Detail is included to make it easier to follow the mathematical arguments, in particular for eqs. 25 and 26 (19 and 20 in the previous version); minor stylistic corrections are also included
对应规则的严格应用表明，量子粒子的角动量算符--对应于经典的幅度$\mathbf{l}= m \mathbf{r} \wedge \mathbf{v}$ --在电磁场的存在下由$\mathbf{\hat{l}}=\mathbf{r}\wedge(-i\hbar\mathbf{\nabla} -\frac{e}{c}\mathbf{A})$给出。因此，尽管对相应的量子化规则有普遍的看法，角动量的本征值取决于电磁场的位形。作为角动量微积分和\emph{spin}理论基础的通常的对易规则$[{\hat{l}}_i,{\hat{l}}_j]=i\hbarε_{ijk}{\hat{l}}_k$--以及玻姆的EPR论证的例子--在电磁场存在的情况下是无效的。算符$\mathbf{\hat{l}}=-i\hbar\mathbf{r}\wedge\mathbf{\nabla}$的期望值不是规范不变的，它依赖于电动势的校准。
英文摘要：
A rigorous application of the correspondence rules shows that the operator of the angular momentum of a quantum particle---corresponding to the classical magnitude $\mathbf{l}= m \mathbf{r} \wedge \mathbf{v}$---is given by $\mathbf{\hat{l}}=\mathbf{r}\wedge(-i\hbar\mathbf{\nabla} -\frac{e}{c}\mathbf{A})$ in the presence of an electromagnetic field. Thus, despite the general opinion on the corresponding rules of quantization, the eigenvalues of the angular momentum depend on the configuration of the electromagnetic field. The usual rules of commutation $[{\hat{l}}_i,{\hat{l}}_j]=i\hbarε_{ijk}{\hat{l}}_k$, that are at the foundation of the calculus of angular momentum and of the theory of \emph{spin}---and Bohm's example of the EPR argument---are not valid in the presence of an electromagnetic field. The expected value of the operator $\mathbf{\hat{l}}=-i\hbar\mathbf{r}\wedge\mathbf{\nabla}$ is not gauge invariant, it depends on the calibration of the electrodynamic potentials.
This paper analyzes the algebraic and physical properties of the spin and orbital angular momenta of light in the quantum mechanical framework. The consequences of the fact that these are not angular momenta in the quantum mechanical sense are worked out in mathematical detail. It turns out that the spin part of the angular momentum has continuous eigenvalues. Particular attention is given to the paraxial limit, and to the definition of Laguerre--Gaussian modes for photons as well as classical light fields taking full account of the polarization degree of freedom.
It is pointed out that the solutions of the Klein-Gordon and the Dirac equation derived in the paper addressed in this Comment (and many more solutions) may be obtained from generating functions.
We demonstrate an angular momentum-enhanced protocol that permits an angular displacement estimation by using tunable squeezed Bell state and parity detection. We consider the resolution and the sensitivity, super-resolution is presented along with Heisenberg scaling sensitivity for arbitrary tunable factor, the tunable factor which can optimize the sensitivity is also discussed. Additionally, we analyze the advantages of using angular momentum via considering and comparing simulation results. Under the situation of the optimal tunable factor, the Heisenberg-limited sensitivity and $2\left(\el…
A new Bateman-Hillion solution to the Dirac equation for a relativistic Gaussian electron beam taking explicit account of the $4$-position of the beam waist is presented. This solution has a pure Gaussian form in the paraxial limit but beyond it contains higher order Laguerre-Gaussian components attributable to the tighter focusing. One implication of the mixed mode nature of strongly diffracting beams is that the expectation values for spin and orbital angular momenta are fractional and are interrelated to each other by \textit{intrinsic spin-orbit coupling}. Our results for these properties …
We consider a system of two particles, each with large angular momentum $j$, in the singlet state. The probabilities of finding projections of the angular momenta on selected axes are determined. The generalized Bell inequalities involve these probabilities and we study them using statistical methods. We show that most of Bells inequalities cannot be violated, or are violated only marginally, in the limit $j\to \infinity$. The precision required to confirm a violation appears to be difficult to achieve. In practice, the quantum system, in spite of being entangled, becomes indistinguishable fro…
In the study of systems that cannot be described classically, the Wigner inequality, has received only a small amount of attention. In this paper we extend the Wigner inequality - originally derived in 1969 - and show how it may be used to contradict local realism with only coincidence detections in the absence of two-outcome measurements - that is, for any system where only one possible result of a pair of potential outcomes can be registered. It thus encapsulates a much broader class of measurement schemes than could previously violate a local-realistic inequality. This is possible due to an…
In optical experiments involving a single photon that takes alternative paths through an optical system and ultimately interferes with itself (e.g., Young's double-slit experiment, Mach-Zehnder interferometer, Sagnac interferometer), there exist fundamental connections between the linear and angular momenta of the photon on the one hand, and the ability of an observer to determine the photon's path through the system on the other hand. This paper examines the arguments that relate the photon momenta (through the Heisenberg uncertainty principle) to the "which path" (German: welcher Weg) questi…
We use the tridiagonal representation approach to solve the radial Schrödinger equation for an inverse power-law potential of a combined quartic and sextic degrees and for all angular momenta. The amplitude of the quartic singularity is larger than that of the sextic but the signs are negative and positive, respectively. It turns out that the system has a finite number of bound states, which is determined by the larger ratio of the two singularity amplitudes. The solution is written as a finite series of square integrable functions written in terms of the Bessel polynomial.
We report on the storage of Orbital Angular Momentum (OAM) of light via the phenomenon of Coherent Population Oscillation (CPO) in cold cesium atoms. The experiment is performed using a delayed four wave mixing configuration where the transverse optical information of a probe field carrying OAM associated with its azimuthal phase dependence is stored in the CPO of Zeeman sublevels of the hyperfine transition $F=3\rightarrow F^{\prime}=2$ of cesium $D_{2}$ line. We also demonstrate experimentally the simultaneous storage and retrieval of different OAM states propagating along different directio…
Magnetostatic modes supported by a ferromagnetic sphere have been known as the Walker modes, each of which possesses an orbital angular momentum as well as a spin angular momentum along a static magnetic field. The Walker modes with non-zero orbital angular momenta exhibit topologically non-trivial spin textures, which we call \textit{magnetic quasi-vortices}. Photons in optical whispering gallery modes supported by a dielectric sphere possess orbital and spin angular momenta forming \textit{optical vortices}. Within a ferromagnetic, as well as dielectric, sphere, two forms of vortices interac…
Coupling of quantum angular momenta: an insight into analogic/discrete and local/global models of computation
在过去的几年里，有一个动荡的活动，旨在为量子计算引入新的概念方案。Marzuoli A and Rasetti M 2002，2005 a中提出的方法依赖于SU（2）角动量的（再）耦合理论，可以被视为对基于“量子位”和布尔门的通常量子电路模型的自旋变量的任意值的推广。计算状态属于由离散和连续参数标记的有限维希尔伯特空间，并且幺正门可以依赖于在有限值集以及连续（角）变量上的量子数。这样一个框架是一个理想的游乐场，讨论离散（数字）和模拟计算过程，以及它们之间的关系发生时，一个一致的半经典限制发生在离散量子门。当使用纯离散的幺正门时，模拟器自然地被建模为量子有限状态的家庭-机器，这些机器反过来代表拓扑量子计算模型的离散版本。我们认为，我们的模型体现了一种统一的计算范式的灵感来自自然，甚至更雄心勃勃的，一个通用的设置，适当编码的量子符号操作的组合，拓扑和代数问题可能会找到他们的“自然”的计算参考模型。
The Wigner rotation matrix ($d$-function), which appears as a part of the angular-momentum-projection operator, plays a crucial role in modern nuclear-structure models. However, it is a long-standing problem that its numerical evaluation suffers from serious errors and instability, which hinders precise calculations for nuclear high-spin states. Recently, Tajima [Phys. Rev. C 91, 014320 (2015)] has made a significant step toward solving the problem by suggesting the high-precision Fourier method, which however relies on formula-manipulation softwares. In this paper we propose an effective and …
