of the field-effect configuration developed during the course of the evolution of conventional microelectronics. However, because electrostatic doping is an interfacial phenomenon, which is largely an unexplored field, real progress will depend on the development of a better understanding of lattice distortion and charge transfer at interfaces in these systems.

A topical review of numerical and experimental studies of supercontinuum generation in photonic crystal fiber is presented over the full range of experimentally reported parameters, from the femtosecond to the continuous-wave regime. Results from numerical simulations are used to discuss the temporal and spectral characteristics of the supercontinuum, and to interpret the physics of the underlying spectral broadening processes. Particular attention is given to the case of supercontinuum generation seeded by femtosecond pulses in the anomalous group velocity dispersion regime of photonic crystal fiber, where the processes of soliton fission, stimulated Raman scattering, and dispersive wave generation are reviewed in detail. The corresponding intensity and phase stability properties of the supercontinuum spectra generated under different conditions are also discussed.

This colloquium surveys a number of theoretical problems and open questions in the field of two-dimensional dilute Bose gases with weak repulsive interactions. In contrast to three dimensions, in two dimensions the formation of long-range order is prohibited by the Bogoliubov-Hohenberg theorem, and Bose-Einstein condensation is not expected to occur. Nevertheless, experimental indications supporting the formation of a condensate in low-dimensional systems have recently been obtained. This unexpected behavior appears to be due to the nonuniformity introduced into a system by the external trapping potential. Theoretical predictions, made for homogeneous systems, require therefore careful reexamination. A number of popular theoretical treatments of the dilute weakly interacting Bose gas are presented and their regions of applicability are discussed. The possibility of Bose-Einstein condensation in a two-dimensional gas, the validity of the perturbative $t$-matrix approximation, and the diluteness condition are issues also discussed in detail.

Hadronic $\tau$ decays provide a clean laboratory for the precise study of quantum chromodynamics (QCD). Observables based on the spectral functions of hadronic $\tau$ decays can be related to QCD quark-level calculations to determine fundamental quantities like the strong-coupling constant, parameters of the chiral Lagrangian $\mid V_{us}\mid$, the mass of the strange quark, and to simultaneously test the concept of quark-hadron duality. Using the best available measurements and a revisited analysis of the theoretical framework, the value ${\alpha }_s\left(m_{\tau }^2\right)=0.345\pm {0.004}_{\exp }\pm {0.009}_{\mathrm{th}}$ is obtained. Taken together with the determination of ${\alpha }_s\left(M_Z^2\right)$ from the global electroweak fit, this result leads to the most accurate test of asymptotic freedom: the value of the logarithmic slope of ${\alpha }_s^{-1}\left(s\right)$ is found to agree with QCD at a precision of 4%. The $\tau$ spectral functions can also be used to determine hadronic quantities that, due to the nonperturbative nature of long-distance QCD, cannot be computed from first principles. An example for this is the contribution from hadronic vacuum polarization to loop-dominated processes like the anomalous magnetic moment of the muon. This article reviews the measurements of nonstrange and strange $\tau$ spectral functions and their phenomenological applications.

The current status of precision measurements in allowed nuclear beta decay is reviewed, including neutron decay, with emphasis on their potential to look for new physics beyond the standard electroweak model. Experimental results are interpreted in the framework of phenomenological model-independent descriptions of nuclear beta decay as well as in some specific extensions of the standard model. The values of the standard couplings and the constraints on the exotic couplings of the general beta decay Hamiltonian are updated. The ratio between the axial and vector couplings obtained is $C_A∕C_V=-1.26992\left(69\right)$ under standard model assumptions. Particular attention is devoted to the discussion of the sensitivity and complementarity of different precision experiments in direct beta decay. The prospects and impact of recent developments of precision tools and of high intensity low-energy beams are also addressed.

Small-molecule organic semiconductors, together with polymers, form the basis for the emerging field of organic electronics. Despite the rapid technological progress in this area, our understanding of fundamental electronic properties of these materials remains limited. Recently developed organic field-effect transistors (OFETs) based on single crystals of small-molecule organic materials are characterized by an unprecedented quality and reproducibility. These devices provide a unique tool to study the fundamentals of polaronic transport on organic surfaces and to explore the limits of OFET performance. This Colloquium focuses on the intrinsic, not limited by static disorder, charge transport in single-crystal OFETs and on the nature of defects on surfaces of organic crystals. In the conclusion, an outline of the outstanding problems that are now becoming within experimental reach owing to the development of single-crystal OFETs is presented.

Basic characteristics of the liquid-glass transition are reviewed, emphasizing its universality and briefly summarizing the most popular phenomenological models. Discussion is focused on a number of alternative models which one way or the other connect the fast and slow degrees of freedom of viscous liquids. It is shown that all these “elastic” models are equivalent in the simplest approximation.

A review of the basic ideas and techniques of the spectral density-functional theory is presented. This method is currently used for electronic structure calculations of strongly correlated materials where the one-electron description breaks down. The method is illustrated with several examples where interactions play a dominant role: systems near metal-insulator transitions, systems near volume collapse transitions, and systems with local moments.

The body of research on (III,Mn)V diluted magnetic semiconductors (DMSs) initiated during the 1990s has concentrated on three major fronts: (i) the microscopic origins and fundamental physics of the ferromagnetism that occurs in these systems, (ii) the materials science of growth and defects, and (iii) the development of spintronic devices with new functionalities. This article reviews the current status of the field, concentrating on the first two, more mature research directions. From the fundamental point of view, (Ga,Mn)As and several other (III,Mn)V DMSs are now regarded as textbook examples of a rare class of robust ferromagnets with dilute magnetic moments coupled by delocalized charge carriers. Both local moments and itinerant holes are provided by Mn, which makes the systems particularly favorable for realizing this unusual ordered state. Advances in growth and postgrowth-treatment techniques have played a central role in the field, often pushing the limits of dilute Mn-moment densities and the uniformity and purity of materials far beyond those allowed by equilibrium thermodynamics. In (III,Mn)V compounds, material quality and magnetic properties are intimately connected. This review focuses on the theoretical understanding of the origins of ferromagnetism and basic structural, magnetic, magnetotransport, and magneto-optical characteristics of simple (III,Mn)V epilayers, with the main emphasis on (Ga,Mn)As. Conclusions are arrived at based on an extensive literature covering results of complementary ab initio and effective Hamiltonian computational techniques, and on comparisons between theory and experiment. The applicability of ferromagnetic semiconductors in microelectronic technologies requires increasing Curie temperatures from the current record of $173\mathrm{K}$ in (Ga,Mn)As epilayers to above room temperature. The issue of whether or not this is a realistic expectation for (III,Mn)V DMSs is a central question in the field and motivates many of the analyses presented in this review.

With the advent of high-energy-density (HED) experimental facilities, such as high-energy lasers and fast $Z$-pinch, pulsed-power facilities, millimeter-scale quantities of matter can be placed in extreme states of density, temperature, and/or velocity. This has enabled the emergence of a new class of experimental science, HED laboratory astrophysics, wherein the properties of matter and the processes that occur under extreme astrophysical conditions can be examined in the laboratory. Areas particularly suitable to this class of experimental astrophysics include the study of opacities relevant to stellar interiors, equations of state relevant to planetary interiors, strong shock-driven nonlinear hydrodynamics and radiative dynamics relevant to supernova explosions and subsequent evolution, protostellar jets and high Mach number flows, radiatively driven molecular clouds and nonlinear photoevaporation front dynamics, and photoionized plasmas relevant to accretion disks around compact objects such as black holes and neutron stars.