I. Rigas, L. L. Sanchez-Soto, A. B. Klimov, J. Rehacek, Z. Hradil
The Wigner function of a pure continuous-variable quantum state is non-negative if and only if the state is Gaussian. Here we show that for the canonical pair angle and angular momentum, the only pure states with non-negative Wigner functions are the eigenstates of the angular momentum. Some implications of this surprising result are discussed.
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Wigner function for twisted photons
一个全面的Weyl-Wigner形式主义的正则对角动量的理论，特别强调的旋转周期性和角动量离散的影响。
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…
Extension of the Jordan-Wigner mapping to nonorthogonal spin orbitals for quantum computing application to valence bond approaches
本文提出一种针对非正交自旋轨道的Jordan-Wigner型映射，旨在实现价键波函数的高效量子模拟，为近期量子设备上的价键算法奠定基础。
The framework of Wigner functions for the canonical pair angle and orbital angular momentum, derived and analyzed in 2 recent papers [H. A. Kastrup, Phys.Rev. A 94, 062113(2016) and Phys.Rev. A 95, 052111(2017)] is applied to elementary concepts of quantum information like qubits and 2-qubits, e.g., entangled EPR/Bell states etc. Properties of the associated Wigner functions of such superposed states (pure and mixed) are discussed and illustrated. The Wigner functions of ERP/Bell states are distinguished by their topologically "twisted" domain on the configuration subspace S^1xS^1, a torus, of…
Semiclassical analysis of Wigner $3j$-symbol
我们分析的Wigner $3j$ -符号作为一个矩阵元素连接的本征函数的一对可积系统，通过提升的问题的附加角动量到Schwinger的振子的空间。一个新的元素是紧凑的拉格朗日流形的外观，是不是环面，由于事实上，定义的量子态的观测值是非交换的。这些流形可以通过广义玻尔-索末菲规则量子化，并产生所有正确的量子数。经典角动量矢量的几何以一种清晰的方式出现。有效的方法计算的泊松括号中的振幅行列式的开发和说明。
Yu and Littlejohn recently studied in arXiv:1104.1499 some asymptotics of Wigner symbols with some small and large angular momenta. They found that in this regime the essential information is captured by the geometry of a tetrahedron, and gave new formulae for 9j, 12j and 15j-symbols. We present here an alternative derivation which leads to a simpler formula, based on the use of the Ponzano-Regge formula for the relevant tetrahedron. The approach is generalized to Wigner 3nj-symbols with some large and small angular momenta, where more than one tetrahedron is needed, leading to new asymptotics…
We derive an asymptotic formula for the Wigner $12j$ symbol, in the limit of one small and 11 large angular momenta. There are two kinds of asymptotic formulas for the $12j$ symbol with one small angular momentum. We present the first kind of formula in this paper. Our derivation relies on the techniques developed in the semiclassical analysis of the Wigner $9j$ symbol [L. Yu and R. G. Littlejohn, Phys. Rev. A 83, 052114 (2011)], where we used a gauge-invariant form of the multicomponent WKB wave-functions to derive asymptotic formulas for the $9j$ symbol with small and large angular momenta. …
The Wigner D-matrix is essential in the course of angular momentum techniques. We here derive the new even- and odd-orthogonality properties of the Wigner D-matrix which was yet to be demonstrated in textbooks and also apply them to identifying optimal measurements for linear phase estimation based on two-mode optical interferometry with two specific quantum states.
In the Wigner framework, one abandons the assumption that the usual canonical commutation relations are necessarily valid. Instead, the compatibility of Hamilton's equations and the Heisenberg equations are the starting point, and no further assumptions are made about how the position and momentum operators commute. Wigner quantization leads to new classes of solutions, and representations of Lie superalgebras are needed to describe them. For the n-dimensional Wigner harmonic oscillator, solutions are known in terms of the Lie superalgebras osp(1|2n) and gl(1|n). For n=3N, the question arises …
Using a position operator obtained for spin 1 particles by the present author and Wigner, we obtain a quantum relativistic result for the hidden momentum force experienced by particles with structure. In particular, our result applies to the hidden magnetic forces manifest in some problems of electromagnetism. We also discuss spin and orbital angular momentum operators, as well as Wigner rotation.
Recently a paper on the construction of consistent Wigner functions for cylindrical phase spaces S^1 x R, i.e. for the canonical pair angle and angular momentum, was presented (arXiv:1601.02520), main properties of those functions derived, discussed and their usefulness illustrated by examples. The present paper is a continuation which compares properties of the new Wigner functions for cylindrical phase spaces with those of the well-known Wigner functions on planar ones in more detail. Furthermore, the mutual (Weyl) correspondence between Hilbert space operators and their phase space function…
Orbital-Free Quasi-Density Functional Theory
本文提出无轨道准密度泛函理论，以准密度为变量计算单体维格纳准概率，规避泡利势与动能近似难题，并揭示其与约化密度矩阵泛函的深层联系及维格纳负性与v-可表示性的关系。
The problem of constructing physically and mathematically well-defined Wigner functions for the canonical pair angle and angular momentum is solved. While a key element for the construction of Wigner functions for the planar phase space (q,p) in R^2 is the Heisenberg-Weyl group, the corresponding group for the cylindrical phase space (theta,p) in S^1 x R is the Euclidean group E(2) of the plane and its unitary representations. Here the angle theta is replaced by the pair (cos theta, sin theta) which corresponds uniquely to the points on the unit circle. The main structural properties of the Wi…
Electrons on helium form a unique two-dimensional electron system on the interface of liquid helium and vacuum. On liquid helium, trapped electrons can arrange into strongly correlated states known as Wigner molecules, which can be used to study electron interactions in the absence of disorder, or as a highly promising resource for quantum computation. Wigner molecules have orbital frequencies in the microwave regime and can therefore be integrated with circuit quantum electrodynamics (cQED), which studies light-matter interactions using microwave photons. Here, we experimentally realize a cQE…
Comment on "Measuring the Orbital Angular Momentum of a Single Photon"
每个光子具有不同轨道角动量（OAM）的光学模式可以通过与光束旋转器结合的马赫-曾德尔干涉仪进行分类，而不需要求助于OAM模式转换器。
We demonstrate experimentally how orbital-angular-momentum entanglement of two photons evolves under influence of atmospheric turbulence. We find that the quantum channel capacity is surprisingly robust: Its typical horizontal decay distance is of the order of 2 kilometers, demonstrating the potential of photonic orbital angular momentum for free-space quantum communication in a metropolitan environment.
We report on an orbital-angular-momentum-enhanced scheme for angular displacement estimation based on two-mode squeezed vacuum and parity detection. The sub-Heisenberg-limited sensitivity for angular displacement estimation is obtained in an ideal situation. Several realistic factors are also considered, including photon loss, dark counts, response-time delay, and thermal photon noise. Our results indicate that the effects of the realistic factors on the sensitivity can be offset by raising orbital angular momentum quantum number $\ell$. This reflects that the robustness and the practicability…
For a circularly polarized single-color field at a central frequency of $2ω$ the final electron momentum distribution upon strong field ionization does not carry any information about the phase of the initial momentum distribution. Adding a weak, co-rotating, circularly polarized field at a central frequency of $ω$ gives rise to a sub-cycle interference pattern (holographic angular streaking of electrons (HASE)). This interference pattern allows for the retrieval of the derivative of the phase of the initial momentum distribution after tunneling $ϕ^{\prime}_{\mathrm{off}}(p_i)$. A trajectory-b…
The role of Wigner rotation in estimating the specific angular momentum of a Kerr spacetime
研究 Kerr 空间时间引力场中偏振旋转及通过地质干涉仪估计特定角动量的方法，利用单光子在干涉仪中的传播，通过干涉可见度表征相对论效应，获得特定角动量估计及不确定性。
Quantum Formulation of Fractional Orbital Angular Momentum
旋转角的量子理论（S. M. Barnett和D. T. Pegg，Phys.Rev.A，41，3427-3425（1990））被推广到轨道角动量的非整数值。这需要引入一个额外的参数，与轨道角动量的分数值相关联的相位不连续的方向。我们应用我们的形式主义的分数轨道角动量在傍轴和非傍轴制度的光模式的传播。
We introduce a matter wave interference scheme based on the quantization of orbital angular momentum in a ring trap. It operates without beam splitters, is sensitive to geometric phases induced by external gauge fields, and allows measuring interatomic scattering lengths. We argue that orbital angular momentum interferometry offers a versatile platform for quantum coherent experiments with cold atoms and Bose-Einstein condensates using state-of-the-art technology.
Large Quantum imaging of nonlocal spatial correlations induced by orbital angular momentum
通过扫描符合计数，我们探测了带有轨道角动量的泵浦光参量下转换产生的量子图像。非局部空间相关性通过将符合点一分为二来表现。
Conservation of Orbital Angular Momentum in Stimulated Down-Conversion
我们报告的实验表明，在受激下转换的轨道角动量守恒。轨道角动量不会转移到自发下转换的单个光束中，但当单独取孪生光子时，它是守恒的。通过无腔受激发射的下转换，我们观察到单个光束的守恒定律。
The conservation of orbital angular momentum and the two-photon detection amplitude in spontaneous parametric down-conversion
考虑角动量守恒和不守恒两种情况，研究了当引入轨道角动量物理量时，自发参量下转换光束的双光子探测幅度.理论计算与实验观测结果一致，表明下转换光束的双光子探测振幅的空间结构携带着关于自发参量下转换中轨道角动量守恒或不守恒的重要信息。
Transverse coincidence-structures in spontaneous parametric down-conversion with orbital angular momentum: Theory
得到了携带轨道角动量的II型自发参量下转换横截面的符合结构。围绕泵浦光束方向的方位角对称性破缺在这些量子图像上显示出来。下转换过程的振幅概率的解析表达式示出包括非线性极化率组件。
A comprehensive theory of the Weyl-Wigner formalism for the canonical pair angle-angular momentum is presented. Special attention is paid to the problems linked to rotational periodicity and angular-momentum discreteness.
In this paper, we propose a protocol for angular displacement estimation based upon orbital angular momentum coherent state and a SU(1,1)-SU(2) hybrid interferometer. This interferometer consists of an optical parametric amplifier, a beam splitter and reflection mirrors, hereon we use a quantum detection strategy $\---$ balanced homodyne detection. The results indicate that super-resolution and super-sensitivity can be realized with ideal condition. Additionally, we study the impact of photon loss on the resolution and the sensitivity, and the robustness of our protocol is also discussed. Fina…
Single-photon interferometry with orbital angular momentum circumvents standard wave-particle duality
从马赫-曾德尔干涉仪（MZI）中射出的具有明确轨道角动量的偏振光子被证明可以绕过波粒二象性。其偏振分辨探测概率形成非正弦干涉图样。对于MZI臂之间的某些相位差，该模式产生可靠的哪个路径信息和高相位灵敏度。
Is orbital angular momentum always conserved in spontaneous parametric down-conversion?
在第二类自发参量下转换的非线性光学过程中，我们提出了一个实验，实验表明下转换光束的双光子探测幅度一般不能再现携带非零轨道角动量的泵浦光束的横向轮廓。我们解释了这一观察的轨道角动量是不守恒的II型非线性过程中由于破缺的旋转对称的哈密顿量。
Light carrying orbital angular momentum constitutes an important resource for both classical and quantum information technologies. Its inherently unbounded nature can be exploited to generate high-dimensional quantum states or for channel multiplexing in classical and quantum communication in order to significantly boost the data capacity and the secret key rate, respectively. While the big potentials of light owning orbital angular momentum have been widely ascertained, its technological deployment is still limited by the difficulties deriving from the fabrication of integrated and scalable p…
The paper studies the Raman quantum memory protocol as applied to quantum light with orbital angular momentum. The memory protocol is implemented on an ensemble of three-level cold atoms with the $Λ$- configuration of energy levels. The possibility of storing quantum statistics of light with an orbital momentum is analysed in the case when the driving field could be treated as a plane wave. The efficiency analysis shows that examined storage/retrieval processes do not cause the efficiency decreasing compared with the spatial multimode memory protocol considered in [Golubeva et al. 2012]]. We a…
Extrinsic orbital angular momentum of entangled photon-pairs in spontaneous parametric down-conversion
从描述自发参量下转换的光学非线性过程的标准哈密顿量出发，理论上证明了由于空间对称性破缺，产生的纠缠光子对在第二类情形下的相对运动自由度上携带不可忽略的轨道角动量.我们还表明，这些自由度中的光子对携带的轨道角动量在传统测量方案中无法检测到，这需要开发新技术进行进一步的实验研究。
We set forth a method to analyze the orbital angular momentum of a light field. Instead of using the canonical formalism for the conjugate pair angle-angular momentum, we model this latter variable by the superposition of two independent harmonic oscillators along two orthogonal axes. By describing each oscillator by a standard Wigner function, we derive, via a consistent change of variables, a comprehensive picture of the orbital angular momentum. We compare with previous approaches and show how this method works in some relevant examples.
The Shannon dimensionality of orbital angular momentum (OAM) entanglement produced in spontaneous parametric down-conversion can be probed by using multi-sector phase analysers. We demonstrate a spatial light modulator-based implementation of these analysers, and use it to measure a Schmidt number of about 50.
We report the first experimental characterization of the first-order continuous variable orbital angular momentum states. Using a spatially non-degenerate optical parametric oscillator (OPO) we produce quadrature entanglement between the two first-order Laguerre-Gauss modes. The family of OAM modes is mapped on an orbital Poincare sphere, and the modes position on the sphere is spanned by the three orbital parameters. Using the non-degenerate OPO we produce squeezing of these parameters, and as an illustration, we reconstruct the "cigar-shaped" uncertainty volume on the orbital Poincare sphere…
Deutsch's algorithm is the simplest quantum algorithm which shows the acceleration of quantum computer. In this paper, we theoretically advance a scheme to implement quantum Deutsch's algorithm in spin-orbital angular momentum space. Our scheme exploits a newly developed optical device called "q-plate", which can couple and manipulate the spin-orbital angular momentum simultaneously. This experimental setup is of high stability and efficiency theoretically for there is no interferometer in it.
Entanglement of the orbital angular momentum states of the photons generated in a hot atomic ensemble
量子协议将更有效地与高维纠缠态。携带轨道角动量的光子可以用来产生高维纠缠态。在本文中，我们实验证明了在热原子系综中利用自发四波混频产生的Stokes光子和反Stokes光子之间的轨道角动量纠缠。实验还表明，热原子系综与Stokes光子之间存在与空间自由度有关的纠缠。
Entanglement and conservation of orbital angular momentum in spontaneous parametric down-conversion
研究表明，泵浦光的平面波谱向自发参量下转换产生的双光子场的四阶横向空间关联函数的转移导致了光的轨道角动量守恒和纠缠。通过一个简单的实验装置的基础上四阶（或双光子）干涉，我们表明，我们的理论模型提供了一个很好的描述携带轨道角动量的下转换字段。
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.
We provide an analytical expression for the entanglement decay of initially maximally entangled orbital angular momentum bi-photon states, when scattered off an obstruction. We show that the decay is controlled by the diffraction-induced mutual overlap between the diffracted field modes, and quantify its dependence on the size and position of the obstruction.
Photons can carry spin angular momentum (SAM) and orbital angular momentum (OAM), which can be used to realize a qubit system and a high-dimension system respectively. This spin-orbital system is very suitable for implementing one-dimensional discrete-time quantum random walks. We propose a simple scheme of quantum walks on the spin-orbital angular momentum space of photons, where photons walk on the infinity OAM space controlled by their SAM. By employing the recent invention of an optical device, the so-called 'q-plate', our scheme is more simple and efficient than others because there is no…
We present an implementation scheme for a quantum walk in the orbital angular momentum space of a laser beam. The scheme makes use of a ring interferometer, containing a quarter-wave plate and a q plate. This setup enables one to perform an arbitrary number of quantum walk steps. In addition, the classical nature of the implementation scheme makes it possible to observe the quantum walk evolution in real time. We use nonquantum entanglement of the laser beam's polarization with its orbital angular momentum to implement the quantum walk.
We propose a new quantum network scheme using orbital angular momentum states of photons to route the network and spin angular momentum states to encode the information. A four-user experimental scheme based on this efficient quantum network is analyzed in detail, which is particularly appealing for the free space quantum key distribution. Users can freely exchange quantum keys with each other.
Orbital Wigner functions and quantum transport in multiband systems
本文提出基于轨道维格纳函数的输运形式体系，精确捕捉多带费米子系统中的量子相干效应，超越玻尔兹曼理论，并验证了弹道输运与拓扑泵浦等非平衡现象。
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 …
"Bottom-up" approaches to the many-body physics of fermions have demonstrated recently precise number and site-resolved preparations with tunability of interparticle interactions in single-well, SW, and double-well, DW, nano-scale confinements created by manipulating ultracold fermionic atoms with optical tweezers. These experiments emulate an analogue-simulator mapping onto the requisite microscopic hamiltonian, approaching realization of Feynman's vision of quantum simulators that "will do exactly the same as nature". Here we report on exact benchmark configuration-interaction computational …
Many methods now exist to prepare free electrons into orbital angular momentum states, and the predicted applications of these electron states as probes of materials and scattering processes are numerous. The development of electron orbital angular momentum measurement techniques has lagged behind. We show that coupling between electron orbital angular momentum and a spatially varying magnetic field produces an angular momentum-dependent focusing effect. We propose a design for an orbital angular momentum measurement device built on this principle. As the method of measurement is non-interfero…
There are two types of asymptotic formulas for the $12j$ symbol with one small and 11 large angular momenta. We have derived the first type of formula previously in [L. Yu, Phys. Rev. A84 022101 (2011)]. We will derive the second type in this paper. We find that this second asymptotic formula for the $12j$ symbol is expressed in terms of the vector diagram associated with two $6j$ symbols, namely, the vector diagram of two adjacent tetrahedra sharing a common face. As a result, two sets of Ponzano-Regge phases appear in the asymptotic formula. This work contributes another asymptotic formula o…
It is shown that the photon picture of the electromagnetic field enables one to determine unambiguously the splitting of the total angular momentum of the electromagnetic field into the orbital part and the spin part.
Structured-light-mediated hybrid entanglement between photon polarization and electronic orbital angular momentum
该研究提出最小量子光学方案，利用自旋 - 轨道结构双光子态激发半导体量子盘的两个通道，经有效相干映射和光子发射产生光子偏振与电子轨道角动量的混合纠缠，主方程分析表明预示态接近目标纠缠态，为相关研究提供途径。
We present a quantum mechanical analysis of the orbital angular momentum of a class of recently discovered elliptically-symmetric stable light fields --- the so-called Ince-Gauss modes. We study, in a fully quantum formalism, how the orbital angular momentum of these beams varies with their ellipticity and discover several compelling features, including: non-monotonic behavior, stable beams with real continuous (non-integer) orbital angular momenta, and orthogonal modes with the same orbital angular momenta. We explore, and explain in detail, the reasons for this behavior. These features may h…
We propose to use an acoustic surface wave as a memory for a photon carrying orbital angular momentum. We clarify the physical mechanism that enables the transfer of information, derive the angular momentum selection rule that must be obeyed in the process, and show how to optimize the optoacoustic coupling. We theoretically demonstrate that high fidelities can be achieved, using realistic parameters, for the transfer of a coherent optical Laguerre-Gaussian state, associated with large angular momentum, to a mechanical shear mode. Our results add a significant possibility to the ongoing effort…
We consider the excitation of Rydberg states through photons carrying an intrinsic orbital angular momentum degree of freedom. Laguerre-Gauss modes, with a helical wave-front structure, correspond to such a set of laser beams, which carry some units of orbital angular momentum in their propagation direction. We demonstrate that, in a proper geometrical setting, this orbital angular momentum can be transferred to the internal degrees of freedom of the atoms, thus violating the standard dipolar selection rules. Higher orbital angular momentum states become accessible through a single photon exci…
We present a complete and consistent quantum theory of generalised X waves with orbital angular momentum (OAM) in dispersive media. We show that the resulting quantised light pulses are affected by neither dispersion nor diffraction and are therefore resilient against external perturbations. The nonlinear interaction of quantised X waves in quadratic and Kerr nonlinear media is also presented and studied in detail.
Many practical sampling patterns for function approximation on the rotation group utilizes regular samples on the parameter axes. In this paper, we relate the mutual coherence analysis for sensing matrices that correspond to a class of regular patterns to angular momentum analysis in quantum mechanics and provide simple lower bounds for it. The products of Wigner d-functions, which appear in coherence analysis, arise in angular momentum analysis in quantum mechanics. We first represent the product as a linear combination of a single Wigner d-function and angular momentum coefficients, otherwis…
The effect of the transversality condition on the quantization of the photon orbital angular momentum is studied. The quantum gauge that is deduced from the transversality condition is shown to be a Berry gauge. It determines a helicity-dependent reference point relative to which the position is canonically conjugate to the momentum. As a result, the photon orbital angular momentum about the origin of the laboratory reference system split into two parts. One is the orbital angular momentum of the photon about the reference point, which is canonical. The other is the orbital angular momentum of…
Projection operator onto spin-S eigenspaces of total and orbital angular momenta
利用 Frobenius 协变构造了总角动量和轨道角动量平方的自旋-S 本征空间上的投影算子，并建立了与核结构研究中 Villars 角动量投影的对应关系。
We present an optomechanical device designed to allow optical transduction of orbital angular momentum of light. An optically induced twist imparted on the device by light is detected using an integrated cavity optomechanical system based on a nanobeam slot-mode photonic crystal cavity. This device could allow measurement of the orbital angular momentum of light when photons are absorbed by the mechanical element, or detection of the presence of photons when they are scattered into new orbital angular momentum states by a sub-wavelength grating patterned on the device. Such a system allows det…
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…
We analyze the effect of Proca mass and orbital angular momentum of photons imposed by a structured plasma in Kerr-Newman and Reissner-Nordstrom-de Sitter spacetimes. The presence of characteristic lengths in a turbulent plasma converts the virtual Proca photon mass on orbital angular momentum, with the result of decreasing the virtual photon mass. The combination of this plasma effect and that of the gravitational field leads to a new astrophysical phenomenon that imprints a specific distribution of orbital angular momentum into different frequencies of the light emitted from the neighborhood…
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