球上相干态的大半径极限

Full Bloch sphere teleportation of spinor Bose-Einstein condensates and spin ensembles

Quantum teleportation is the transfer of quantum information between two locations by the use of shared entanglement. Current teleportation schemes broadly fall under one of two categories, of either qubit or continuous variables teleportation. Spin coherent states on spin ensembles can be teleported under the continuous variables approximation for states with small deviations from a given polarization. However, for spin coherent states with large deviations, no convenient teleportation protocol exists. Recently, we introduced a teleportation scheme where a spin coherent state lying on the equ…

源自量子矩阵几何的完美球形 Bloch 超球面

Perfectly Spherical Bloch Hyper-spheres from Quantum Matrix Geometry

本研究利用量子自旋与电荷-单极子系统的类比，在任意维度构造了具有精确球对称性的 Bloch 超球面，揭示了其与量子 Nambu 几何的等价性，并阐明了简并自旋相干态诱导的非阿贝尔几何相位及量子几何张量等统计与几何性质。

Van der Waals interaction between an atom with spherical plasma shell

We consider the van der Waals energy of an atom near the infinitely thin sphere with finite conductivity which model the fullerene. We put the sphere into spherical cavity inside the infinite dielectric media, then calculate the energy of vacuum fluctuations in framework of the zeta-function approach. The energy for a single atom is obtained from this expression by consideration of the rare media. In the limit of the infinite radius of the sphere the Casimir-Polder expression for an atom and plate is recovered. For finite radius of sphere the energy of an atom monotonously falls down as $d^{-3…

Geometry of spin coherent states

Spin states of maximal projection along some direction in space are called (spin) coherent, and are, in many aspects, the "most classical" available. For any spin $s$, the spin coherent states form a 2-sphere in the projective Hilbert space $\mathbb{P}$ of the system. We address several questions regarding that sphere, in particular its possible intersections with complex lines. We also find that, like Dali's iconic clocks, it extends in all possible directions in $\mathbb{P}$. We give a simple expression for the Majorana constellation of the linear combination of two coherent states, and use …

Quantum beats of the rigid rotor

The dynamics is investigated of a free particle on a sphere (rigid rotor or rotator) that is initially in a coherent state. The instability of coherent states with respect to the free evolution leads to nontrivial time-development of averages of observables representing the position of a particle on a sphere that can be interpreted as quantum beats.

Coherent coupling between multiple ferrimagnetic spheres and a microwave cavity in the quantum-limit

The spin resonance of electrons can be coupled to a microwave cavity mode to obtain a photon-magnon hybrid system. These quantum systems are widely studied for both fundamental physics and technological quantum applications. In this article, the behavior of a large number of ferrimagnetic spheres coupled to a single cavity is put under test. We use second-quantization modeling of harmonic oscillators to theoretically describe our experimental setup and understand the influence of several parameters. The magnon-polariton dispersion relation is used to characterize the system, with a particular …

On relation between geometric momentum and annihilation operators on a two-dimensional sphere

With a recently introduced geometric momentum that depends on the extrinsic curvature and offers a proper description of momentum on two-dimensional sphere, we show that the annihilation operators whose eigenstates are coherent states on the sphere take the expected form αx+iβp, where α and β are two operators that depend on the angular momentum and x and p are the position and the geometric momentum, respectively. Since the geometric momentum is manifestly a consequence of embedding the two-dimensional sphere in the three-dimensional flat space, the coherent states reflects some aspects beyon…

球上带电粒子在磁场和库仑力作用下的Heun函数和能谱

Heun Functions and the energy spectrum of a charged particle on a sphere under magnetic field and Coulomb force

研究了磁场、库仑斥力和空间曲率对带电粒子运动的竞争作用。这三种类型的相互作用的特征在于三个基本长度：l_{B}的磁长度，l_{0}的玻尔半径和R的半径的球。粒子的能谱是通过求解Heun型的薛定谔方程，使用连分式技术得到的。它显示了一组丰富的功能机制，其中比率\frac{R}{l_{B}}和\frac{R}{l_{0}}取确定的值。

球上量子力学的Bargmann表示

The Bargmann representation for the quantum mechanics on a sphere

在K中引入球上粒子的相干态，构造了相应的巴格曼表象。Kowalski和J.Rembielinski，J.Phys.A：Math.Gen.33，6035（2000）。讨论了所引入的形式主义与基于球面S^2上平方可积函数的希尔伯特空间的标准方法之间的联系。

Casimir interaction between a sphere and a grating

We derive the explicit expression for the Casimir energy between a sphere and a 1D grating, in terms of the sphere and grating reflection matrices, and valid for arbitrary materials, sphere radius, and grating geometric parameters. We then numerically calculate the Casimir energy between a metallic (gold) sphere and a dielectric (fused silica) lamellar grating at room temperature, and explore its dependence on the sphere radius, grating-sphere separation, and lateral displacement. We quantitatively investigate the geometrical dependence of the interaction, which is sensitive to the grating hei…

具有大四阶项的自旋 Hamiltonian：三势阱与 Bloch 球可视化

Spin Hamiltonian with large fourth order terms: Triple well potentials and Bloch sphere visualization

研究了含四阶项的广义自旋Hamiltonian，利用相干态与突变理论构建参数空间，发现大四阶参数下存在三势阱区域，施加振荡磁场可引发多次基态量子相变，并实现了基态在Bloch球上局域化的可视化。