具有格点各向异性的一维铁磁链中的量子孤子和内禀局域模(英文)

基于Hartree-Fock方法和多标度方法,我们考察了具有格点各向异性的一维铁磁链中的量子孤子和内禀局域模,量子磁振子的波函数由量子包络孤子来描述.在布里渊区边界,量子包络孤子变成了量子内禀局域模,它的量子本征频率在简谐波带的顶部上方,量子磁振子主要集中在中心位置j=j0的附近.     

Quantum Solitons and Localized Modes in a One-Dimensional Lattice Chain with Nonlinear Substrate Potential

In the classical lattice theory, solitons and localized modes can exist in many one-dimensional nonlinear lattice chains, however, in the quantum lattice theory, whether quantum solitons and localized modes can exist or not in the one-dimensional lattice chains is an interesting problem. By using the number state method and the Hartree approximation combined with the method of multiple scales, we investigate quantum solitons and localized modes in a one-dimensional lattice chain with the nonlinear substrate potential. It is shown that quantum solitons do exist in this nonlinear lattice chain, and at the boundary of the phonon Brillouin zone, quantum solitons become quantum localized modes, phonons are pinned to the lattice of the vicinity at the central position j=j₀.     

在一维均匀铁磁链中磁振动的内禀局域模

利用多标度方法和准离散近似,我们考察了在一维均匀铁磁链中磁振动的内禀局域模; 结果表明磁振动的内禀局域模在许多方面都与晶格振动的内禀局域模相类似;它们是近邻自旋之间非线性相互作用的结果.这种内禀局域模的存在并没有破坏系统的平移对称性,它们能在任何晶格位被激发.它们的量子本征频率在简谐磁振动频带的上方.     

Parametric solitons

We develop a general framework for understanding the characteristics of multi-frequency (multi-colour) parametric solitons. We identify two special classes of such solitons: cascaded parametric solitons, where the optical energy is shared between several harmonically-related frequency bands; and isolated-bandwidth solitons, where all of the optical energy is localized within a single frequency band. As an example, we consider the case of a five-colour isolated-bandwidth parametric soliton in a Kerr medium.     

Intrinsic Localized Spin-Wave Modes in an Anisotropic Ferromagnet with Dzyaloshinsky-Moriya Interaction

The existence and properties of intrinsic localized spin-wave modes in a ferromagnetic XXZ spin chain with Dzyaloshinsky-Moriya interaction are investigated analytically in the semiclassical limit. The model Hamiltonian is quantized by introducing the Dyson-Maleev transformation and the coherent state representation is chosen as the basic representation of the system. By making use of the method of multiple scales combined with a quasidiscreteness approximation, the equation of motion for the coherent-state amplitude is reduced to the nonlinear Schrödinger equation. It is shown that a bright intrinsic localized spin-wave mode whose eigenfrequency lies below the bottom of the magnon frequency band can exist in the ferromagnetic system. We also show that the system can produce a dark intrinsic localized spin-wave mode, i.e., nonpropagating kink, whose eigenfrequency is below the upper of the magnon frequency band. In addition, we find that the introduction of the Dzyaloshinsky-Moriya interaction changes wave numbers in the Brillouin-zone corresponding to the appearance of intrinsic localized spin-wave modes.     

Intrinsic Localized Modes in Quantum Ferromagnetic XXZ Chains in an Oblique Magnetic Field

A semiclassical study of intrinsic localized spin-wave modes in a one-dimensional quantum ferromagnetic XXZ chain in an oblique magnetic field is presented in this paper. We quantize the model Hamiltonian by introducing the Dyson-Maleev transformation, and adopt the coherent state representation as the basic representation of the system. By means of the method of multiple scales combined with a quasidiscreteness approximation, the equation of motion for the coherent-state amplitude can be reduced to the standard nonlinear Schrödinger equation. It is found that, at the center of the Brillouin zone, when θ < θ _c a bright intrinsic localized spin-wave mode appears below the bottom of the magnon frequency band and when θ > θ _c a dark intrinsic localized spin-wave resonance mode can occur above the bottom of the magnon frequency band. In other words, the switch between the bright and dark intrinsic localized spin-wave modes can be controlled via varying the angle of the magnetic field. This result has potential applications in quantum information storage. In addition, we find that, at the boundary of the Brillouin zone, the system can only produce a dark intrinsic localized spin-wave mode, whose eigenfrequency is above the upper of the magnon frequency band.     

A New Approach to Energy Integral for Investigation of Dust-Ion Acoustic(DIA)Waves in Multi-Component Plasmas with Quantum Effects in Inertia Less Electrons

Dust-ion acoustic waves are investigated in this model of plasma consisting of negatively charged dusts,cold ions and inertia less quantum effected electrons with the help of a typical energy integral.In this case,a new technique is applied formulating a differential equation to establish the energy integral in case of multi-component plasmas which is not possible in general.Dust-ion acoustic(DIA) compressive and rarefactive,supersonic and subsonic solitons of various amplitudes are established.The consideration of smaller order nonlinearity in support of the newly established quantum plasma model is observed to generate small amplitude solitons at the decrease of Mach number.The growths of soliton amplitudes and potential depths are found more sensitive to the density of quantum electrons.The small density ratio r(=1-f) with a little quantized electrons supplemented by the dust charges Z_d and the in-deterministic new quantum parameter C_2 are found responsible to finally support the generation of small amplitude solitons admissible for the model.     

Dynamical behaviour of non-linear quantum ion acoustic wave in weakly magnetized electron–positron–ion plasma

In order to investigate the propagation characteristics of linear and non-linear ion acoustic waves (IAWs) in electron–positron–ion quantum plasma in the presence of external weak magnetic field, we have used a quantum hydrodynamic model, and degenerate statistics for the electrons and positrons are taken into account. It is found that the linear dispersion relation of the IAW was modified by the externally applied magnetic field. By using the reductive perturbation technique, a gyration-modified Korteweg-de Vries equation is derived for finite amplitude non-linear IAWs. Time-dependent numerical simulation shows the formation of an oscillating tail in front of the ion acoustic solitons in the presence of a weak magnetic field. It is also seen that the amplitude and width of solitons and oscillating tails are affected by the relevant plasma parameters such as quantum diffraction, positron concentration, and magnetic field. We have performed our analysis by extending it to account for approximate soliton solution by asymptotic perturbation technique and non-linear analysis via a dynamical system approach. The analytical results show the distortion of the shape of the localized soliton with time, and the non-linear analysis confirms the generation of oscillating tails.     

Effective mass in quantum effects of radiation pressure

We study the quantum effects of radiation pressure in a high-finesse cavity with a mirror coated on a mechanical resonator. We show that the optomechanical coupling can be described by an effective susceptibility which takes into account every acoustic modes of the resonator and their coupling to the light. At low frequency this effective response is similar to a harmonic response with an effective mass smaller than the total mass of the mirror. For a plano-convex resonator the effective mass is related to the light spot size and becomes very small for small optical waists, thus enhancing the quantum effects of optomechanical coupling.     

Two-dimensional matter-wave solitons and vortices in competing cubic-quintic nonlinear lattices

The nonlinear lattice — a new and nonlinear class of periodic potentials — was recently introduced to generate various nonlinear localized modes. Several attempts failed to stabilize two-dimensional (2D) solitons against their intrinsic critical collapse in Kerr media. Here, we provide a possibility for supporting 2D matter-wave solitons and vortices in an extended setting — the cubic and quintic model — by introducing another nonlinear lattice whose period is controllable and can be different from its cubic counterpart, to its quintic nonlinearity, therefore making a fully “nonlinear quasi-crystal”.A variational approximation based on Gaussian ansatz is developed for the fundamental solitons and in particular, their stability exactly follows the inverted Vakhitov–Kolokolov stability criterion, whereas the vortex solitons are only studied by means of numerical methods. Stability regions for two types of localized mode — the fundamental and vortex solitons — are provided. A noteworthy feature of the localized solutions is that the vortex solitons are stable only when the period of the quintic nonlinear lattice is the same as the cubic one or when the quintic nonlinearity is constant, while the stable fundamental solitons can be created under looser conditions. Our physical setting (cubic-quintic model) is in the framework of the Gross–Pitaevskii equation or nonlinear Schrödinger equation, the predicted localized modes thus may be implemented in Bose–Einstein condensates and nonlinear optical media with tunable cubic and quintic nonlinearities.     

Optical vortex solitons in parametric wave mixing

We analyze two-component spatial optical vortex solitons supported by parametric wave mixing processes in a nonlinear bulk medium. We study two distinct cases of such localized waves, namely, parametric vortex solitons due to phase-matched second-harmonic generation in an optical medium with competing quadratic and cubic nonlinear response, and vortex solitons in the presence of third-harmonic generation in a cubic medium. We find, analytically and numerically, the structure of two-component vortex solitons, and also investigate modulational instability of their plane-wave background. In particular, we predict and analyze in detail novel types of vortex solitons, a "halo-vortex," consisting of a two-component vortex core surrounded by a bright ring of its harmonic field, and a "ring-vortex" soliton which is a vortex in a harmonic field that guides a ring-like localized mode of the fundamental-frequency field.     

Soliton microdynamics and thermal conductivity of uranium nitride at high temperatures

The microdynamics of soliton waves and localized modes of nonlinear vibrations of the acoustic and optical types in uranium nitride has been investigated. It has been shown that, with an increase in the excitation energy in the spectral gap between the bands of optical and acoustic phonons, the energies of solitons increase, whereas the energies of local modes decrease. The previously experimentally observed unidentified quasi-resonant features, which shift in the gap with variations in the temperature, can represent the revealed soliton waves and local modes. The microdynamics of heat conduction of uranium nitride has been studied for the stochastic generation of soliton waves and local modes in the case of spatially distant energy absorption. The thermal conductivity coefficient determined from the temperature gradient and the absorbed energy flux insignificantly exceeds the experimentally observed values, which are decreased because of the presence of structural defects of different types in the material.     

A unified description of sum frequency generation,parametric down conversion and two-photon fluorescence

A superoperator non-equilibrium Green's function formalism is presented for computing nonlinear optical processes involving any combination of classical and quantum optical modes. Closed correlation-function expressions based on superoperator time-ordering are derived for the combined effects of causal response and non-causal spontaneous fluctuations. Coherent three wave mixing (sum frequency generation and parametric down conversion) involving one and two quantum optical modes, respectively, are compared with their incoherent counterparts: two-photon-induced fluorescence and two-photon-emitted fluorescence.     

Vibration Spectrums of Polar Interface Optical Phonons in GaAs/AlAs Cylindrical Quantum Dots

The dispersions of the top interface optical phonons and the side interface optical phonons in cylindrical quantum dots are solved by using the dielectric continuum model. Our calculation mainly focuses on the frequency dependence of the IO phonon modes on the wave-vector and quantum number in the cylindrical quantum dot system. Results reveal that the frequency of top interface optical phonon sensitively depends on the discrete wave-vector in z direction and the azimuthal quantum number, while that of the side interface optical phonon mode depends on the radial and azimuthal quantum numbers. These features are obviously different from those in quantum well, quantum well wire, and spherical quantum dot systems. The limited frequencies of interface optical modes for the large wave-vector or quantum number approach two certain constant values, and the math and physical reasons for this feature have been explained reasonably.     

光磁共振实验中双量子跃迁及射频场谐波干扰

由于射频场谐波的存在,致使其二次谐波的共振跃迁与双量子跃迁信号重叠。因此观察双量子跃迁,必须首先排除射频场二次谐波共振的影响,本文分析了光磁双共振实验中关于双量子跃迁产生的条件、判断和观测,并分析了多频率共振的原因。     

LATTICE VIBRATION SPECTRA IN ONE-DIMENSIONAL CONDUCTORS

For one-dimensional conductors with half- filled band, the lattice vibration spectra, both acoustic and optical branches, are obtained analytically in the dimerized state. It is shown that, there exist not only a gap in k=π/2 Brillouin zone boundary,but also a gap between the optical and acoustic phonon branches when the electron-lattice coupling cons- taut λ is Larger than λ_c(=0.21). Then,the frequency of the Staggered mode around solitons can be described analytically for any coupling constant λ.     

Polar interface and surface optical vibration spectra in multi-layer wurtzite quantum wires： transfer matrix method

The polar interface optical （IO） and surface optical （SO） phonon modes and the corresponding Froehlich electron phonon-interaction Hamiltonian in a freestanding multi-layer wurtzite cylindrical quantum wire （QWR） are derived and studied by employing the transfer matrix method in the dielectric continuum approximation and Loudon＇s uniaxial crystal model. A numerical calculation of a freestanding wurtzite GaN/AlN QWR is performed. The results reveal that for a relatively large azimuthal quantum number m or wave-number kz in the free z-direction, there exist two branches of IO phonon modes localized at the interface, and only one branch of SO mode localized at the surface in the system. The degenerating behaviours of the IO and SO phonon modes in the wurtzite QWR have also been clearly observed for a small kz or m. The limiting frequency properties of the IO and SO modes for large kz and m have been explained reasonably from the mathematical and physical viewpoints. The calculations of electron-phonon coupling functions show that the high-frequency IO phonon branch and SO mode play a more important role in the electron phonon interaction.     

Stable helical solitons in optical media

We present a review of new results which suggest the existence of fully stable spinning solitons (self-supporting localised objects with an internal vorticity) in optical fibres with self-focusing Kerr (cubic) nonlinearity, and in bulk media featuring a combination of the cubic self-defocusing and quadratic nonlinearities. Their distinctive difference from other optical solitons with an internal vorticity, which were recently studied in various optical media, theoretically and also experimentally, is that all the spinning solitons considered thus far have been found to be unstable against azimuthal perturbations. In the first part of the paper, we consider solitons in a nonlinear optical fibre in a region of parameters where the fibre carries exactly two distinct modes, viz., the fundamental one and the first-order helical mode. From the viewpoint of application to communication systems, this opens the way to doubling the number of channels carried by a fibre. Besides that, these solitons are objects of fundamental interest. To fully examine their stability, it is crucially important to consider collisions between them, and their collisions with fundamental solitons, in (ordinary or hollow) optical fibres. We introduce a system of coupled nonlinear Schrödinger equations for the fundamental and helical modes with nonstandard values of the cross-phase-modulation coupling constants, and show, in analytical and numerical forms, results of collisions between solitons carried by the two modes. In the second part of the paper, we demonstrate that the interaction of the fundamental beam with its second harmonic in bulk media, in the presence of self-defocusing Kerr nonlinearity, gives rise to the first ever example of completely stable spatial ring-shaped solitons with intrinsic vorticity. The stability is demonstrated both by direct simulations and by analysis of linearized equations.     

Quasicontinuum approximation and iterative method for envelope solitons in anharmonic chains

For solitary waves on a monoatomic chain with nearest neighbor interactions the continuum approximation has a limited validity range and exhibits certein mathematical problems. For pulse solitons these problems are overcome by the Quasicontinuum Approach (QCA), and the validity range is considerably extended. We generalize the QCA to oscillatory excitations and derive analytic expressions for bright and dark envelope solitons, limiting ourselves to a polynomial interaction potential with harmonic, cubic and quartic terms. Moreover we describe and apply a numerical iteration procedure in Fourier space in order to take into account discreteness effects in a systematic way. This procedure yields envelope solitons with a width in the order of the lattice constant. In the case of zero velocity these solutions can be compared with intrinsic localized modes derived by other authors. The stability and accuracy of all our solutions are tested by numerical simulations.     

Coupled Band Gap Solitons in One-Dimensional Alternating Heisenberg Ferromagnetic Chains

The dynamics of coupled band gap solitons in one-dimensional Heisenberg ferromagnetic chains with bond alternation is considered analytically. Using the method of multiple scales the nonlinear coupled-mode equations (i.e.Manakov equations) for the upper cutoff mode of acoustic band and the lower cutoff mode of optical band are derived under the quasi-discreteness approximation. Due to the cross-phase modulation the type of soliton excitations may be changed and the vibrating frequencies of these soliton excitations may locate within or outside the gap of magnon frequency bands.``