Heisenberg-limited Measurements and Sub-Planck Structures in Phase Space

It is shown how sub-Planck phase-space structures can be used to achieve Heisenberg-limited sensitivity in weak force measurements. Nonclassical states of harmonic oscillators, such as superpositions of coherent states, are shown to be useful for the measurement of weak forces that cause translations or rotations in phase space, which is done by entangling the quantum oscillator with a two-level system. This method is closely related to the Loschmidt echo techniques employed in nuclear magnetic resonance experiments. Implementations of this strategy in cavity QED and ion traps are described.     

Single Qubit and Its Universal Logic Gate Made of a Heisenberg Spin Cluster with Five Particles

We investigate an anisotropic Heisenberg spin cluster with five particles controlled by a time-dependent magnetic field. With the algebraic dynamical method, we obtain the exact analytical solution to the time dependent Schr6dinger equation. Based on the analytical solution, it is shown that the system can be used as a universal single qubit logic gate controlled by the strength and frequency of the magnetic field, and the six special single qubit logic gates can be realized physically. We also discuss the anti-decoherence property of the qubit and its logic gates resulted from particle coupling effect and collectivity of the cluster.     

Quantum Phase Transition in Quasi-two-dimensional Heisenberg Antiferromagnet with Single-Ion Anisotropy

In the present paper, we investigate the quantum phase transition in a spatially anisotropic antiferrornagnetic Heisenberg model of S =1 with single-ion energy anisotropy. By using the Schwinger boson representation, we calculate the Gaussian correction to the critical value J⊥^c caused by quantum spin fluctuations. We find that, for the positive single-ion energy, a nonzero value of J⊥^c is always needed to stabilize the antiferromagnetic long-range order in this model. It resolves a difference among literature and shows clearly that the effect of quantum fluctuations may qualitatively change a result obtained by the mean-field theories on lower-dimensional systems.     

不对称四核环状Co3^IIM^II簇合物的磁化学

本文用一种新的方法对三个核环状化合物Co3Fe(mp)4(Hmp)(PBu3^n)3(1) Co4(mp)4(Hmp)(PMe2Ph)3(2)(H2mp=2-巯基苯酚)和Co4(mp)4(PBu3^n)3Cl(MeOH)(3)进行了1。5-300K温度范围的磁性质研究, 即在各向同性海森堡模型的基础上, 用全矩阵对角化方法求自旋态能量本征值, 从而得到化合物的磁化率, 然后用阻尼最小二乘法拟合变温磁化率, 得到磁交换常数。因避免了使用Kambe理论, 无须对化合物进行模型简化处理, 所以得到更多、更准确的磁交换信息。拟合结果显示三个化合物都呈较弱的磁偶合作用。对化合物1得到J1=-3.14cm^-^1, J2=-3.04cm^-^1, J3=2.92cm^-^1和J4=4.08cm^-^1, 对2得到J1=-3.07cm^-^1, J2=-3.19cm^-^1,J3=-0.33cm^-^1和J4=-1.91cm^-^1; 对3得到J1=-4.818cm^-^1,J2=-4.244cm^-^1, J3=-1.164cm^-^1和J4=-2.634cm^-^1, 其中J1和J2代表通过双重μ2-S桥, J3和J4分别代表通过单重和双重μ2-O桥进行的磁交换作用常数。     

多模海森堡代数的算符恒等式

利用算符代数中的分析方法,得到了多模海森堡(Heisenberg)代数中的BCH公式和压缩算符的展开式。     

Smooth solutions for a stochastic hydrodynamical equation in Heisenberg paramagnet

In this article, we consider a stochastic hydrodynamical equation in Heisenberg paramagnet driven by additive noise. We prove the existence and uniqueness of smooth solutions to this equation with difference method.     

Multipartite Entanglement in Heisenberg Model

The effects of anisotropy and magnetic field on multipartite entanglement of ground state in Heisenberg XY model are investigated. The multipartite entanglement increases as a function of the inverse strength of the external field when the degree of anisotropy is finite. There are two peaks when the degree of anisotropy is γ=±1. When the degree of anisotropy increases further, the multipartite entanglement will decrease and tend to a constant. The threshold of the inverse strength of the external field for generating multipartite entanglement generally decreases with the increasing of qubits.     

Hardy-Type Inequalities on H-Type Groups andAnisotropic Heisenberg Groups

The author obtains some weighted Hardy-type inequalities on H-type groups and anisotropic Heisenberg groups. These inequalities generalize some recent results due to N. Garofalo, E. Lanconelli, I. Kombe and P. Niu et al.     

Thermal Entanglement of a Three-Qubit Heisenberg Chain with a Nonuniform Magnetic Field

The thermal entanglement of a three-qubit Heisenberg chain under a nonuniform magnetic field is studied. It is very interesting to note that the next nearest neighbor entanglement （NNNE） could be larger than the nearest neighbor entanglement （NNE）. We analyze the ground state entanglement, and give the conditions that NNNE is larger than NNE near zero temperature. Our results also show that the nonuniform field could induce the entanglement and improve the threshold temperature at certain parameter region.