Modern Physics Letters B

We investigate the optical properties of Gaussian beams diffracted by a variable π-phase plate clinging tightly to the lens with long focal depth and its dependence on the size of the π-phase plate and the preset long focal depth of the lens. The numerical results show that the π-phase plate with appropriate size plus the multifunctional lens illuminated by Gaussian beam can produce bi-focus along the propagation direction and a center hollow light, and the distance between two focal planes along the longitudinal direction and the transverse and longitudinal spot size of the hollow beam will vary when changing the size of the π-phase plate or the preset long focal depth. This investigation indicates that the distance between the focal planes and the spot sizes of the hollow light can be controlled by the appropriately chosen size of the π-phase plate and the preset long focal depth of the lens. Furthermore, we compare the optical characteristics produced by three existing phase functions of the lens with long focal depth. It is expected that this investigation will provide useful information in various optical tweezers for operating and controlling.

The Baonza and mGLJ equations of state (EOS) modified previously to consider the thermal effect are applied to study the thermodynamic properties of Zirconium (Zr). It is proposed that the zero-point vibration term should be deleted in a thermal EOS, and the parameters cannot be directly taken as experimental data at a reference temperature, and , but their values at absolute zero temperature, and . Based on the Einstein model, an approach is proposed to solve and from and . For the hcp (α phase), bcc (β phase) and hexagonal structure (ω phase) of Zr, the molar volume (V), isothermal bulk modulus (B) and thermal expansion coefficient (α) was calculated as a function of pressure and temperature. The predictive capabilities of the complete EOS are discussed and compared with experimental data.

In this paper, the generalized projective synchronization of a class of delayed neural networks is investigated. Based on the Lyapunov stability theorem, a kind of controller is designed. The generalized projective synchronization of delayed neural networks can be achieved by using this kind of controller. Theoretical analysis and numerical simulations are provided to verify the feasibility and effectiveness of the proposed scheme.

A novel dmit^2- complex: [(C₂H₅)₄N][Co(dmit)²], abbreviated as EtCo, was synthesized and its third-order optical nonlinearities were characterized by Z-scan technique at the wavelength of 1064 nm with laser duration of 40 ps. Z-scan curves revealed a negative nonlinear refraction at 1064 nm and a positive absorption was observed. The nonlinear refraction coefficient n₂, the nonlinear absorption coefficient β and the molecular second hyperpolarizability γ have been determined to be as large as 9.51×10^-19m²/W, 2.19×10^-12 m/W and 5.41×10^-31 esu respectively, suggesting that this material has potential applications in optical limiting.

Teleportation of quantum gates using partially entangled states is considered. Different from the known probability schemes, we propose and study a method for teleporting a prototypical single-qubit rotation on a remote receiver with unit fidelity and unit probability by using two partially entangled pairs. The method is applicable to any two partially entangled pairs satisfying the condition that their smaller Schmidt coefficients γ and η are (2γ+2η-2γη-1)≥0. In our scheme, the sender's local generalized measurement described by a positive operator-valued measurement (POVM) lies at the heart. We construct the required POVM. The fact that the controlled teleportation of single-qubit rotation could be realized exactly using two partially entangled pairs is also notable. A sender could teleport a rotation on a remote receiver, an arbitrary one of the two receivers, via the control of the other in a network.

Pressure profiles P(R) for non-interacting bosons in an isotropic trap have been calculated exactly by applying the grand canonical method of quantum statistics to particles in a subsphere of the system. The results are compared with those of local Fermi–Thomas (semi-classical) theory both for non-interacting bosons as well as for bosons having weakly repulsive interactions between them. The essential conclusions are (i) that in the non-degenerate regions, both below as well as above the critical temperature, the pressure profiles remain essentially unaffected by weak interactions, and (ii) that near the center of the trap, the exact quantum mechanical profiles are appreciably lower than the semi-classical profiles.

The amplitude squeezing properties of the electromagnetic field is investigated in the fundamental, Stokes (probe) and signal mode in six-wave mixing process under short-time approximation based on a fully quantum mechanical approach. The interaction is looked upon as a process involving absorption of two pump photons and emission of three probe photons and one signal photon at different frequencies. The coupled Heisenberg quantum mechanical equations of motion involving real and imaginary parts of the quadrature operators are established and solved under short-time scale. The occurrence of amplitude squeezing effects in both the quadrature of the radiation field in the fundamental mode as well as in the Stokes (probe) mode is investigated using the required conditions of squeezing in each of the cases. It is also shown that the squeezing in the signal mode is found to be dependent on amplitude-squared squeezing of the initial pump field. This gives a method of converting higher-order (amplitude-squared) squeezing into normal squeezing.