Dromion Excitations in Self—Defocusing Optical Media

We investigate the nonlinear dynamics of multi-dimensional optical pulses propagating in an isotropic selfdefocusing medium,Using a method of multiple-scales we show that the nonlinear evolution of the pulses is governed by Davey-Stewartson equations.Dromion-like nonlinear localized structures(high-dimensional Optical solitons) excited from a continuous wave badckground and decaying in all spatial directions are predicted through the interaction between a wavepacket superposed by short-wavelength components and a long-wavelength mean field generated by an optical rectification.     

Effects of transverse trapping on the ground state of a cigar-shaped two-component Bose-Einstein condensate

We derive the coupled nonpolynomial nonlinear Schro¨dinger equations for a two-component Bose-Einstein condensate in a quasi-one-dimension geometry and investigate the effects of a tightly transverse trapping on the ground state and the miscibility-immiscibility threshold. We find that the density profile of the matter wavepacket is remarkably dependent on the transverse width and the effective one-dimension nonlinear coupling strengths in miscible and immiscible regimes.     

Characteristics of nonlinear evolution of wavepackets in boundary layers

The nonlinear evolution of a finite-amplitude disturbance in a 3-D supersonic boundary layer over a cone was investigated recently by Liu et al.using direct numerical simulation(DNS).It was found that certain small-scale 3-D disturbances amplified rapidly.These disturbances exhibit the characteristics of second modes,and the most amplified components have a welldefined spanwise wavelength,indicating a clear selectivity of the amplification.In the case of a cone,the three-dimensionality of the base flow and the disturbances themselves may be responsible for the rapid amplification.In order to ascertain which of these two effects are essential,in this study we carried out DNS of the nonlinear evolution of a spanwise localized disturbance(wavepacket) in a flat-plate boundary layer.A similar amplification of small-scale disturbances was observed,suggesting that the direct reason for the rapid amplification is the three-dimensionality of the disturbances rather than the three-dimensional nature of the base flow,even though the latter does alter the spanwise distribution of the disturbance.The rapid growth of 3-D waves may be attributed to the secondary instability mechanism.Further simulations were performed for a wavepacket of first modes in a supersonic boundary layer and of Tollmien-Schlichting(T-S) waves in an incompressible boundary layer.The results show that the amplifying components are in the band centered at zero spanwise wavenumber rather than at a finite spanwise wavenumber.It is therefore concluded that the rapid growth of 3-D disturbances in a band centered at a preferred large spanwise wavenumber is the main characteristic of nonlinear evolution of second mode disturbances in supersonic boundary layers.     

Periodic electron oscillation in coupled two-dimensional lattices

We study the time evolution of electron wavepacket in the coupled two-dimensional(2D) lattices with mirror symmetry, utilizing the tight-binding Hamiltonian framework. We show analytically that the wavepacket of an electron initially located on one atomic layer in the coupled 2D square lattices exhibits a periodic oscillation in both the transverse and longitudinal directions. The frequency of this oscillation is determined by the strength of the interlayer hopping. Additionally, we provide nume...     

General Symmetry Approach to Solve Variable—Coefficient Nonlinear Equations

After considering the variable coefficient of a nonlinear equation as a new dependent variable,some special types of variable-coefficient equation can be solved from the corresponding constant-coefficient equations by using the general classical Lie approach.Taking the nonlinear Schrodinger equation as a concrete example,the method is recommended in detail.     

Transport dynamics of an interacting binary Bose Einstein condensate in an incommensurate optical lattice

We investigate the transport dynamics of an interacting binary Bose-Einstein condensate in an incommensurate optical lattice and predict a novel splitting of a matter wavepacket induced by disorder potential and inter-species interaction. The effect of atomic interaction on the dynamics of the mobile and localized atoms are also studied in detail. We also discuss the behavior of the balanced and inbalanced mixtures in the incommensurate optical lattice.     

Quantum Statistical Properties in Two—Species Bose—Einstein Condensates

We have studied quantum statistical properties in a zero-temperature two-species Bose-Einstein condensate system in the presence of the nonlinear self-interaction of each species,the interspecies nonlinear interaction,and the Jisephson-like tunneling interaction.It is found that the two condensates may periodically exhibit sub-Poissonian distribution.It is revealed that the correlation between the two condensates can be nonclassical,which means that there exists a violation of Cauchy-Schwartz inequality.The nonclassical effect about the correlation between the two condensates can be realized experimentally by properly preparing the total number of atoms in the two condensates.     

Three—Wave Resonant Interactions in Self—Defocusing Optical Media

A three-wave resonant interaction for nonlinear excitations created from a continuous-wave background is shownto be possible in an isotropic optical medium with a self-defocusing cubic nonlinearity. Under suitable phase-matching conditions the nonlinear envelope equations for the resonant interaction are derived by using a methodof multiple-scales. Some explicit three-wave solitary wave and lump solutions are discussed.     

Propagation and collision of compacton-like kinks in Klein—Gordon lattice system

We study the propagation and collision of the compacton-like kinks in the system of an anharmonic lattice with a double well on-site potential by a direct algebraic method and numerical experiments. It is found that the localization of the compacton-like kinks is related to the nonlinear coupling parameter Cnl and the potential barrier height V0 of the double well potential. The velocity of the propagation of the compacton-like kinks is determined by the linear coupling parameter Cl, the nonlinear coupling parameter Cnl and the localization parameter q. Numerical experiments demonstrate that appropriate Cl is not detrimental to a stable propagation of the compacton-like kinks. However, the collision of compacton-like kinks and anti-kinks in the lattice with comparatively small Cl leads to the emergence of a discrete stationary breather and small amplitude nonlinear oscillation background, while moderate Cl results in the emergence of two deformed kinks with radiating oscillations and lower propagation velocities.     

A Simple Method to Obtain Exact Soliton Solutions for a Nonlinear Equation in a Loss Fibre System

We show that the nonlinear equation governing wave propagation in a loss fibre system considered by Nakkerian in J.Phys.A34(2001) 5111 can be brought into the standard nonlinear schroedinger equation by a simple transformation.     

Random Phases and Energy Dispersion

Using 2N 1 successive stationary states centred at nth,we construct a rectangular wavepacket in which the stationary states are superimposed with the equal weight 2N 1.With the requirement of the wavepacket to be a quasi-classical state,the number N is determined by minimizing the uncertainty ΔxΔp,Since the stationary state can only be determined to within an arbitrary multiplicative complex phase factor of unit magnitude,a number of N is obtained as a set of the phases are given.For a harmonic oscillator,when all of the phase factors are essentially the same,we have N≈[6^1/3n^2/3] with [x] signifying the integral part of positive number x,When every phase in the phase factors is given by a random number generated in a closed interval [0,2π] and when n≥10,the probability of appearance of N is roughly 1/2^N when N=1 to 7,and does not exceed 0.01 when N≥8.     

Coalescence and Anti-Coalescence Interference of Two-Photon Wavepacket in a Beam Splitter

We study theoretically the interference of a two-photon wavepacket in a beam splitter.We find that the spectrum symmetry for the two-photon wavepacket dominates the perfect coalescence and anti-coalescence interference.The coalescence interference is unrelated to photon entanglement.Only the anti-coalescence interference has evidence of photon entanglement.We prove that the two-photon wavepacket with an anti-symmetric spectrum is transparent to pass the 50/50 beam splitter,showing perfect anti-coalescence interference.     

Spatiotemporal optical vortex wavepackets with phase singularities embedded in multiple domains

Spatiotemporal optical vortex(STOV) wavepacket carrying transverse photonic orbital angular momentum(OAM) has been extensively studied in the past few years. In this Letter, we propose and study a novel STOV wavepacket with multiple phase singularities embedded in different space–time domains using analytical and numerical approaches. By tuning different parameters used for designing the wavepacket, it is possible to engineer both the magnitude and orientation of the photonic OAM in space–time. ...     

Time-Dependent Quantum Dynamics of T＋CH4 → CH3＋HT Reaction

Reaction probability, cross section and rate constant are studied for polyatomic reaction T CH4 → CH3 HT using the semirigid vibrating rotor target (SVRT) model. The numerical calculation for the reaction system is carried out using the time-dependent wavepacket method, and the wavepacket is propagated by the splitoperator method. The calculation exhibits a variety of features that can be used for comparison with future experimental investigations. The reaction probability as a function of the translational energy shows slight oscillatory structures, similar to those observed in H abstraction reactions H H2 and H CH4. The comparisons with the H CH4 reaction are described.     

Propagation dynamics of dipole breathing wave in lossy nonlocal nonlinear media

In the framework of nonlinear wave optics,we report the evolution process of a dipole breathing wave in lossy nonlocal nonlinear media based on the nonlocal nonlinear Schr?dinger equation.The analytical expression of the dipole breathing wave in such a nonlinear system is obtained by using the variational method.Taking advantage of the analytical expression,we analyze the influences of various physical parameters on the breathing wave propagation,including the propagation loss and the input power on the beam width,the beam intensity,and the wavefront curvature.Also,the corresponding analytical solutions are obtained.The validity of the analysis results is verified by numerical simulation.This study provides some new insights for investigating beam propagation in lossy nonlinear media.     

An extension of the modified Sawada—Kotera equation and conservation laws

Based on the modified Sawada-Kotera equation, we introduce a 3 × 3 matrix spectral problem with two potentials and derive a hierarchy of new nonlinear evolution equations. The second member in the hierarchy is a generalization of the modified Sawada-Kotera equation, by which a Lax pair of the modified Sawada-Kotera equation is obtained. With the help of the Miura transformation, explicit solutions of the Sawada-Kotera equation, the Kaup-Kupershmidt equation, and the modified Sawada-Kotera equation are given. Moreover, infinite sequences of conserved quantities of the first two nonlinear evolution equations in the hierarchy and the modified Sawada-Kotera equation are constructed with the aid of their Lax pairs.     

Nonlinear optical behaviors in a silver nanoparticle array at different wavelengths

The optical nonlinearities of an Ag nanoparticle array are investigated by performing Z-scan measurements at the selected wavelengths (400, 600, 650, and 800 nm). The nonlinear refraction index in the resonant region (around 400 nm) exhibits a significant enhancement by two orders compared with that in the off-resonant region (around 800 nm)), and exhibits an sign alternation of the resonant nonlinear absorption, which results in a negligible nonlinear absorption at a certain excitation intensity. Moreover, a low degree of nonlinear absorption was measured at the edges of the resonant region (600 and 650 nm), which is attributed to the competition of the saturated absorption and the two-photon absorption processes.     

Coherent Transport Through a Quantum Dot Embedded in a Double—Slit—Like Aharonov—Bohm Ring

Coherent transport through a quantum dot embedded in one arm of a double-slit-like Aharononv-Bohm(AB) ring is studied using the green‘s function approach.We obtain experimental obsevations such as continous phase shift along a single resonance peak and sharp inter-resonance phase drop.The AB oscillations of the differential conductance of the whole device are calculated by using the nonequilibrium Keldysh formalism.It is shown that the oscillating conductance has a continuous bias-voltage-dependent phase shift and is asymmetric in both linear and nonlinear response regimes.     

Cyclic State Orientation of Polar Molecules Produced by a Train of Half-Cycle Pulse Clusters of a Long Repetition Period

Using a variational method, we derive the optimal population distribution of angular momentum eigenstates for any given population range in a rotational wavepacket within the field-free cyclic state orientation framework. Correspondingly, we devise a train of half-cycle pulse clusters to purposively make the structure of the computed wavepacket approach the optimal population distribution, so that we can now utilize much more powerful means to realize an ideal orientation goal.     

Ultraslow optical solitons via electromagnetically induced transparency: a density-matrix approach

We study the ultraslow optical solitons in a resonant three-level atomic system via electromagnetically induced transparency under a density-matrix (DM) approach. The results of linear and nonlinear optical properties are compared with those obtained by using an amplitude variable (AV) approach. It is found that the results for both approaches are the same in the linear regime if the corresponding relations between the population-coherence decay rates in the DM approach and the energy-level decay rates in the AV approach are appropriately imposed. However, in the nonlinear regime there is a small difference for the self-phase modulation coefficient of the nonlinear Schr\"{o}dinger equation that governs the time evolution of probe pulse envelope. All analytical predicts are checked by numerical simulations.