Approximate time-optimal control of quantum ensembles based on sampling and learning

For a general quantum ensemble with Hamiltonian fluctuations, this paper proposes a sampling-based two-stage approximate time-optimal control algorithm with momentum terms and achieves a high-fidelity state transition of all member systems to a common target state within an approximate minimum time. The fidelity and the control time are respectively optimized in the two stages. In particular, the introduction of momentum terms greatly improves the convergence rate of the algorithm. Simulation experiments on a two-level quantum ensemble verify the effectiveness of the proposed algorithm.     

Investigation of the local structure and the effects of the orbit reduction factor on the EPR g-factors for octahedral (CrO6) cluster in TiO2:Cr and MgO:Cr systems

A theoretical method for studying the inter-relation between electronic and molecular structure has been proposed based on the complete energy matrices for a d³ configuration ion in a tetragonal ligand-field. By means of this method, the local structure for Cr³⁺ ion doped in oxides TiO₂ (anatase) and MgO has been determined. The calculated results indicate that the local structure of the (CrO₆)⁹⁻ cluster in TiO₂:Cr³⁺ and MgO:Cr³⁺ systems exists as a compressed distortion relative to the regular octahedron. Meanwhile, the dependence of the EPR zero-field splitting parameter D on the local structure parameter ΔR (ΔR=R₁−R₂) has been revealed. In addition, the relation between the EPR g-factors (g,g,Δg) and the orbit reduction factor k has been discussed for the two systems, suggesting that the orbit reduction factor k is very important to understand the EPR g-factors.     

Four-mode continuous-variables entangled state: generation from beam splitter, a parametric down-conversion and a polarizer

We introduce a new kind of four-mode continuous variable entangled state in Fock space. The completeness relation and the partly nonorthonormal property of such a state are proven. The scheme to generate this state is presented by combining a symmetrical beamsplitter, a parametric down-conversion and a polarizer. After making a single-mode quadrature amplitude measurement, the remaining three modes are kept in entanglement. And its applications are also discussed.     

一类小波的正则阶估计

１引言我们知道,一个可生成Ｌ２（Ｒ）中的多分辩分析的尺度函数（ｘ）满足双尺度差分方程（１）式的Ｆｏｕｒｉｅｒ变换为其中（ω）是函数（ｘ）的Ｆｏｕｒｉｅｒ变换,而叫做小波的共轭滤波器（简称滤波器）,它满足若将滤波器Ｈ（ω）设成则条件（３）成为可形式地写出Ｄａｕｂｅｃｈｉｅｓ［１］给出了（６）式无穷乘积收敛的条件．她还针对Ｆ（ｚ）为多项式情形（此时称滤波器为多项式滤波器）,给出了产生紧支小波的方法并给出了正则阶估计［２］．在［３］中,作者给出了小波分式滤波器的定义（即（４）式中Ｆ（ｚ））是实系数有理…     

The fine structure levels and spin-singlet contributions to zero-field-splitting parameters of Cr2+ ion in CdGa2S4

A theoretical investigation is reported of the fine structure levels and the spin-singlet contributions to zero-field-splitting (ZFS) parameters for Cr²⁺ ion in CdGa₂S₄ crystals. Firstly, the complete energy matrix including all spin states for a 3d ⁴ ion in tetrahedral D _2d symmetry is constructed according the double-group chain in the strong-field scheme. Then, by diagonalizing the complete energy of electron–electron interactions, the crystal field and the spin–orbit coupling for the Cr²⁺ (3d ⁴) ion in CdGa₂S₄ crystal, the fine structure levels and the spin-singlet contributions to ZFS parameters a, D and F are calculated. The results show that the spin-singlet contribution to D is negligible, but the contributions to a and F are very important. So, to obtain more accurate ZFS parameters for 3d ⁴ ions in the tetrahedral crystals, all spin states should be considered.     

滞时Volterra积分方程数值方法的数值稳定性分析

本文给出数值方法解Volterra积分方程的稳定性分析,我们判定可约积分方法的数值稳定性基于如下试验方程其中τ是正常数,p和q是复值的。在上述试验方程的情况下,我们研究θ-方法及可约积分方法的稳定性。     

THE NUMERICAL STABILITY OF THE BLOCK θ-METHODS FOR DELAY DIFFERENTIAL EQUATIONS

This paper focuses on the numerical stability of the block θ-methods adapted to differential equations with a dday argument. For the block θ-methods, an interpolation procedure is introduced which leads to the mumerical processes that satisfy an important asymptotic stability condition related to the class of test problems y＇ (t)=ay(t)+by(t-r) with a,b∈C, Re(a)＜- ｜b｜ and τ>0. We prove that the block θ-method is GP-stable if and only if the method is A-stable for ordinary differential equations. Furthermore, it is proved that the P-and GP-stability are equivalent for the block θ-method.     

Propagation of Bleustein-Gulyaev waves in a prestressed layered piezoelectric structure

Based on the theories of nonlinear continuum mechanics, piezoelectricity and elastic waves in solids, theoretical analysis of Bleustein-Gulyaev surface acoustic wave propagation in a prestressed layered piezoelectric structure are described. Numerical calculations are performed for the case that the layer and the substrate are identical LiNbO(3) except that they are polarized in opposite directions. It is found that an almost linear behavior of the relative change in phase velocity versus the initial stress is obtained for both surface electrically free and shorted cases. Potential applications in the design of acoustic wave devices are suggested.     

Distributed quantum information processing via quantum dot spins

We propose a scheme to engineer a non-local two-qubit phase gate between two remote quantum-dot spins. Along with one-qubit local operations, one can in principal perform various types of distributed quantum information processing. The scheme employs a photon with linearly polarisation interacting one after the other with two remote quantum-dot spins in cavities. Due to the optical spin selection rule, the photon obtains a Faraday rotation after the interaction process. By measuring the polarisation of the final output photon, a non-local two-qubit phase gate between the two remote quantum-dot spins is constituted. Our scheme may has very important applications in the distributed quantum information processing.