By using the improved CK’s method, the symmetry group theorem of (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada equation is derived. Some new exact solutions of (2+1)-dimensional CDGKS equation are obtained by applying the theorem and given solutions, which expands the scope of solutions of CDGKS equation. Infinite conservation laws of (2+1)-dimensional CDGKS equation are also found by the symmetries and adjoint equation.

Various kinds of methods of entanglement detection and definitions of entanglement measurement in quantum systems were reviewed. For entanglement of two or more particles, some separability criterions were summarized. Their relationships with positive map and the relationships between themselves were also analyzed. Particularly, concentrations on entanglement witness are paid which is a special criterion involving its definition and construction methods. Further, its applications are also investigated from the viewpoint of experiment. Based on axiomatic hypothesis of entanglement measurement, the theoretical definitions of two-particle and multipartite entanglement, and their estimations in experiment were discussed. At last, various nonlinear separability criterions were analyzed.

A new method was proposed to prepare excited coherent states and two-order excited coherent states, which is based on the interaction of atom inside high- cavity with a traveling wave light field. Compared with other presented methods, this method has some merits that the perturbation theory is not used and one step preparation is taken except for the final measurement. However, the success probability for this method is only 50%.

A scheme of generating the Bell-type and cluster-type entangled coherent states (ECSs) via a single two-level atom and cavity modes initially prepared in coherent states is proposed. Discussions on the two ECSs are presented. When the atom interacts separately with two Ramsey zones and two cavity modes, the generation of Bell-type ECSs in separate cavities is realized after an atomic measurement. By adding the Ramsey zones and cavity modes, the cluster-type ECSs can be generated. The interaction time between the atom and cavity modes are all , where is the effective atom-cavity coupling constant. At last the experimental feasibility of such proposal is discussed.

Inspired by the idea of Wang and Yan’s, i.e., a two-step exact remote state preparation (RSP) of an arbitrary qubit, the remote preparation of arbitrary two-qubit state was studied. In the scheme, two non-maximally entangled GHZ states act as quantum channels. The sender Alice divides the full information encoded in known state into two parts, one purely real coefficient and the other purely real phase factor. After twice projective measurements and the transmission of 4-bit classical information by Alice, the remote receiver Bob can obtain the desired state with the success probability which is higher than that in Liu’s protocol and it is also the advantage of our scheme, because only two-qubit state in real Hilbert space or equatorial-like state can reach this success probability value in Liu’s protocol.

Three experimentally feasible schemes are proposed for generating multipartite entangled states of cold trapped ions. In the first scheme, a GHZ state can be simply synthesized in a single step. The second scheme is to prepare fully symmetric W states with two steps. The third scheme describes the sequential generation of linear cluster states. In addition, a method to create a larger cluster state was also presented by fuzing the end qubits of two smaller cluster states in order to decrease the distortion caused by decoherence, which can speed up the generation of large cluster states. The above schemes involve the collective interaction between multiple ions with the vibrational ground state and a large detuned laser. Compared with previous schemes, the above schemes have four advantages. Firstly, they do not require the vibrational mode of ions as memory. Secondly, they do not need to address the ions individually. Thirdly, they are free from the effects of phase fluctuation of laser field. Finally, they need less operations.

A scheme for implementing three-qubit quantum controlled phase gate is proposed in the trap-ion system. It only requires the resonant interaction between trapped ions and lasers. Compared to the scheme in other papers, the steps needed are much less. In addition, the scheme doesn’t need any type of measurement.

The effects of optical field coherence parameter, modular photon number, Kerr medium coefficient and detuning on the entanglement evolution of cascade three-level atom in Kerr medium are studied based on quantum theory and numerical calculation. The results show that the entanglement between atoms is enhanced in stronger optical field and the entanglement become steady by increasing the modular photon number. Kerr effect is remarkable in more photon number. With invariable Kerr medium, the increase of detuning will strengthen the entanglement strength, but this effect primarily incarnates on initial time of interacting.

By means of the quantum theory and negative eigenvalues of the partial transposition, properties of entanglement evolution in system of two two-level atoms coupled to a light field in the Fock state are investigated in the presence of phase decoherence in the multiphoton Tavis-Cumming Model. The influences of the phase decoherence coefficient, dipole-dipole coupling intensity and number of transitional photons on properties of entanglement evolution between two atoms were discussed. The results show that the phase decoherence doesn’t destroy coherence completely but attenuates oscillated amplitude of the entanglement degree between two entangled atoms. With increasing of the dipole-dipole coupling intensity and number of transitional photons, the two entangled atoms approach the entanglement state in which there is a stable entanglement degree finally. The better coherences between two atoms are, the larger value of entanglement degree between two entangled atoms can be obtained, and state in the two entangled atoms are more stable.

Quantum discord(QD) can be used to characterize quantum correlation of a quantum system. Based on geometric measurement of QD(GMQD), quantum correlation of the single-parameter X- state was calculated, and the results for the case were also given under three different quantum channels. For the amplitude-damping channel, by comparing concurrence and GMQD of the X-state mentioned above using graphical method, it’s concluded that GMQD exhibits more robust than concurrence when the quantum system is exposed to environment.

The time evolution of atom’s occupation in a double Jaynes-Cummings model, where two atoms are in mixed state, was investigated by full quantum theory and numerical method, and the influences of atomic initial state and mean photon number in cavity on atom’s occupancy are discussed. The results show when the two cavities have the same photon number, evolution of atom’s occupation is only related to the purity of atomic initial state and field intensity, but not influenced by initial entanglement. If the mean photon number in cavities is not equal, the evolution of atom’s occupation is not only related to the purity and field intensity, but also strongly influenced by the initial entanglement.

In terms of photoelastic effect of medium, the band characteristics of two-dimensional (2D) photonic crystals were analyzed by finite element method. The photoelastic effect of the medium composing 2D photonic crystals causes change of its refractive index when imposed by stress, the band structure of 2D photonic crystals varies accordingly. The effect of stress on the structural characteristics of band gap in 2D Si/SiO photonic crystals was analyzed in detail. And for each band gap, the variation of start wavelength, cut-off wavelength and bandwidth is proportional to stress.

The interaction between two neighboring third-order solitons was numerically studied under quintic nonlinear effect. The results show that the positive quintic nonlinear effect can lead to the shape of third-order soliton pair further worsening, in-phase and out-phase third-order soliton pair are both split under negative quintic nonlinear quickly. If the third-order soliton pair has the same phase, the two split optical pulses with lower peak value lie inside. It is found that the third-solitons attract each other and collide into one optical pulse. If the third-order soliton pair has the opposite phase, the two split optical pulses with lower peak value lie outside and keep the state of repulsion. When the third-soliton pair has opposite phase, the bigger the absolute value of negative quintic nonlinear parameter is, the more the number of solitons split from third-order soliton pair are. The results also show that the interactions between two neighboring third-order solitons may be well suppressed under appropriate parameters of the negative quintic nonlinearity.

Using a standard split-step Fourier method, the coupled nonlinear Schrodinger equations were numerically solved. A theoretical investigation on the nonlinear propagation of two optical pulses in a photonic crystal fiber was presented. The role of pulse walk-off and intra-pulse stimulated Raman scattering on the propagation and compression of the signal pulse was highlighted. It was found that the signal pulse can be compressed through the cooperation by group velocity dispersion, self-phase modulation and cross-phase modulation, when the pump pulse with a wavelength of 800 nm is input in the anomalous dispersion region while the signal pulse with a wavelength of 740 nm is input in the normal dispersion region. Pulse walk-off not only leads to the degradation of the compression ratio and compressed peak power of the signal pulse, but also leads to a longer fiber length at which the width of the compressed signal pulse is minimum, and leads to the non-symmetry of the compressed signal pulse. It was also found that the quality factor of the signal pulse can be improved in the presence of intra-pulse stimulated Raman scattering.

Exciton effects on the third-harmonic generation in GaAs/AlGaAs infinite and finite square quantum wells are calculated within the framework of the fractional-dimensional space approach. The wave functions and bound energies are obtained as functions of spatial dimensionality and the dimension is a function of the well width. For an infinite confining potential the dimension (D) has a transition from the 3D limit to 2D limit when the well width decreases. However, in a finite well, when the well width decreases below a given value, the dimension increases. The analytical expression of the third-harmonic generation is described using the compact density method and the iterative procedure. The numerical results show that the third-harmonic generation coefficient with considering exciton effects is 40% greater than the one without considering exciton effects and it is very sensitively dependent on the exciton confinement. In addition, the smaller the relaxation constant is, the larger the third-harmonic generation will be.

The properties of bound magnetopolaron, which is weakly coupled to LO-phonon in an asymmetric quantum dot (QD) were studied by using Tokuda modified linear combination operator and unitary transformation methods. The expression of ground-state energy as functions of the transverse and longitudinal confinement lengths and magnetic field was derived. After a simple numerical calculation, it’s found that the ground-state energy of bound magnetopolaron splits into two branches after taking the spin influence into account. The ground-state energy and spin-up(down) splitting energy decrease with increasing the transverse and longitudinal confinement lengths, and they are increasing functions of magnetic field.

The influence of Coulomb field on the properties of the excited state of weak-coupling polaron in an asymmetric quantum dot was studied by the linear combination operator and unitary transformation method. Relations of vibrational frequency, the first excited state energy of weak-coupling polaron in an asymmetric quantum dot with effective confinement length of quantum dot, Coulomb bound potential of weak-coupling polaron in an asymmetric quantum dot are obtained. It is shown by evaluating numerically that the vibrational frequency, the first internal excited state energy increase rapidly with the effective confinement length decreasing when the Coulomb bound potential is determined, and the vibrational frequency increases with the Coulomb bound potential increasing, the first internal excited state energy has minimal value with the Coulomb bound potential increasing when effective confinement length is determined.

In practice, the measurement precision of fiber Bragg grating sensor is limited by noise, cost and other factors. In order to achieve low-cost and high-precision fiber Bragg grating sensor system, a method is proposed which uses adaptive threshold wavelet denoising and B-spline fitting algorithm on the fiber Bragg grating reflection spectrum. Two results are obtained by experiment and simulation. One is that adaptive threshold wavelet denoising can effectively improve SNR of the system.The other is that the error of the wavelength testing is 0.01 nm before fitting and 0.0017 nm after fitting under the same sampling precision and error is lowed about an order of magnitude. Experimental results prove that the method can effectively reduce reading errors caused by noise, and improve the resolution for measurement of fiber Bragg grating wavelength shift in order to achieve high-precision measurement of temperature, strain and other external parameters.

The propagation properties of TE mode in three layer slab waveguides with left-hand materials as substrate and single-negative materials as cover layer were investigated, providing theoretical support for the design of waveguide device. The dependence of normalized effective waveguide thickness on normalized frequency for the modes of three layer slabs was worked out. The propagation properties of TE mode in three slab waveguides were analyzed. The results show that the change rate of the normalized effective refractive index with normalized effective frequency is decreased with increasing the ratio of permeability of guided wave layer to substrate or superstratum. As the asymmetric value approaches to zero, varies with monotonically. While the asymmetric value is big enough, there is two-value phenomenon for TE, TE, TE, TE and TE modes near cutoff frequency. When the asymmetric value increases, the curve-shifts from left to right. will be negative for TE mode.

A novel 1.31/1.55 μm wavelength-division demultiplexer based on selectively liquid-filled three-core photonic crystal fibers (PCFs) is proposed. It consists of a normal central silica core and other two cores selectively filled with different refractive indices of liquid materials. According to coupling mode theory, there exists wavelength-selective coupling of evanescent fields between nonidentical single-mode fibers. Two optial fibers with different response mavelength are set up respectively when two cores filled with different materials couple with the central core at two particular wavelengths. There are two corresponding wavelengths in three-core PCFs and then two beams of light with different wavelengths can be separated from each other if appropriate parameters are chosen. Full-vectorial finite element method (FEM) is employed to analyze the properties of PCFs and simulate its coupling wavelength and length with different filled refractive indices. Numerical results by beam propagation method (BPM) demonstrate that it is possible to obtain a 4.88 mm-long 1.31/1.55 μm wavelength-division demultiplexer.