Small is Beautiful

1 Introduction

In a celebrated 1959 lecture, Richard Feynman [1] described his vision of a frontier where an enormous amount of research could be carried out to manipulate and control objects at small length scales. He specified several advantages of engineering at atomic and molecular scales, such as biological emulation and perfect atomic duplication. There is no doubt that Feynman proposed a new technology that, about four decades later, is among the hottest areas in technoscience. This area is called nanotechnology.

The term nanotechnology can be traced back to more than two decades ago. In 1981, Eric Drexler [2] described an approach for the nanoscale fabrication of complex structures by means of nanoscale chemical machinery. In his 1986 book [3], Drexler used the term to describe this capability, giving the term its initial widely accepted meaning. Since then, the area of nanotechnology has broadened to include any novel structures and phenomenons at the 1- to 100-nm scale that are created by any possible mechanism. With the coming of the twenty-first century, nanotechnology began to occupy a vast mindscape in the world of academic, industrial, and governmental research. Nanotechnology is now shaping up as a megaideology in the minds of many researchers as well as those who control research funds that seek a solution to any problem afflicting humankind [4]. The hype as well as the expectations of nanotechnology have also engendered socioethical and sociopolitical issues, which must be addressed in dialogs between technoscientists and the rest of humankind [5].

By consulting such electronic sources as

http://www.nano.gov, http://www.nanotechweb.org, and http://www.vjnano.org,

one will quickly realize that a huge fraction of nanotechnology research is focused on experiments chiefly, novel syntheses and characterizations of nanostructures. Reported research on theoretical modeling in nanotechnology the scope of this volume is scanty; the contents of relevant journals as well as conference proceedings will confirm that assessment. The preponderance of experimental research over theoretical research in nanotechnology is due, in part, to the natural excitement about a revolutionary enterprise. It may also be due in part to something Feynman pointed out 45 years ago: the value of nanotechnology may lie not in the discovery of fundamental principles, but in the discovery and exploitation of extraordinary phenomenons that occur at the nanoscale.

Nevertheless, physical principles must still be applied to nanotechnology, at least for the purpose of explaining the strange phenomenons. Both macroscopic and atomic approaches apply at the nanoscale, sometimes compatibly, sometimes not; and it becomes difficult to either use both together or decide between the two approaches. This attribute of theoretical nanotechnology is clearly evident from a recent handbook volume [6], and is also brought out by the papers reproduced en facsimile in this volume.

2 Outline

This volume is intended to provide technoscientists with an anthology of significant papers for the understanding of nanotechnological principles and relevant electromagnetic phenomenons. Our selection is strongly focused on the theory and modeling of nanoscale materials and structures. We hope to deliver a comprehensive knowledge of nanotechnology for technoscientists ranging from novices to experts, and that most of the selected papers will come to be regarded as seminal during the coming decades.

In addition to two introductory papers of general importance, papers selected for this volume were classified into the following nine categories:

- carbon nanotubes,
- nanoelectronics,
- nanooptics,
- photonic crystals,
- sculptured thin films,
- nanomagnetics,
- DNA-based nanotechnology,
- atomistic simulation methods, and
- nanostructure formation and evolution.

Both theoretical and modeling studies on these topics have acquired a sufficient degree of maturity as to merit consideration. The current state of the art in most of these categories is substantially summarized elsewhere [6].

The technical level of the papers included in this volume generally requires the reader to have experienced graduate studies in science or engineering. Limitations on the physical size of this volume forced us to prune our initial selection, perhaps a bit too severely. The final selection was based on our presumption that all technoscientists ought to have easy access to certain papers in original. We humbly tender our apologies for any error of judgment, and we hope that the following

3 Carbon Nanotubes

Carbon nanotubes are long molecules, best conceptualized as rolled up sheets of carbon atoms situated uniformly on a lattice. Their electronic, optical, and mechanical properties could lead to nanoscale devices [7, 8]. Electron transport in nanotubes and through nanotube junctions has been extensively studied, and two broad theoretical approaches have emerged. The first approach encompasses firstprinciples numerical simulations, as exemplified by Miyamoto et al. [9]. The second approach is phenomenological and can yield analytically tractable results [10, 11]. Thus, Slepyan et al. [11] modeled a single nanotube as a conducting sheath with prescribed boundary conditions. In particular, they investigated conduction and the surface wave propagation in a nanotube exposed to both dc and highfrequency fields, and thereby proposed the concept of nanotubes as nanowaveguides. Later, Woods and Mahan [12] found that two processes of electronphonon interaction namely, modulated hopping and exchange scattering govern the room-temperature electron transport.

Junctions of nanotubes form naturally due to defects [13], while different types of nanotubes can be made to form T- and Y-junctions [14]. Quantum conduction in nanotube junctions was first examined by Chico et al. [15], who used the tight-binding approximation for electrons to formulate the Hamiltonian. They also formulated a Greens function for a junction by following the principles of wave scattering. A conduction gap was found to appear in a nanotube junction with defects that preserve the rotational symmetry of the nanotubes. Soon after, Tamura and Tsukada [16] deduced a remarkable two-parameter scaling law for conduction in metallic nanotube junctions. Furthermore, they proposed an analytic expression for conduction in nanotube junctions by using the effective-mass theory [17] and thus provided a clear physical interpretation of the scaling law.

The electronic properties of nanotubes have been exploited for quantum wires [18] and single-electron transistors [19]. Nanotubes can be mechanically modulated to tune their energy band structures [20, 21]. Extraordinarily high thermal conductivity in carbon nanotubes was theoretically discovered by Berber [22] via nonequilibrium molecular dynamics simulations. The effective permittivity of nanotube-based composite materials [23] was derived by Garcia-Vidal et al. [24] based on photonic band structure calculations. Lakhtakia et al. [25] established theoretically the manipulation of the transparency of such composites by a magnetostatic field.

4 Nanoelectronics

4.1 Quantum dots

A quantum dot is between 1 and 10 nm in diameter: a length scale that is compatible with quantum confinement of quasiparticle wave functions [26]. Due to quantum confinement as well as the breaking of the translational symmetry [27], a quantum dot possesses discrete energy levels that depend on its diameter. This quantumsize effect was first described by a simple quantum box model [28] for single-particle states, wherein the electron motion is restricted in all three dimensions by impenetrable walls. Based on this model, Schmitt-Rink et al. [29] elucidated the optical properties of an isolated small quantum dot. In particular, they found that the lowest interband transition in a quantum dot can saturate like a two-level system, and that local-field effects [30, 31] can substantially affect the dots nonlinear properties.

More sophisticated models for calculating excitonic or absorption spectrums of quantum dots were proposed, based on single- and multi-band pseudopotentials for single-particle states [32, 33] and the solutions of the two-body problems associated with phenomenons such as electron-hole exchange and Coulomb screening [34]. Typically, the pseudopotential approach yields electron wave functions that exhibit strong oddeven mixing and large valence- conduction coupling, and predicts an excitonic gap that is considerably smaller than that predicted by simple models [28, 35]. Also, quantum-confined absorption in ensembles of quantum dots was theoretically investigated by Williamson and Zunger [33] by using a size- scaling law formulated for isolated dots.

In order to measure the transport properties of a semiconductor quantum dot, it is connected to external leads via point contacts. As the point contacts are pinched off, transport is dominated by resonant tunneling through electron resonances. This leads to a series of narrow peaks known as the Coulomb-blockade peaks in the conductivity as functions of gate voltage. Based on the random-matrix theory [36] for quantum chaotic systems, Jalabert et al. [37] developed a statistical treatment. The distributions of the Coulomb-blockade peak heights were derived theoretically, and then confirmed experimentally [38]. Furthermore, Alhassid et al. [39] described a crossover phenomenon of the peak spacing distribution from a Wigner-Dyson to a Gaussian-like distribution.

4.2 Singleelectron and molecule devices

Siliconbased microelectronic devices continue to shrink in size, and may reach a lower limit within a few years. Quantum effects are expected to play significant roles in nanoscale devices, and may necessitate new device architectures. A particularly simple and notable example of such a nanoscale device is the single-electron transistor (SET), in which quantum tunneling is exploited to control and measure the movement of single electrons. SETs may be regarded as extremely precise solid-state electrometers that can closely approach the quantum limit of sensitivity for the detection of charge signals [40]. The quantum-mechanical operating principles of SETs were ably reviewed by Devoret and Schoelkopf [41], who also suggested that quantum shot noise would mean that a SET can approach but not quite reach the quantum limit.

Devices made of single molecules are currently attracting attention for subnm miniaturization, and prototypes have already been fabricated [42, 43]. The prospects of single-molecule devices for high-performance information processing have been carefully examined [44], while quantum-mechanical modeling of molecular systems has been strategically developed to provide fundamental insights [45, 46]. In particular, Di Ventra et al. [47] proposed a first-principles calculation of transport properties of a single-molecule device based on the self-consistent treatment of the molecule-electrode system without empirical adjustments. Most notably, the shape of the experimentally obtained currentvoltage curve was successfully simulated.

4.3 Toward spintronics

The study of electronic devices that exploit both the charge and the spin of electrons constitutes the new field of spintronics [48]. Because the spin of an electron engenders a magnetic moment, spintronic devices can be manipulated by applied magnetic fields. In fact, considerable impetus came from the discovery of giant magnetoresistance (GMR) in ferromagnetic/ferromagnetic and ferromagnetic/nonmagnetic/ferromagnetic multilayers [49]. Depending on the relative orientation of the magnetization in the ferromagnetic layers, the resistance of a multilayer heterostructure can be altered profoundly by an applied magnetic field, from small (parallel magnetization) to large (antiparallel magnetization) magnitudes. Similarly, a giant tunneling magnetoresistance (TMR) [50] was found in ferromagnet/ insulator/ferromagnet junctions, with the tunneling current depending on the spin polarization of the ferromagnetic electrodes. Very recently, spin-polarized injection and transport through semiconductor junctions promise to make spintronics compatible with the existing chip technology; prototype semiconductor spin field-effect transistors have also been fabricated [51].

Several theories have been proposed to explain TMR. A simple one is primarily based on the conventional theory that the tunneling current is proportional to the product of the densities of states of the two electrodes [52]. Another approach is to analyze the transmission of the spindependent currents through a rectangular barrier separating the two ferromagnetic electrodes wherein electrons can move freely [53]. The effect of an applied electric field on TMR (i.e., the decrease of TMR with dc bias), has been investigated using the same approach [54]. Landauers scattering theory of transport was used by Mathon for a tight-binding model of spin-dependent scattering to bridge the transition from the perpendicular GMR of a metallic system to the TMR of a tunneling junction [55].

5 Nano-optics

From both the fundamental and applied points of view, it is compelling to consider optical phenomenons that are simultaneously ultrafast and localized on the nanoscale [5660]. The preponderance of research in this context has been experimental, and is therefore outside the scope of this volume.

Advances in particle synthesis and fabrication have enabled a practically motivated study of electromagnetic interaction between metal nanoparticles in ordered arrays with various interparticle spacings. The optical properties of metal nanoparticles are dominated by collective oscillations of the conduction electrons called surface plasmons [61, 62]. In contrast to plasmons in bulk materials, these collective oscillations can be excited by light, which leads to distinct resonances in the optical spectrums. One effect that is related to surface plasmons is the enhancement of the field intensity near the surface of metal nanoparticles by several orders of magnitude. Many applications of metal nanoparticles, such as surface-enhanced Raman scattering [63, 64] and fluorescence [65], have been shown to benefit from this effect. The ultrafast dephasing of surface phasmons, which occurs on a time scale of only a few femtoseconds, is a key factor in the local field enhancement effect [66].

An intriguing application of the interaction between metal nanoparticles is the construction of waveguides at visible and near-infrared frequencies [67]. Interaction between adjacent nanoparticles in plasmonic waveguides has been shown to set up coupled plasmonpolariton modes, thereby leading to coherent energy transport. A point-dipole model [68], which allows the determination of the dispersion relation and the pulse group velocity of the plasmonic modes, was confirmed by the finite-difference timedomain (FDTD) modeling of pulse propagation in metal-nanoparticle-chain waveguides [69].

6 Photonic Crystals

Photonic crystals are two and three-dimensionally periodic dielectric or metallodielectric structures with forbidden spectral zones or band gaps for optical propagation [70, 71]. The first papers were published about 15 years ago [72, 73]. Photonic crystals with complete band gaps can find many applications, including the fabrication of lossless dielectric mirrors and resonant cavities for optical light. The morphological scale of a photonic crystal is typically of the order of one wavelength, which is much larger that that required for the observation of quantum confinement effects in quantum dots. Nevertheless, devices based on photonic crystals are expected to enable rapid progress in nanotechnology.

Computational techniques are commonly used to study electromagnetic wave propagation in photonic crystals. Based on the Bloch theorem, the simple planewave expansion method is applicable to delineate the band structures of photonic crystals of infinite size [74, 75]. However, this method is rather inefficient and timeconsuming, and suffers from poor convergence [76]. A transfer matrix method was developed from the finite-difference formulation of the frequency-domain Maxwell equations to deal with photonic crystals of finite size and complicated morphology [77, 78]. The FDTD method, which is widely used by microwave technoscientists [79], has also been adopted by the photonic-crystal community [80].

The calculated photonic band structures can be compared with measured planewave transmission spectrums, often quite successfully for band gaps. Yet, there may be uncoupled eigenmodes in photonic crystals that cannot be excited by an external plane wave [81, 82]. By exploiting the symmetries of lattice structures, a group-theoretical analysis was shown to identify those uncoupled modes in 2D photonic crystals [83]. Some of those uncoupled eigenmodes can be identified as the totalreflection regimes in spite of their nonzero density of states.

If a small defect is introduced in a photonic crystal, a set of defect modes can be created in the band gap. The defect modes are highly localized around the defect, which physically corresponds to the phenomenon of light confinement in the vicinity of the defect. Sakoda and Shiroma [84] identified the defect modes in 2D photonic crystals in terms of radiation by an oscillating electric dipole, and showed that defect modes can have all possible symmetries.

The strong localization of light by defects is expected to have many applications. A defect behaves like a microcavity, whose quality factor increases exponentially with the size of the disordered photonic crystal [85]. Line defects in photonic crystals were theoretically examined and experimentally tested to function as waveguides [86, 87]. Line defects can even be bent and still guide waves efficiently [86], a feature that is in striking contrast to the large transmission losses observed on bending conventional optical waveguides. Photonic crystal fibers have also been theoretically studied [88, 89].

Since the linear optical properties of photonic crystals are now understood quite well through standard computational techniques, attention has begun to shift to their nonlinear optical properties. Bhat and Sipe [90] proposed a general theoretical approach for the derivation of nonlinear dynamic equations to describe the propagation of optical pulses in nonlinear photonic crystals. When they approximated the optical signal by an envelope function to modulate a single Bloch function acting as the carrier wave, they obtained a nonlinear Schrdinger equation with effective coefficients characterizing Kerr nonlinearity, linear gain and loss, and material dispersion.

7 Sculptured Thin Films

Sculptured thin films (STFs) are nanostructured anisotropic materials with unidirectionally varying properties that can be engineered using physical vapor deposition [91, 92]. The STF concept emerged in the mid-1990s [93, 94] and became concrete within a few years [92]. The ability to virtually instantaneously change the growth direction of the nanowire morphology of STFs, through simple variations in the direction of the incident vapor flux, leads to a wide spectrum of nanowire assemblies, ranging from slanted columns and chevrons to helixes and superhelixes. Because their structure can be engineered at the 1- to 3-nm scale, STFs can serve as laboratories to test the effects of nanostructure on light, theoretically as well as experimentally, and to develop useful structureproperty relationships [95].

Some success has been reported in simulating the growth of STFs [96]. A nominal nanoscopic- to-macroscopic model for the optical response properties of linear STFs was established using the concept of local homogenization [92, 95]. Electromagnetic wave propagation in chiral STFs was formulated and characterized thereby in the frequency domain, and led to the exploitation of the circular Bragg phenomenon in the visible and infrared wavelength regimes for polarization filters, optical sensors, and other applications [92, 97]. The circular Bragg phenomenon was examined in the time domain as well [98], and a pulse-bleeding phenomenon was identified as the underlying mechanism, which can drastically affect the shapes, amplitudes, and spectral components of femtosecond pulses. More recently, slanted chiral STFs were proposed [99] to couple the characteristic optical responses of volume gratings and diffraction gratings in the STF architecture. The circular Bragg phenomenon then appears in a nonspecular reflection mode, and is affected strongly by the slant angle. Several other phenomenons have been predicted and theoretically understood [100102] using a rigorous coupled-wave analysis.

8 Nanomagnetics

Magnetic nanostructures display a fascinating diversity of geometries and are becoming increasingly important by providing new functionality and miniaturization, most notably for sensors and data storage [103]. The length scales of magnetic nanostructures range from a few interatomic distances to about 1000 nm, thereby bridging the gap between atomic-scale magnetism and macroscopic magnetism. Moreover, because a magnetic field extends considerably beyond the physical extent of its source, the interplay between size confinement and proximity effects becomes particularly important in magnetic nanostructures [104]. We have included a comprehensive review of nanomagnetics to present a rich variety of physical phenomenons that would affect intrinsic and extrinsic magnetic properties due to nanostructuring [105].

9 DNAbased Nanotechnology

Biology is quintessentially nanoscale. DNA, RNA, and proteins are nanoscale biocomponents important for the execution of the cellular and higher functions of life and thus are the best natural nanomaterials. Their electronic and photonic properties now provide a new interdisciplinary frontier between life sciences and material sciences [106].

Although many fundamental problems remain unclear in DNAbased sciences, great advances have been made in the development of nanobiotechnology which has been heralded by the emergence of biochips, molecular motors, nanoscale biomimetic and composite materials, nanobiosensors, and nano drug-delivery systems. A review plus an insightful discussion, written by Cui and Gao [107], is highly recommended.

Electron transport in DNA has attracted considerable interest for possible use in molecular electronics [108]. DNA can behave as a metallic conductor, a semiconductor, or an insulator depending on different contacts, molecular lengths, and surrounding mediums [109, 110]. Furthermore, spin-polarized transport and the spinvalve effect have been predicted in short DNA molecules sandwiched between ferromagnets [111].

10 Atomistic Simulation Methods

Over several decades, atomistic simulation methods such as molecular dynamics (MD) and Monte Carlo (MC) methods have led to great strides in the description of materials [112]. In contrast to macroscopic modeling, atomistic modeling can greatly speed up the development of materials at the nanoscale. The characteristic feature size of nanomaterial systems is intermediate between those of isolated atoms and macroscopic systems, ranging from several to hundreds of nanometers. Such nanosystems are ideal for atomistic simulation methods, because simulations can be done for realistic sizes [113, 114].

MD and MC methods originated from classical statistical mechanics. Once a model for the atomic interactions has been chosen, one can sample the microscopic states of a system either deterministically (MD) or stochastically (MC). The microscopic degrees of freedom or states usually consist of a set of positions and momentums of atomic particles. Temporal averaging of the sampled microscopic states is used for MD simulations [115], and ensemble averaging for MC simulations [116], in order to determine the macroscopic properties.

Whereas MC methods are extensively used to obtain finitetemperature equilibrium properties, MD methods are applicable to both finitetemperature equilibrium and nonequilibrium problems. The aim of MD methods is to trace the trajectory of the collection of atoms in its phase space. The trajectories are calculated by integrating the equations of motion obtained from the systems Hamiltonian. Various algorithms are used to integrate the equations of motion in MD simulations, as reviewed by Gunsteren and Berendsen [117] for macromolecular dynamics. Nanosystems must be modeled under isothermal conditions, because such systems are often in thermal contact with the surrounding environment acting as a heat bath for which purpose the Nose-Hoover thermostat [118, 119] is often employed.

Already there exists an extensive literature on atomistic simulations of nanosystems. A few illustrative examples include MD simulations of carbon nanotubes [120, 121], DNA-nanotubes [122], and nanoclusters [123]. Self-assembly is regarded as an extremely powerful approach in the construction of nanoscale structures; and MD and MC methods have also been extensively employed to simulate the formation of selfassembled monolayers on solid substrates [124].

11 Nanostructure Formation and Evolution

Progress in epitaxial growth and advances in deposition and patterning processes have made it possible to fabricate dedicated nanostructures for microelectronics. Molecular beam epitaxy (MBE) and its variants remain attractive for the production of high-quality semiconductor thin-film nanostructures [125, 126]. Alternatively, atomic layer epitaxy (ALE) may be used for layer-by-layer deposition [127]. Although growth can be controlled with subnanometer precision, and nonplanar or topographic substrates can be used, the growth rate is restricted by the interactions between adatoms on the evolving surface. A recipe was proposed to overcome the limitation, as a result of MC simulations of ALE [128].

Plasma-enhanced chemical vapor deposition (PECVD) from silane-containing discharges is commonly used to grow nanocrystalline silicon as well as amorphous silicon films. MD simulations were utilized to identify the growth precursors and the plasma radical-surface reactions in the PECVD process [129131], thereby assisting in the development of control paradigms.

Self-assembly techniques are low-cost and high-throughput ways of fabricating nanostructures [132]. Self-assembled monolayers are formed by spontaneous chemisorption of organic molecules on a solid surface. By combining DNA molecular recognition and self-assembly, DNA-programmed assembly [133] and molecular lithography [134] are engendering a promising strategy to make molecular-scale devices and circuits. Lithographically induced self- assembly (LISA) [135] and self-construction (LISC) [136] techniques have been proposed as well, indicating the capabilities of producing sub-100-nm structures rapidly and in a controlled manner. Theoretical models of LISA and LISC were developed to decide the lower and upper limits of the size of patterned nanostructures [136, 137].

Although the selection of papers for facsimile reproduction in this volume has been restricted to the previously stated categories, we felt it necessary to discuss two additional topics in our editorial essay: nanomechanics and quantum information processing.

12 Nanomechanics

Nanomechanics is an essential part of nanotechnology [138], not the least because of concern for robustness during fabrication of any device as well as reliability during its subsequent operation. Impurities and defects play a major role in the physical performances of nanomaterials. Some nanostructures are formed solely due to the mechanical processes that occur at the interfaces of different material phases, an excellent example being the self- assembly of monolayers on solid surfaces. The monolayer molecules are diffused and combined into a variety of nanoscale features, whose formation is heavily influenced by surface stress [139] and substrate elasticity [140]. Also, the enormous mechanical strength of carbon nanotubes has made them attractive for nanoscale reinforcement of composite materials [141143].

Conventional mechanics of materials and structures is a continuum science. As the feature size of structures becomes close to the atomic dimensions, the traditional continuum mechanics breaks down due to the absence of an intrinsic length scale therein. Atomistic models, which explicitly acknowledge the discrete nature of matter, must be resorted to for modeling nanoscale dynamics [144]. However, it is difficult to extend atomistic approaches to mesoscopic length scales, and therefore transitional theoretical frameworks and modeling techniques must be developed. Multiscale modeling strategies have enjoyed some success for both nanomechanics [145] and micromechanics [146].

Nanoscale fluid mechanics, or nanofluidics, is the study of fluid flow around and inside nanoscale structures [114]. The development of nanoscale sensors and actuators for biomolecular systems is providing a great impetus to nanofluidics. MD simulations and theoretical studies in nanofluidics were triggered by cumulative experimental evidence [147, 148], which resulted in a microscopic theory of nonequilibrium phenomenons in nonhomogeneous fluids [149, 150]. Pozhar and Gubbin [151, 152] developed a rigorous statistical mechanical approach to nonequlibrium phenomenons in very nonhomogeneous fluids, including nanofluids. Their theory was later coupled with MD simulations to calculate the viscosity of fluids confined in nanopores [153].

Interfaces between nanostructures play a critical role in nanoscale thermal transport. For example, experiments have demonstrated that the close proximity of interfaces and the extremely small volume of thermal dissipation significantly modify thermal transport in siliconbased nanostructures [154]. Similarly, the thermal conductivity of superlattices may differ from predictions by the Fourier heat conduction theory due to the presence of phase interfaces. In fact, a large reduction in thermal conductivity of superlattices has been observed [155], which is in agreement with predictions using the Boltzmann transport equation [156].

For about a century, it has been generally recognized that all microscopic phenomenon can be described and explained by the principles of quantum mechanics. These principles have been extensively tested, and some of them are commonly used in current technologies. Other principles, like the ones related to the superposition principle and the measurement process, have only recently become important in some applications. In particular, they form the basis of the theory of quantum information processing, which may revolutionize the fields of communication and computation [157].

A major goal in quantum information science is to faithfully transfer quantum information between a stable quantum memory and a reliable quantum communication channel. Because quantum states cannot in general be copied, quantum information can only be distributed by entangling the quantum memory with the communication channel.

The underlying issue in quantum communication is the generation of nearly perfect entangled states between distant sites [158, 159]. All realistic schemes for quantum communication are at present based on the use of photonic channels. However, the degree of entanglement generated between two distant sites normally decreases exponentially with the length of the connecting channel because of optical absorption and channel noise (e.g., due to thermal fluctuations that are due to optical absorption) [160]. To regain a high degree of entanglement, quantum repeaters must be used for long-distance communication [161]. Alternatively, it is possible to realize high-fidelity quantum communication over long lossy channels by means of the collective excitations in atomic ensembles rather than in single atoms [162]. This approach could be realized with simple linear optical systems, benefitting in part from the ease of laser manipulation of atomic ensembles.

The existence of entangled states is attractive for rapid computation, but very few quantum systems can fulfill the necessary requirements [163]. It is crucial to identify systems wherein the quantum bits (qubits) are isolated sufficiently from their environments. In many quantum optical systems, qubits can be manipulated very efficiently using lasers [164, 165]. It is also possible to realize quantum computation with the quantum dot spin- spin interactions in a single microcavity [166].

14 Concluding Remarks

Through this editorial essay, and by the selection of significant publications for facsimile reproduction in this compact volume, we hope to provide a clear picture of the successes of theoretical and modeling efforts relevant to nanoelectromagnetics. Nanotechnology is barely postembryonic, and very few of us can claim to see the future clearly. Yet, we venture to state here that a large fraction of our selection will be viewed as seminal after a decade or two.

Although our selection is limited in scope by our own inability to grasp all the essential attributes of an ongoing revolution of broad impact in technosciences, we feel that the promise of nanotechnology has been brought out sufficiently clearly by the 50 selected publications spanning 10 categories. Additional illumination is cast by the bibliography attached to this essay. We expect that this volume shall inspire the production of anthologies of papers on other aspects of nanotechnology.

We gratefully acknowledge consultations with Fredrik Boxberg and Jukka Tulkki (Helsinki University of Technology); Joseph W. Haus (University of Dayton, Ohio); Vijay B. Shenoy (India Institute of Science, Bangalore); and Gregory Ya. Slepyan and Sergey A. Maksimenko (Belarus State University, Minsk); but none of them is to blame for our shortcomings. We are grateful to Brian J. Thompson, Milestone Series Editor, for inviting us to edit this volume, and to Margaret Thayer and Beth Huetter for efficiently coordinating its production. Finally, we are appreciative of SPIE for undertaking this project at a pivotal point in the evolution of nanotechnology, just when actual devices and applications seem poised to spring forth.

In closing, we affectionately dedicate our editorial efforts to Russell Messier, friend, mentor, and colleague, on the occasion of his retirement.

Fei Wang
Micron Technology, Inc.

Akhlesh Lakhtakia
The Pennsylvania State University

March 2006