A theoretical scheme for generation of nonlinear coherent states in a micromaser under intensity-dependent Jaynes-Cummings model

In this paper we propose a theoretical scheme to show the possibility of generating various families of nonlinear (f-deformed) coherent states of the radiation field in a micromaser. We show that these states can be provided in a lossless micromaser cavity under the weak Jaynes-Cummings interaction with intensity–dependent coupling of large number of individually injected two-level atoms in a coherent superposition of the upper and lower states. In particular, we show that the so-called nonlinear squeezed vacuum and nonlinear squeezed first excited states, as well as the even and odd nonlinear coherent states can be generated in a two-photon micromaser.     

Explicit Multi-Symplectic Splitting Methods for the Nonlinear Dirac Equation

In this paper, we propose two new explicit multi-symplectic splitting methods for the nonlinear Dirac (NLD) equation. Based on its multi-symplectic formulation, the NLD equation is split into one linear multi-symplectic system and one nonlinear infinite Hamiltonian system. Then multi-symplectic Fourier pseudospectral method and multi-symplectic Preissmann scheme are employed to discretize the linear subproblem, respectively. And the nonlinear subsystem is solved by a symplectic scheme. Finally, a composition method is applied to obtain the final schemes for the NLD equation. We find that the two proposed schemes preserve the total symplecticity and can be solved explicitly. Numerical experiments are presented to show the effectiveness of the proposed methods.     

Carrier-less amplitude and phase modulated visible light communication system based on a constellation-shaping scheme

In this Letter,we propose a novel constellation-shaping carrier-less amplitude and phase(CAP) modulation scheme to alleviate the systematic nonlinearity in visible light communication(VLC) systems.A simple geometric transformation shaping method is employed to convert the normal square lattice constellation into multiple circular constellations.The feasibility and performance are investigated and experimentally demonstrated by a 1.25 Gb/s CAP-modulated VLC system.The results indicate that the circular constellation has better resistance to systematic nonlinearity compared with a rectangular constellation.The dynamic range of input signal peak-to-peak values promotes 20% at a low bias voltage nonlinear area and 50% at a high bias voltage nonlinear area.To the best of our knowledge,this is the first time constellation-shaping CAP has ever been reported in indoor high data rate VLC systems.     

Joint Remote Preparation of a General Three-Qubit State via Non-maximally GHZ States

In this paper, we use three non-maximally GHZ states as the quantum channel and then propose two schemes to realize joint remotely preparing the general three-qubit state. For the first scheme, we show that the joint remotely state preparation (JRSP) can be successfully realized with a certain probability by performing information splitting, introducing an ancilla and proper measurement. Moreover, for the second scheme, we establish a new method to split information which needn’t to introduce the ancilla on the receiver’s side and can achieve better security.     

Detecting nonlinearity of action surface EMG signal

The action surface EMG (ASEMG) signal contains the electrical properties of limb muscle contraction that undergo many complex transitions in limb different movement states; however, because of the small data nature of this kind signal, it is not clear whether its essence is stochastic or deterministic nonlinear (even chaotic). In this Letter, we show for the first time that ASEMG has deterministic nonlinear character by using the surrogate data method. Furthermore, we study the nonlinear dynamic features of ASEMG by computing its correlation dimension and applying correlation dimension as test statistics. These results indicate that ASEMG is a high-dimension nonlinear signal (even chaotic). In addition, this Letter improves the surrogate data method based on Fourier transform (FT) algorithm to avoid limitations of the previous FT algorithm.     

All-optical method for maintaining a fixed intensity level of a light signal in optical computation

In data and image processing the role of optics is already well established. Due to inherent parallelism the optical systems run faster than its electronic counterparts. Optical nonlinear material can be used as a successful optical switch. The primary requirement for proper functioning of such nonlinear material based logic devices is a fixed intensity level of the optical signal against a specific logic state. In this communication, the authors propose a new concept to obtain a fixed intensity level of optical signal against a specific logic state for data processing. The scheme may extend a tremendous application not only to the area of all-optical computation, but also to optical communication process.     

A dispersion-relation-preserving algorithm for a nonlinear shallow-water wave equation

The paper presents an iterative algorithm for studying a nonlinear shallow-water wave equation. The equation is written as an evolution equation, involving only first-order spatial derivatives, coupled with the Helmholtz equation. We propose a two-step iterative method that first solves the evolution equation by the implicit midpoint rule and then solves the Helmholtz equation using a three-point sixth-order compact scheme. The first-order derivative terms in the first step are approximated by a sixth-order dispersion-relation-preserving scheme that preserves the physically inherent dispersive nature. The compact Helmholtz solver, on the other hand, allows us to use relatively few nodal points in a stencil, while achieving a higher-order accuracy. The midpoint rule is a symplectic time integrator for Hamiltonian systems, which may be a preferable method to solve the spatially discretized evolution equation. To give an assessment of the dispersion-preserving scheme, we provide a detailed analysis of the dispersive and dissipative errors of this algorithm. Via a variety of examples, we illustrate the efficiency and accuracy of the proposed scheme by examining the errors in different norms and providing the rates of convergence of the method. In addition, we provide several examples to demonstrate that the conserved quantities of the equation are well preserved by the implicit midpoint time integrator. Finally, we compare the accuracy, elapsed computing time, and spatial and temporal rates of convergence among the proposed method, a complete integrable particle method, and the local discontinuous Galerkin method.     

Nonlinear coherent states of the Fokas-Lagerstrom potential

In this paper, we introduce an algebraic approach to construct Fokas-Lagerstrom coherent states. To do so, we define deformed creation and annihilation operators associated to this system and investigate their algebra. We show that these operators satisfy the f-deformed Weyl-Heisenberg algebra. Then, we propose a theoretical scheme to generate the aforementioned coherent states. The present contribution shows that the Fokas-Lagerstrom nonlinear coherent states possess some non-classical features.     

Generation of a four-particle entangled state via cross-Kerr nonlinearity

We propose a scheme for generating a genuine four-particle polarisation entangled state ︱χ00 that has many interesting entanglement properties and potential applications in quantum information processing. In our scheme, we use the weak cross-Kerr nonlinear interaction between field-modes and the non-demolition measurement method based on highly efficient homodyne detection, which is feasible under the current experiment conditions.     

Chaos Synchronization of Nonlinear Bloch Equations Based on Input-to-State Stable Control

In this paper, we propose a new input-to-state stable （ISS） synchronization method for chaotic behavior in nonlinear Bloch equations with external disturbance. Based on Lyapunov theory and linear matrix inequality （LMI） approach, for the first time, the ISS synchronization controller is presented to not only guarantee the asymptotic synchronization but also achieve the bounded synchronization error for any bounded disturbance. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. Simulation study is presented to demonstrate the effectiveness of the proposed synchronization scheme.     

Real-time surface profile measurement using a feedback type of sinusoidal phase modulating interferometer

In this paper, we propose a sinusoidal phase modulating (SPM) interferometer that is insensitive to external disturbances, and its measuring principle is analyzed theoretically. In the SPM interferometer, the interference signal is detected by a high-speed image sensor based on a low-speed CCD and a signal processing circuit is used to obtain the phase of each point on the surface. Therefore, the surface profile can be measured real-time. The experiments measuring the surface profile of a wedge-shaped optical flat show that the measurement time of the SPM interferometer is less than 10 ms, the repetitive measurement accuracy is 4.2 nm. The results show that the impacts of nonlinear distortion of the piezoelectric transducer (PZT) and part external disturbance are removed.     

Enhanced phase sensitivity with a nonconventional interferometer and nonlinear phase shifter

We propose a theoretical scheme of an enhanced phase sensitivity by introducing a nonlinear phase shifter to the nonconventional interferometer consisting of a balanced beam splitter (BBS) and an optical parameter amplifier (OPA), a modified nonlinear interferometer (MNI). Then we use coherent state and even coherent state as inputs and homodyne detection at one output port of the MNI for phase sensitivity, both without and with photon losses. We find that the nonlinear phase shifter can not only improve phase sensitivity, but also significantly resist the decoherence from photon losses. In comparison to both the BBS+OPA scheme with linear phase shifter and the traditional Mach–Zehnder interferometer with nonlinear one, the phase sensitivity of the MNI scheme shows the best performance. It is interesting that the nonlinear phase shifter can stimulate potential of the OPA, although there is no improvement in signal-to-noise ratio beyond standard quantum limit for the BBS+OPA scheme with a linear phase shifter.     

Directly generating vortex beams in the second harmonic by a spirally structured fundamental wave

Based on nonlinear wave mixing, we experimentally propose a scheme for directly generating optical orbital angular momentum(OAM) by a spirally structured fundamental wave interacting with a nonlinear medium, in which the nonlinear susceptibilities are homogenous. In the experiment, the second-harmonic generation of a fundamental wave carrying positive(negative) integers and fractional OAM states was investigated. This study presents a convenient approach for dynamic control of OAM of vortex beams, which may feature their applications in optical manipulation and optical communication.     

Generation of indistinguishable and pure heralded single photons with tunable bandwidth

We describe a new scheme to fully control the joint spectrum of paired photons generated in spontaneous parametric downconversion. We show the capability of this method to generate frequency-uncorrelated photon pairs that are pure and indistinguishable and whose bandwidth can be readily tuned. Importantly, the scheme we propose can be implemented in any nonlinear crystal and frequency band of interest.     

A new surface-tension formulation for multi-phase SPH using a reproducing divergence approximation

In this paper, we propose a new surface-tension formulation for multi-phase smoothed particle hydrodynamics (SPH). To obtain a stable and accurate scheme for surface curvature, a new reproducing divergence approximation without the need for a matrix inversion is derived. Furthermore, we introduce a density-weighted color-gradient formulation to reflect the reality of an asymmetrically distributed surface-tension force. We validate our method with analytic solutions and demonstrate convergence for different cases. Furthermore, we show that our formulation can handle phase interfaces with density and viscosity ratios of up to 1000 and 100, respectively. Finally, complex three-dimensional simulations including breakup of an interface demonstrate the capabilities of our method.     

基于搜索平均法的气象观测数据的非线性去噪

介绍了一种新型基于相空间重构和返回图法的非线性降噪方法——搜索平均法，首先将该方法应用于被高斯白噪声所污染的Henon映射时间序列，说明根据降噪理论所编写的计算程序的正确性；然后应用于中国气象局公布全国435站1960—2000年的逐日气温观测时间序列，并利用非线性预报方法衡量降噪的效果，验证了该方法的有效性.     

Excitation of surface polaritons by nondegenerate four-wave mixing of evanescent waves

We propose a method for exciting a surface polariton wave by nonlinear mixing of three evanescent waves. The nonlinear polarization and phase matching conditions are analyzed for diatomic cubic crystals and a numerical example is given for GaP showing that this scheme is possible. Furthermore, by consideration of the energy balance in the crystal, the gain coefficient for the surface wave and the intensity of the wave coupled to the vacuum are also calculated.     

Controlled switching of surface waves in 1D photonic crystals by a thin nonlinear cap layer

In this paper, we investigate the electromagnetic surface waves localized at the interface of the homogeneous dielectric medium and a semi-infinite one-dimensional photonic crystal (1D PC), theoretically. The semi-infinite 1D PC is made of alternative layers of left-handed (LH) and right-handed (RH) materials in the presence of a thin nonlinear cap layer. We consider magnetic permeability and electric permittivity of LH layers being dispersive and non-dispersive. We used an analytical direct matching procedure within the Kronig-Penny model to analyze the dispersion behavior of surface waves with controllable localization. It is shown that the thin nonlinear cap layer acts as a tool to change the backward surface waves to forward ones and vice versa and it plays an important role on the localization of them. Also we show that when the LH layers are chosen dispersive, negative dispersion of surface waves are obtained in a wide range of radiation angle and frequency, and we propose an approach to calculate the applied electric field intensity that leads to switching of surface waves from backward to forward and creating a surface mode with maximum localization.     

Cancer detection on a cell-by-cell basis using a fractal dimension analysis

We show that the application of imaging and pattern recognition techniques developed for basic heavy ion research has useful applications in medical imaging. In particular, we utilize the fractal dimension of the perimeter surface of cell sections as a new observable to characterize cells of different types. We propose that it is possible to distinguish cancerous from healthy cells with the aid of this new approach. As a first application we show in an exploratory study that it is possible to perform this distinction between patients with hairy-cell lymphocytic leukemia and those with normal blood lymphocytes.     

Monoslope and multislope MUSCL methods for unstructured meshes

We present new MUSCL techniques associated with cell-centered finite volume method on triangular meshes. The first reconstruction consists in calculating one vectorial slope per control volume by a minimization procedure with respect to a prescribed stability condition. The second technique we propose is based on the computation of three scalar slopes per triangle (one per edge) still respecting some stability condition. The resulting algorithm provides a very simple scheme which is extensible to higher dimensional problems. Numerical approximations have been performed to obtain the convergence order for the advection scalar problem whereas we treat a nonlinear vectorial example, namely the Euler system, to show the capacity of the new MUSCL technique to deal with more complex situations.