Schr Dinger Equation Research Articles

Dynamics of cubic and quintic nonlinear Schrdinger equations

We solve one-dimensional(1D) cubic and quintic nonlinear Schrdinger equations by the symplectic method. The dynamical property of the nonlinear Schrdinger equation is studied with using diffenent nonlinear coefficients. The results show that the system presents quasiperiodic solution, chaotic solution, and periodic solution with the cubic nonlinear coefficient increasing, and the breather solution reduced into a fundamental soliton solution under the modulation of the quintic nonlinear coefficient.

Single attosecond pulse generated by model helium atom exposed to the combined field of an intense few-cycle chirped laser pulse and a half cycle pulse

We propose an efficient method to generate an ultrashort attosecond pulse when a model He is exposed to the combination of an intense few-cycle chirped laser pulse and a half cycle pulse. By solving the time-dependent Schrdinger equation numerically, we find that the cut-off energy of the harmonics is extended effectively to Ip+21.6Up. By superimposing some high-order harmonics in different regions for the second plateau, the obtained pulses are all single attosecond ones. Minimum pulse achieves 37 as. Especially, by superimposing the lower order harmonics of the second plateau, one can obtain single attosecond pulse, and also the intensity of the single pulse is three order of magnitude higher than the attosecond pulse obtained near cut-off of harmonics.

Multireference configuration interaction study on spectroscopic parameters and molecular constants of AsN(X1 +) radical

The potential energy curve (PEC) of the AsN(X1 +) radical is investigated by the highly accurate valence internally contracted multireference configuration interaction method in combination with the correlation-consistent basis sets, aug-cc-pV5Z for As and aug-cc-pV6Z for N atom. The PEC is fitted to the Murrell-Sorbie function, which is used to accurately derive the spectroscopic parameters. The parameters De, Re, e, exe, e and Be are obtained to be 4.97 eV, 0.16259 nm, 1061.14, 5.4715, 0.53919, 0.003409 cm-1 respectively; which accord well with the available measurements. With the obtained PEC of AsN(X1 +), a total of 67 vibrational states are predicted when J=0 for the first time by numerically solving the radical Schrdinger equation of nuclear motion. For each vibrational state, the vibrational level, the classical turning points, the inertial rotation and the centrifugal distortion constants are completely reported for the first time.

数值模拟亚纳秒脉冲产生超连续谱的一种改进方法

In this paper,a method of twice sampling based on split-step Fourier method was developed to analyze and simulate the supercontinuum generation in photonic crystal fiber pumped by sub-nanosecond laser pulse.Applying this method to generalized nonlinear Schr(o|¨)dinger equation,much operation time was saved in Supercontinuum simulation,and the simulated spectrum agrees well with the experimental result under the same conditions.Also,the slight dissimilarities between the simulated spectrum and the experimental one were discussed.The simulated supercontinuum with 1.15W power generated in 1.8 m Photonic Crystal Fiber and the evolution of spectrum by our work can give reference for improving further experiment setup.

Applications of spectral renormalization method to the research of nonlocal optical spatial soliton

We use spectral renormalization method to solve the nonlocal nonlinear Schrdinger equation, which gives accurate waveform of nonlocal optical spatial soliton. The relation between critical power and critical beamwidth is acquired in different nonlocal conditions. We discovered that optical spatial soliton exists stably in any nonlocal degree. Comparing analytic solution with numerical solution for different response functions, we find that they are consistent only under strong nonlocal and weak nonlocal conditions. The effective range of analytic solution is also given.

准连续光抽运光子晶体光纤产生超连续谱中的调制不稳定性

A phenomenon experimentally emerging in super-continuum generation with a piece of photonic crystal fiber pumped by quasi-continuum wave is reported.According to the numerical simulation which contains using the gain spectrum theory of modulation instability and solving nonlinear Schrdinger equation,it is proved that this phenomenon is generated by modulation instability.After the results of the simulation and the experiment being contrasted and analyzed,it is found that the simulation result including two mentioned methods is in excellent agreement with the experiment result which the wavelength difference between the two spectrum lobes and the central wavelength are 27.08 nm and 32.72 nm respectively.

Quantum theory of neutron double-slit diffraction

By solving Schrdinger equation exactly, we obtain the neutron wave function in the slit. With the Kirchhoff’s law, we obtain the neutron diffraction function. Finally, we obtain the mathematical relation between the relative diffraction intensity of neutron double-slit diffraction and the diffraction position. The calculation result is in accordance with the experimental data.

Two-dimensional Kummer-Gaussian soliton clusters in strongly nonlocal nonlinear media

We solve the two-dimensional strongly nonlocal nonlinear Schrdinger equation in polar coordinates. An exact analytical solution of self-similar waves, namely Kummer-Gaussian soliton clusters, is obtained. Numerical simulations confirm the validity of the analytical solutions. It is shown that the nonlocal optical spacial solitons have large phase shift.

Nonlinear Schr?dinger equation for internal waves in deep sea

Considering two-layer fluid bounded by the thermocline, under the condition of weak nonlinearity, based on the dynamic equations of two-layer fliud, the nonlinear Schrdinger equation for internal waves in deep sea is obtained by adopting hierarchical method. The coefficients of dispersion and nonlinearity are analysed, the soliton solution of the nonlinear Schrdinger equation is obtained, and the exactitude of the theory is demonstrated by a numerical experiment.

Measurement of entanglement in coupled dots

Using the method developed by Gurvitz of solving Schrdinger equations and the numerical calculation, we investigate the oscillation and the entanglement of the two opposite-spin electrons in coupled quantum dots, and show how to read out the entanglement by quantum point-contact detector. The results show that the two electrons start to entangle due to Coulomb interaction, and then they move together with Coulomb interaction augmenting, similar to the oscillation of an electron in a qibit. In this case, we locate a quantum point contact detector near one of the quantum dots, and the entanglement information can be obtained by changing the current.

两量子位Grover量子算法NMR脉冲序列参量的研究

Based on physical model of two-qubit quantum computer,two kinds of rules were proposed by solving single-body and two-body the time-dependent Schrdinger equation for designing nuclear magnetic resonance pulse sequence parameter of Grover quantum algorithm.Specified parameters were given through two kinds of designing rules and numerical simulations were carried out as specifying parameters.Results from the simulations show that target state is a pure basis state after running specified parameters by solving two-body the time-dependent Schrdinger equation and the expectation value of z-component of target state agrees with the theoretical values with a precision about 10-3.It is confirmed that rules of designing parameter is correct.

Theoretical study of the influence of laser intensity on the population of the NO molecule electronic states

Using the time-dependent wavepacket method and employing the four-state model，the influence of the laser intensity on the population of the NO molecule electronic states are calculated in this paper. The populations of the electronic states of the NO are given by the wavefunctions obtained by solving the Schrdinger equation through the split-operator Fourier transform method. The calculated results show that different pump pulse intensities have different influences on the population of the electronic states of NO. By changing the pulse intensity，the ionization ratio can be controlled，which will benefit the light manipulation of atomic and molecular processes.

Multi-reference configuration interaction of the ground and low-lying excited states of LiC

The potential energy curves (PECs) for the ground electronic state X4Σ-and five low-lying excited electronic states (a2Π, b2Δ, c2Σ-, d2Σ+, A4Π) of LiC have been calculated using the multiconfiguration reference configuration interaction method including Davidson correction (MRCI+Q). And PECs were fitted to analytical Murrell-Sorbie potential function to deduce the spectroscopic parameters of equilibrium bond length Re, rotation coupling constant ωe, anharmonic constant ωeχe, equilibrium rotation constant Be and vibration-rotation coupling constant αe. Those values were also compared with the other results currently available. By solving the radial Schrdinger equation of nuclear motion, the vibration levels, inertial rotation constant and six centrifugal distortion constants (Dν, Hν, Lν, Mν,Nν,and Oν) are reported for the first time.

The pulsating propagation of spatial soliton in strongly nonlocal optical lattice

Based on the nonlocal nonlinear Schrdinger equation, which is the evolution equation of propagation of spatial soliton in the nonlocal media, the pulsating propagation of spatial solitons in one-dimensional strongly nonlocal optical lattice are researched numerically by the split-step Fourier method. The pulsating propagation period of spatial soliton is analyzed for different parameters of propagation, such as the initial energy of the beam, the nonlocality degree, the modulation degree of lattice, the period of the transverse modulation and the asymptotic rate of the longitudinal modulation of linear refractive index. And the inherent physical mechanisms of pulsating propagation of spatial soliton are discussed for the different parameters of lattice structure. Furthermore, the controllable switching behavior of spatial optical soliton has been achieved in the strongly nonlocal optical lattice with longitudinal modulation of linear refractive index.

Frequency, internuclear distance distance-, and angle-resolved imaging of the rotational-vibrational dynamics in D2+

By solving the time-dependent Schrdinger equation in full dimensionality, we simulate the coherent evolution of rotational-vibrational nuclear wave packets in D+− in an external intense linearly polarized infrared laser field and analyze the ro-vibrational dynamics in terms of quantum-beat spectra.

Hidden statistics of Schrödinger equation.

Work was carried out in determination of the mathematical origin of randomness in quantum mechanics and creating a hidden statistics of Schr dinger equation; i.e., to expose the transitional stochastic process as a bridge to the quantum world. The governing equations of hidden statistics would preserve such properties of quantum physics as superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods.

Increasing line-density of high-order harmonic generation spectra with bichromatic fields

By numerically solving time-dependent Schrdinger equation, we obtain high-order harmonic generation （HHG） spectra from the one-dimensional H atom model submitted to linear polarization bichromatic field. It is found that, appropriate bichromatic field could be a source of attosecond pulse generation since it produces a ligher line-density in harmonic generation spectra （HGS）. Based on it, we analyze the mechanism of generating denser HHG spectral lines in detail, and give density-selection numerical experiential formulas for different pulses duration, to achieve further control of the line density of HGS.

The spatial degrees of freedom of MIMO quantum channels

Quantum communication is a process of quantum key distribution （QKD）. Current QKD technology restricts communication to a low bit rate. To improve the QKD bit rate and develop high rate and capacity, we propose a multiple-input-multiple-output quantum key distribution system. However, quantum field itself inevitably involves quantum noise （which is determined by the quantum mechanics ）, which restrains the increase of capacity, and limits space resource utilization, that is, the problem of spatial degrees of freedom arises. The quantumization of the photon field and the electromagnetic wave equation satisfying the Schrdinger equation condition are adopted to investigate the upper bound of the spatial degrees of freedom for MIMO quantum channels, which will provide theoretical support and technical basis for developing robust space time processing algorithm for MIMO quantum communication and designing high performance systems.

Dispersion properties and supercontinuum generation in nanofiber

The dispersion properties of nanofibers was numerically simulated and caculated in details, and different dispersion properties in different diameters and materials were compared. The results show that, there are two zero dispersion wavelengths in nanofibers with silica core. With the increase of fiber diameter, the disperison curve tends to smooth and the zero dispersion wavelength also changes. When the core is silicon, it only have one zero dispersion wavelength. With the increase of diameter, its zero dispersion wavelength moves to the long-wavelength end. The generalized nonlinear Schrdinger equation is adopted to describe the evolution of ultra-short laser pulse propagating in nanofibers, and is solved by using the split-step Fourier method. The influence of dispersion on the generation of supercontinuum and the evolution of pulse profile in different dispersion regions are compared. In the normal dispersion region, the output spectral width is narrow. While in the zero dispersion region and the anomalous dispersion region, the super continuum spectrum can be obtained easily.

The single attosecond pulse generated by atom exposed to two-color combined laser field

By solving the time-dependent Schrdinger equation with split-operator method, we study the high harmonics of one-dimensional helium atom exposed to the two-color laser field composed of IR field and UV field, and analyze the characteristics of the attosecond pulse produced by the high-order harmonics. It is found that the width of the attosencond pulse is shortened by the increasing intensity of IR field in the combined laser field. By adjusting the time delay between two lasers, we can enhance the contribution of one of the electron trajectories and suppress that of the other. Thus we can obtain an isolated sub-100 as pulse.