Collective Excitations

High-speed laser-modulator transmitters fabricated using InGaAsP quantum-well intermixing exhibit negative chirp over a wavelength range of more than 30nm. Photocurrent spectroscopy is used to examine the multiple band edges in these devices. An exciton peak is found in the photocurrent data, and the evolution of the band edge as a function of quantum-well intermixing and applied bias voltage is revealed. The photocurrent data are then exploited to verify and explain the negative chirp characteristics of the wavelength-agile transmitters.

Here, we theoretically analyze spectra of weakly attenuated electromagnetic waves which may appear in a Fermi-liquid of charge carriers in quasi-two-dimensional (Q2D) layered conductors when an external magnetic field is applied perpendicularly to the conducting layers. We study transverse modes propagating along the magnetic field. The frequencies of the modes are assumed to be lower than the cyclotron frequency of the charge carriers. It is shown that Fermi-liquid interaction of the charge carriers in Q2D conductors gives rise to a mode which cannot appear in a gase of charged quasiparticles, as well as it happens in conventional metals. Also, we show that the Fermi surface plofile may cause significant changes in the waves spectra and we analyze these changes.

Bose-Einstein condensates confined in traps exhibit unique features which have been the object of extensive experimental and theoretical studies in the last few years. In this paper I will discuss some issues concerning the behaviour of the order parameter and the dynamic and superfluid effects exhibited by such systems.

The Bose-Einstein condensation (BEC) of magnetoexcitonic polaritons in two-dimensional (2D) electron-hole system embedded in a semiconductor microcavity in a high magnetic field B is predicted. There are two physical realizations of 2D electron-hole system under consideration: a graphene layer and quantum well (QW). A 2D gas of magnetoexcitonic polaritons is considered in a planar harmonic potential trap. Two possible physical realizations of this trapping potential are assumed: inhomogeneous local stress or harmonic electric field potential applied to excitons and a parabolic shape of the semiconductor cavity causing the trapping of microcavity photons. The effective Hamiltonian of the ideal gas of cavity polaritons in a QW and graphene in a high magnetic field and the BEC temperature as functions of magnetic field are obtained. It is shown that the effective polariton mass M eff increases with magnetic field as B 1/2 . The BEC critical temperature T (0) c decreases as B -1/4 and increases with the spring constant of the parabolic trap. The Rabi splitting related to the creation of a magnetoexciton in a high magnetic field in graphene and QW is obtained. It is shown that Rabi splitting in graphene can be controlled by the external magnetic field since it is proportional to B -1/4 , while in a QW the Rabi splitting does not depend on the magnetic field when it is strong.

A novel type of spaser with the net amplification of surface plasmons (SPs) in doped graphene nanoribbon is proposed. The plasmons in THz region can be generated in a dopped graphene nanoribbon due to nonradiative excitation by emitters like two level quantum dots located along a graphene nanoribbon. The minimal population inversion per unit area, needed for the net amplification of SPs in a doped graphene nanoribbon is obtained. The dependence of the minimal population inversion on the surface plasmon wavevector, graphene nanoribbon width, doping and damping parameters necessary for the amplification of surface plasmons in the armchair graphene nanoribbon is studied.

Bose-Einstein condensates confined in traps exhibit unique features which have been the object of extensive experimental and theoretical studies in the last few years. In this paper I will discuss some issues concerning the behaviour of the order parameter and the dynamic and superfluid effects exhibited by such systems.

Experimental and theoretical evidence of plasmon-enhanced Kerr rotation in purely ferromagnetic membranes with sufficiently small dimensions to be out of extraordinary optical transmission conditions (45 nm pore diameter, 90nm lattice constant), is reported in this work. It is shown that the spectral location of the enhanced Kerr rotation region varies as the refractive index of the material inside the pore is modified. A similar behavior is obtained if the pore radius changes while keeping the pore concentration unchanged. Those are clear signatures indicating that localized surface plasmon resonances propagating along the pores govern the magneto-optical response of the membrane.

We analyze theoretically the oscillations that the magnetoresistivity of twodimensional electron systems present when a high intensity direct current is applied. In the model presented here we suggest that a plasma wave is excited in the system producing an oscillating motion of the whole two-dimensional electron gas at the plasma frequency. This scenario affects dramatically the way that electrons interact with scatterers giving rise to oscillations in the longitudinal resistivity. With this theoretical model experimental results are well reproduced and explained.

We study the transport properties of the quantum Hall bilayers systems looking closely at the effect that disorder and electron-phonon interaction have on the interlayer tunnelling current in the presence of an in-plane magnetic field B . We find that it is important to take into account the effect of disorder and electron-phonon interactions in order to predict a finite current at a finite voltage when an in-plane magnetic field is present. We find a broadened resonant feature in the tunnelling current as a function of bias voltage, in qualitative agreement with experiments. We also find the broadening due to electron-phonon coupling has a non-monotonic dependence on B , related to the geometry of the double quantum well. We also compare this with the broadening effect due to spatial fluctuations of the tunnelling amplitude. We conclude that such static disorder provides only very weak broadening of the resonant feature in the experimental range.

Starting from thin film planar technology, we designed and fabricated a visible optical source that produces a localized bright spot with nanometric dimensions. The structure consists of exciting surface plasmons through the illumination of a subwavelength hole in a silver film and in confining them at the vicinity of the aperture by surrounding the hole of Bragg mirrors resonant with the plasmons generated. Both finite element method computations and experimental results evidence the performances of this device that could find applications, for example, in nanolithography or optical data storage.

We calculate the nonlinear dipole and quadrupole moments induced at the second-harmonic ͑SH͒ frequency 2 in a small dielectric sphere by an inhomogeneous monochromatic electric field of frequency. We neglect finite-size effects and assume that the selvedge region of the sphere is thin enough so that the surface may be considered locally flat. The second-order dipole displays resonances corresponding to the excitation of dipolar and quadrupolar plasmons at and a dipolar plasmon at 2, besides the resonances in the nonlinear surface response parameters a, b, and f. The second-order quadrupole, on the other hand, has resonances corresponding to those of a, b, and f, and to the excitation of dipolar surface plasmons at only. Depending on the relation between the size of the sphere and the spatial scale of variation of the field, the SH radiation may be dominated by either dipolar or quadrupolar scattering, with a crossover region. As an application, we calculate the SH scattering of a Si sphere lying at various distances above a dielectric substrate.

We calculate the optical second harmonic ͑SH͒ radiation generated by small spheres made up of a homogeneous centrosymmetric material illuminated by inhomogeneous transverse and/or longitudinal electromagnetic fields. We obtain expressions for the hyperpolarizabilities of the particles in terms of the multipolar bulk susceptibilities and dipolar surface susceptibilities of their constitutive material. We employ the resulting response functions to obtain the nonlinear susceptibilities of a composite medium made up of an array of such particles and to calculate the radiation patterns and the efficiency of SH generation from the bulk and the edge of thin composite films illuminated by finite beams. Each sphere has comparable dipolar and quadrupolar contributions to the nonlinear radiation, and the composite has comparable bulk and edge contributions which interfere among themselves yielding nontrivial radiation and polarization patterns. We present numerical results for Si spheres and we compare our results with recent experiments.

We present a formalism for calculating the absorption coefficient of a pair of coaxial tubules. A spatially nonlocal, dynamical self-consistent field theory is obtained by calculating the electrostatic potential produced by the charge density fluctuations as well as the external electric field. There are peaks in the absorption spectrum arising from plasma excitations corresponding either to plasmon or particle-hole modes. In this paper, we numerically calculate the plasmon contribution to the absorption spectrum when an external electric field is applied. The number of peaks depends on the radius of the inner as well as outer tubule. The height of each peak is determined by the plasmon wavelength and energy. For a chosen wave number, the most energetic plasmon has the highest peak corresponding to the largest oscillator strength of the excited modes. Some of the low-frequency plasmon modes have such weak coupling to an external electric field that they are not seen on the same scale as the modes with larger energy of excitation. We plot the peak positions of the plasmon excitations for a pair of coaxial tubules. The coupled modes on the two tubules are split by the Coulomb interaction. The energies of the two highest plasmon branches increase with the radius of the outer tubule. On the contrary, the lowest modes decrease in energy as this radius is increased. No effects due to inter-tubule hopping are included in these calculations.

(0) c decreases as B −1/4 and increases with the spring constant of the parabolic trap. The Rabi splitting related to the creation of a magnetoexciton in a high magnetic field in graphene and QW is obtained. It is shown that Rabi splitting in graphene can be controlled by the external magnetic field since it is proportional to B −1/4 , while in a QW the Rabi splitting does not depend on the magnetic field when it is strong.

Large phase differences between transverse electric (TE) and transverse magnetic (TM) waves were investigated in plasmonic nanoslit arrays. The phase of the TE wave shifts ahead because of its low propagation constant. On the other hand, the phase of the TM wave is retarded due to the propagation of surface plasmons. The opposite phase shift forms a giant birefringence. Its magnitude was dependent on the width of nanoslits. The birefringence magnitude was ∼1 for 300-nm-wide nanoslits and up to ∼2.7 for 100 nm ones. The spectroscopic measurements indicate that waveplates made of gold nanoslits have large bandwidths.

We have studied the interaction of charged particles with single-walled metallic nanotubes by solving Poisson's equation with appropriate boundary conditions. Numerical results for the energy dispersion relations as a function of the wave vector are presented when the charged particle is inside or outside the nanotube.

Highly ordered two-dimensional arrays of monodisperse coinage metal nanowires embedded in an alumina matrix have been prepared. When light is propagating in the direction of the long axis of the nanowire, plasmon-enhanced absorption and light guidance of the nanowire were observed by optical microspectroscopy and scanning near-field optical spectroscopy and compared to Mie scattering theory. By selectively dissolving the matrix at a constant etching rate, we detected in situ and ex situ the surface-enhanced Raman scattering (SERS) of organic dyes. In contrast to earlier publications, we find that the SERS signal is linearly proportional to the free-surface area of the nanowires that are in contact with the dye. We cannot detect any change in the enhancement factor due to the releasing of the nanowires from the host structure.

Organic thin film based excitonic nanostructures are of a great interest in modern resonant nanophotonics as a promising alternative for plasmonic systems. Such nanostructures sustain propagating and localized surface exciton modes which can be exploited in refractive index sensing and near-field enhanced spectroscopy. To realize these surface excitonic modes and to enhance their optical performance, the concentration of the excitonic molecules present in the organic thin film has to be quite high so that a large oscillator strength can be achieved. Unfortunately, this often results in a broadening of the material response which might prevent achieving the very goal. Therefore, systematic and in-depth studies are needed on the molecular concentration dependence of the surface excitonic modes to acquire optimal performance from them. Here, we study the effect of molecular concentration in terms of oscillator strength and Lorentzian broadening on various surface excitonic modes when e...

We have applied the quantum Monte Carlo method and tight-binding modeling to calculate the binding energy of biexcitons in semiconductor carbon nanotubes for a wide range of diameters and chiralities. For typical nanotube diameters we find that biexciton binding energies are much larger than previously predicted from variational methods, which easily brings the biexciton binding energy above the room temperature threshold.

Nanostructured metal surfaces comprised of periodically arranged spherical voids are grown by electrochemical deposition through a self-assembled template. Detailed measurements of the angleand orientation-dependent reflectivity reveal the spectral dispersion, from which we identify the presence of both delocalized Bragg-and localized Mie-plasmons. These couple strongly producing bonding and anti-bonding mixed plasmons with anomalous dispersion properties. Appropriate plasmon engineering of the void morphology selects the plasmon spatial and spectral positions, allowing these plasmonic crystal films to be optimised for a wide range of sensing applications.

We have presented here results of a low temperature transport study of polypyrrole nanowires having low electron densities, which shows characteristics of charge density waves observed in structurally ordered materials. The current-voltage characteristics of all these nanowires show a power-law dependence on voltage and temperature and a "gap" that decreases rapidly as the temperature is increased, confirming the existence of a long-range electron-electron interaction in the nanowires. A switching transition to highly conducting state has been observed above a threshold voltage, which can be tuned by changing the diameters of the nanowires and the temperature. Negative differential resistance and enhancement of noise have been observed above the threshold. These experimental results give evidence in favor of Wigner crystallization in these nanowires.

Femtosecond laser excitation of bulk n-doped GaAs leads to coherent plasmon excitations that emit intense submillimeter wave radiation. We investigated the underlying plasmon dynamics in time-resolved experiments on the emitted THz radiation. The results show that THz pulses are emitted due to the coherent oscillation of the extrinsic electron plasma in the bulk. The plasmon excitations are started by single-sided screening of the surface depletion field after photoexcitation. Temperature-dependent measurements indicate that the plasmon damping is due to phonon scattering. ͓S0163-1829͑98͒00328-2͔

We give three methods for entangling quantum states in quantum dots. We do this by showing how to tailor the resonant energy (Förster-Dexter) transfer mechanisms and the biexciton binding energy in a quantum dot molecule. We calculate the magnitude of these two electrostatic interactions as a function of dot size, interdot separation, material composition, confinement potential and applied electric field by using an envelope function approximation in a two-cuboid dot molecule. In the first implementation, we show that it is desirable to suppress the Förster coupling and to create entanglement by using the biexciton energy alone. We show how to perform universal quantum logic in a second implementation which uses the biexciton energy together with appropriately tuned laser pulses: by selecting appropriate materials parameters high fidelity logic can be achieved. The third implementation proposes generating quantum entanglement by switching the Förster interaction itself. We show that the energy transfer can be fast enough in certain dot structures that switching can occur on a timescale which is much less than the typical decoherence times.

Monopoles and vortices are fundamental topological excitations that appear in physical systems spanning enormous scales of size and energy, from the vastness of the early universe to tiny laboratory droplets of nematic liquid crystals and ultracold gases. Although the topologies of vortices and monopoles are distinct from one another, under certain circumstances a monopole can spontaneously and continuously deform into a vortex ring with the curious property that monopoles passing through it are converted into anti-monopoles. However, the observation of such Alice rings has remained a major challenge, due to the scarcity of experimentally accessible monopoles in continuous fields. Here, we present experimental evidence of an Alice ring resulting from the decay of a topological monopole defect in a dilute gaseous 87Rb Bose–Einstein condensate. Our results, in agreement with detailed first-principles simulations, provide an unprecedented opportunity to explore the unique features of a...

A novel type of spaser with the net amplification of surface plasmons (SPs) in doped graphene nanoribbon is proposed. The plasmons in THz region can be generated in a dopped graphene nanoribbon due to nonradiative excitation by emitters like two level quantum dots located along a graphene nanoribbon. The minimal population inversion per unit area, needed for the net amplification of SPs in a doped graphene nanoribbon is obtained. The dependence of the minimal population inversion on the surface plasmon wavevector, graphene nanoribbon width, doping and damping parameters necessary for the amplification of surface plasmons in the armchair graphene nanoribbon is studied. Besides, a new method for high-sensitivity plasmon spectroscopy is proposed based on the usage of a graphene spaser. The plasmon generation is suppressed and even break down near threshold due to absorption at the transition frequencies of the neighbouring nano-objects (molecules or clusters) under study. In result a dip in the spaser generation spectra appears. The sensitivity of this spaser spectroscopy near (slightly above) generation threshold can be very high.

Non-Abelian anyons can exist as point-like particles in two-dimensional systems, and have particle exchange statistics which are neither bosonic nor fermionic. Like in spin systems, the role of fusion (Heisenberg-like) interactions between anyons has been well studied. However, unlike our understanding of the role of bosonic and fermionic statistics in the formation of different quantum phases of matter, little is known concerning the effect of non-Abelian anyonic statistics. We explore this physics using an anyonic Hubbard model on a two-legged ladder which includes braiding and nearest neighbour Heisenberg interactions among anyons. We study two of the most prominent non-Abelian anyon models: the Fibonacci and Ising type. We discover rich phase diagrams for both anyon models, and show the different roles of their fusion and braid statistics.

We demonstrate the imaging capabilities of energy-filtered transmission electron microscopy at high energy resolution in the low energy-loss region, reporting the first direct image of a surface plasmon of an elongated gold nanoparticle at energies around 1 eV. Using complimentary model calculations performed within the boundary element method approach we can assign the observed results to the plasmon eigenmodes of the metallic nanoparticle.

The excitation modes of electrons in symmetric, neutral jellium slabs are studied within the timedependent local density and related approximations, in the regime when there are several bound states below the Fermi level. Unlike most previous calculations, the present ones do not require all single-particle wave functions to vanish at some small distance from the slab. This modification of the boundary conditions significantly affects the excitation spectra, generally reducing the number of peaks that appear. In particular, from our calculations modeling excitation by longitudinal near fields with nonzero surface-parallel wave vector, we do not find resolvable peaks above the bulk plasmon frequency~"which could be interpreted as standing plasma waves resonating across the neutral slab. This is in contrast to the case of a symmetric but non-neutral jellium slab (wide parabolic quantum well or embedded electron gas) where we do predict distinct (but weak) standing plasmon resonances above~~at nonzero surface-parallel wave vector, even for a well with only a few occupied bound states. Although bulk plasmon resonances seem to be unobservable in the relatively narrow, symmetric, neutral jellium slabs studied here, we do find the following peaks consistently at low surface-parallel wave vector: an "intraband" mode near the two-dimensionalplasmon frequency and a "multipole surface plasmon" mode near 0.8u", the latter being amenable also to other interpretations for very thin slabs. Further peaks, including a cluster near u~, are harder to interpret. They can be related to single-particle transitions in the case of thin slabs. However, in the intermediate-thickness regime it is difticult to assign a unique physical cause to each peak in a spectrum, and various ways to help sort out ambiguities are illustrated. These do not always resolve matters since for neutral jellium slabs one has a relatively wide transition region between quantum and classical size effects.

Effective material parameters for metamaterials are usually extracted for a single thin layer only. We show that, in general, these parameters cannot directly be assigned to a multilayered ͑bulk͒ metamaterial. The principal issue is the presence of higher-order Bloch modes. These modes are usually negligible for a single layer but can have considerable influence on the results for a periodically stacked structure. In particular, we show examples where a stack of single-layer negative refractive index metamaterials exhibits a positive index. Furthermore, on the basis of the dispersion relation of the respective Bloch modes, we derive criteria for the validity of the effective parameter approach.

We have applied the quantum Monte Carlo method and tight-binding modeling to calculate the binding energy of biexcitons in semiconductor carbon nanotubes for a wide range of diameters and chiralities. For typical nanotube diameters we find that biexciton binding energies are much larger than previously predicted from variational methods, which easily brings the biexciton binding energy above the room temperature threshold.

Recently it has been predicted that “cylindrical” surface plasmons (CSP’s) on cylindrical interfaces of coaxial ring apertures produce a different form of extraordinary optical transmission that extends to ever increasing wavelengths as the dielectric ring narrows. This letter presents experimental confirmation of this CSP assisted extraordinary transmission. Nanoarrays of submicron coaxial apertures are fabricated in a thin silver film on a glass substrate and far-field transmission spectra are measured. The experimental spectrum is in close agreement with predictions from finite-difference time-domain simulations and CSP dispersion theory. The role of cylindrical surface plasmons in producing extraordinary transmission is thus confirmed.

The structure of the edge excitations of a quantum Hall droplet, confined in a double quantum well, is studied using a generalized version of the Wen-Stone chiral boson action. As the interwell tunneling t is increased, one finds a "metal-insulator" transition from a phase where the optic edge mode is ungapped to a phase where the optic mode is gapped. The large-t phase exhibits edge quasiexcitons whose charge is half that of a quasiparticle-quasihole bound state. The critical behavior of the conductances, the exciton gap, and the excitonic order parameter is discussed.

By use of electron-energy-loss spectrometer with high-momentum resolution, we have measured a collective electronic excitation in a surface-state band on Si(1 1 1)± p 3 Â p 3-Ag. We have clari®ed that the energy dispersion is isotropic with respect to the azimuthal orientation and shows no dependence on the electron probing depth. The obtained energy dispersion agreed very well with the plasmon dispersion calculated from two-dimensional (2D) nearly free-electron theory. As hallmarked from these observations, we identify the measured loss as a longitudinal intraband 2D plasmon in the surface-state band.

As an efficient nanolens, we propose a self-similar linear chain of several metal nanospheres with progressively decreasing sizes and separations. To describe such systems, we develop the multipole spectral expansion method. Optically excited, such a nanolens develops the nanofocus (''hottest spot'') in the gap between the smallest nanospheres, where the local fields are enhanced by orders of magnitude due to the multiplicative, cascade effect of its geometry and high Q factor of the surface plasmon resonance. The spectral maximum of the enhancement is in the near-ultraviolet region, shifting toward the red region as the separation between the spheres decreases. The proposed system can be used for nanooptical detection, Raman characterization, nonlinear spectroscopy, nanomanipulation of single molecules or nanoparticles, and other applications.

Li, Stockman, and Bergman Reply: In their Comment [1], Li, Yang, and Xu (LYX) contend that, within their electrodynamic computation, the maximum enhancement is about 2 times smaller than in our original Letter [2], and with the finite-size effects taken into account it is less by an additional factor of 2. There were two main results reported in our original Letter [2]. The first is based on a qualitative idea of transfer of the excitation and field down the scale of sizes in selfsimilar systems, which leads to multiplicative enhancement of the local field. The maximum enhancement occurs in a small nanofocus (''the hottest spot'') in the gap between the smallest nanospheres. This is the main part of our Letter, and it is not contested in the Comment, which actually confirms the existence of this nanofocus and large field enhancement in it. The second part of Ref. [2] provides an illustration: some computations for three-, five-, and six-sphere nanolenses, which show that the fields are enhanced at the nanofocus, depending on the geometry, by a factor from 500 to 2200. These numbers are stated by LYX to be by a factor of 2-4 larger than their results. In our original Letter, we clearly stated that we solve the problem in the quasistatic approximation, neglecting spatial dispersion and Landau damping. The parameters of our systems were deliberately chosen to be at the limits of applicability of that approximation. The Comment actually shows that these parameters are reasonable: An error by factor 2, when the total enhancement is 1200, is a reasonably good accuracy given that there are many other physical effects which were ignored in our model, and also in the Comment (see below). We do maintain that our model was solved accurately. A careful perusal of Fig. 1(a) shows that the field at the nanofocus, seen as the very narrow high peak just outside the smallest sphere in the 1.5 nm intersphere gap, changes by more than an order of magnitude in the tangential direction and in the radial direction as soon as that sphere is entered. This abrupt change occurs over a distance of less than 0.5 nm-the grid size used by LYX is too coarse. The great enhancement of field strength arises due to the fact that the frequency is close to that of one or more localized scattering resonances of the system [2]. The generalized Mie theory used by LYX is a multiple scattering theory [3,4]. Such a procedure cannot be expected to be accurate at a frequency close to a scattering resonance: Precisely at the resonance, it will diverge. For our part, we do not understand why the two different approaches, which were used by LYX, yield results that are so close to each other-perhaps this is fortuitous? Finally, LYX discuss numerical consequences for the surfaceenhanced Raman scattering enhancement factor G RS , ignoring the fact that G RS Þ jEj 4 , where jEj is the enhancement factor of the local electric field. Figure 1(b) shows our original Green's function computations [5] of G RS along with jEj 4. Evidently, G RS differs from jEj 4 by orders of magnitude.

We study an optomechanical system in which the collective density excitations (Bogoliubov modes) of a Bose Einstein condensate (BEC) is coupled to a cavity field. We show that the optical force changes the frequency and the damping constant of the collective density excitations of the BEC. We further analyze the occurrence of normal mode splitting (NMS) due to mixing of the fluctuations of the cavity field and the fluctuations of the condensate with finite atomic two-body interaction. The NMS is found to vanish for small values of the two-body interaction. We further show that the density excitations of the condensate can be used to squeeze the output quantum fluctuations of the light beam. This system may serve as an optomechanical control of quantum fluctuations using a Bose Einstein condensate.

We propose a scheme to transfer the quantum state of light fields to the collective density excitations of a Bose Einstein condensate (BEC) in a cavity. This scheme allows to entangle two BECs in a double cavity setup by transferring the quantum entanglement of two light fields produced from a nondegenerate parametric amplifier (NOPA) to the collective density excitations of the two BECs. An EPR state of the collective density excitations can be created by a judicious choice of the system parameters.

For a long time, people believe that all possible states of matter are described by Landau symmetry-breaking theory. Recently we found that string-net condensation provide a mechanism to produce states of matter beyond the symmetry-breaking description. The collective excitations of the string-net condensed states turn out to be our old friends, photons and electrons (and other gauge bosons and fermions). This suggests that our vacuum is a stringnet condensed state. Light and electrons in our vacuum have a unified origin-string-net condensation.

We investigate the insertion of holes in conjugated polymers bearing polarons. We use a Su-Schrieffer-Heeger model modified to include electron-electron interactions via an extended Hubbard Hamiltonian, a Brazovskii-Kirova symmetry breaking term, and an external electric field. We study the dynamics performing numerical calculations within the time-dependent unrestricted Hartree-Fock approximation. We find that adding a hole in a conducting polymer bearing a single positively charged polaron leads to the direct transition of polaron to bipolaron state. The transition produced is a single-polaron to biplaron transition whose excitation spectrum explains the experimental data. The competing mechanism of two polarons merging to form a bipolaron is not observed. We also find that depending on how fast the hole is inserted, a structure that contains a bipolaron coupled to a breather is created. The bipolaron-breather pair can be decoupled under the action of an external electric field. We determine the value of the critical electric field to untrap the bipolaron from the breather.

We explore the behavior of collective nuclear excitations under a multi-parameter deformation of the Hamiltonian. The Hamiltonian matrix elements have the form P (|H ij |) ∝ 1/ |H ij | exp(−|H ij |/V), with a parametric correlation of the type log H(x)H(y) ∝ −|x − y|. The studies are done in both the regular and chaotic regimes of the Hamiltonian. Model independent predictions for a wide variety of correlation functions and distributions which depend on wavefunctions and energies are found from parametric random matrix theory and are compared to the nuclear excitations. We find that our universal predictions are observed in the nuclear states. Being a multi-parameter theory, we consider general paths in parameter space and find that universality can be effected by the topology of the parameter space. Specifically, Berry's phase can modify short distance correlations, breaking certain universal predictions.

Plasmonic systems are known for their distinct nonlinear optical properties when compared to purely dielectric materials. Although it is well accepted that the enhanced nonlinear processes in plasmonicdielectric compounds are related to the excitation of localized plasmon resonances, their exact origin is concealed by the local field enhancement in the surrounding material and the nonlinearity in the metal. Here, we show that the origin of third-harmonic generation in hybrid plasmonic-dielectric compounds can be unambiguously identified from the shape of the nonlinear spectrum.

As an efficient nanolens, we propose a self-similar linear chain of several metal nanospheres with progressively decreasing sizes and separations. To describe such systems, we develop the multipole spectral expansion method. Optically excited, such a nanolens develops the nanofocus (''hottest spot'') in the gap between the smallest nanospheres, where the local fields are enhanced by orders of magnitude due to the multiplicative, cascade effect of its geometry and high Q factor of the surface plasmon resonance. The spectral maximum of the enhancement is in the near-ultraviolet region, shifting toward the red region as the separation between the spheres decreases. The proposed system can be used for nanooptical detection, Raman characterization, nonlinear spectroscopy, nanomanipulation of single molecules or nanoparticles, and other applications.

Li, Stockman, and Bergman Reply: In their Comment [1], Li, Yang, and Xu (LYX) contend that, within their electrodynamic computation, the maximum enhancement is about 2 times smaller than in our original Letter [2], and with the finite-size effects taken into account it is less by an additional factor of 2. There were two main results reported in our original Letter [2]. The first is based on a qualitative idea of transfer of the excitation and field down the scale of sizes in selfsimilar systems, which leads to multiplicative enhancement of the local field. The maximum enhancement occurs in a small nanofocus (''the hottest spot'') in the gap between the smallest nanospheres. This is the main part of our Letter, and it is not contested in the Comment, which actually confirms the existence of this nanofocus and large field enhancement in it. The second part of Ref. [2] provides an illustration: some computations for three-, five-, and six-sphere nanolenses, which show that the fields are enhanced at the nanofocus, depending on the geometry, by a factor from 500 to 2200. These numbers are stated by LYX to be by a factor of 2-4 larger than their results. In our original Letter, we clearly stated that we solve the problem in the quasistatic approximation, neglecting spatial dispersion and Landau damping. The parameters of our systems were deliberately chosen to be at the limits of applicability of that approximation. The Comment actually shows that these parameters are reasonable: An error by factor 2, when the total enhancement is 1200, is a reasonably good accuracy given that there are many other physical effects which were ignored in our model, and also in the Comment (see below). We do maintain that our model was solved accurately. A careful perusal of Fig. 1(a) shows that the field at the nanofocus, seen as the very narrow high peak just outside the smallest sphere in the 1.5 nm intersphere gap, changes by more than an order of magnitude in the tangential direction and in the radial direction as soon as that sphere is entered. This abrupt change occurs over a distance of less than 0.5 nm-the grid size used by LYX is too coarse. The great enhancement of field strength arises due to the fact that the frequency is close to that of one or more localized scattering resonances of the system [2]. The generalized Mie theory used by LYX is a multiple scattering theory [3,4]. Such a procedure cannot be expected to be accurate at a frequency close to a scattering resonance: Precisely at the resonance, it will diverge. For our part, we do not understand why the two different approaches, which were used by LYX, yield results that are so close to each other-perhaps this is fortuitous? Finally, LYX discuss numerical consequences for the surfaceenhanced Raman scattering enhancement factor G RS , ignoring the fact that G RS Þ jEj 4 , where jEj is the enhancement factor of the local electric field. Figure 1(b) shows our original Green's function computations [5] of G RS along with jEj 4. Evidently, G RS differs from jEj 4 by orders of magnitude.

We examine whether single molecule sensitivity in surface-enhanced Raman scattering ͑SERS͒ can be explained in the framework of classical electromagnetic theory. The influence of colloid particle shape and size, composition ͑Ag or Au͒ and interparticle separation distance on the wavelength-dependent SERS enhancement factor is reported. Our calculations indicate that the maximum enhancement factor achievable through electromagnetics is of the order 10 11. This is obtained only under special circumstances, namely at interstitial sites between particles and at locations outside sharp surface protrusions. The comparative rarity of such sites, together with the extreme spatial localization of the enhancement they provide, can qualitatively explain why only very few surface sites seem to contribute to the measured signal in single-molecule SERS experiments. Enhancement factors of the order 10 14 Ϫ10 15 , which have been reported in recent experiments, are likely to involve additional enhancement mechanisms such as chemisorption induced resonance Raman effects.

In this study, a standing wave in an optical nanocavity with Bose-Einstein condensate (BEC) constitutes a one-dimensional optical lattice potential in the presence of a finite two bodies atomic interaction. We report that the interaction of a BEC with a standing field in an optical cavity coherently evolves to exhibit Fano resonances in the output field at the probe frequency. The behaviour of the reported resonance shows an excellent compatibility with the original formulation of asymmetric resonance as discovered by Fano [U. Fano, Phys. Rev. 124, 1866 (1961)]. Based on our analytical and numerical results, we find that the Fano resonances and subsequently electromagnetically induced transparency of the probe pulse can be controlled through the intensity of the cavity standing wave field and the strength of the atom-atom interaction in the BEC. In addition, enhancement of the slow light effect by the strength of the atom-atom interaction and its robustness against the condensate fluctuations are realizable using presently available technology.

Bilayer quantum Hall states support a flow of nearly dissipationless staggered current which can only decay through collective channels. We study the dominant finite-temperature dissipation mechanism which in narrow bars is driven by thermal nucleation of pseudospin solitons. We find the finitetemperature resistivity, predict the resulting staggered current-voltage characteristics, and calculate the associated zero-temperature critical staggered current and gate voltage.

In this work we present a model and a method to study integer quantum Hall (IQH) systems. Making use of the Landau levels structure we divide these two dimensional systems into a set of interacting one dimensional gases, one for each guiding center. We show that the so-called strong field approximation, used by Kallin and Halperin and by MacDonald, is equivalent, in first order, to a forward scattering approximation and analyze the IQH systems within this approximation. Using an appropriate variation of the Landau level bosonization method we obtain the dispersion relations for the collective excitations and the single particle spectral functions. For the bulk states, these results evidence a behavior typical of non-normal strongly correlated systems, including the spin-charge splitting of the single particle spectral function. We discuss the origin of this behavior in the light of the Tomonaga-Luttinger model and the bosonization of two dimensional electron gases.