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The issue of gauge choice in the Landau problem and the physics of canonical and mechanical orbital angular momenta
One intriguing issue in the nucleon spin decomposition problem is the existence of two types of decompositions, which are representably characterized by two different orbital angular momenta (OAMs) of quarks. The one is the mechanical OAM, while the other is the so-called gauge-invariant canonical (g.i.c.) OAM, the concept of which was introduced by Chen et al. An especially delicate quantity is the g.i.c. OAM, which must be distinguished from the ordinary (gauge-variant) canonical OAM. We find that, owing to its analytically solvable nature, the famous Landau problem offers an ideal tool to understand the difference and the physical meaning of the above three OAMs, i.e. the standard canonical OAM, g.i.c. OAM, and the mechanical OAM. We analyze these three OAMs in two different formulations of the Landau problem, first in the standard (gauge-fixed) formulation and second in the gauge-invariant (but path-dependent) formulation of DeWitt. Especially interesting is the latter formalism. It is shown that the choice of path has an intimate connection with the choice of gauge, but they are not necessarily equivalent. Then, we answer the question about what is the consequence of a particular choice of path in DeWitt’s formalism. This analysis also clarifies the implication of the gauge symmetry hidden in the concept of g.i.c. OAM. Finally, we show that the finding above offers a clear understanding about the uniqueness or non-uniqueness problem of the nucleon spin decomposition, which arises from the arbitrariness in the definition of the so-called physical component of the gauge field.
Nonequilibrium Quasiparticle Dynamics in Bi-Based Superconductors Measured by Modulation Photoexcitation Spectroscopy
We develop an orbital angular momentum (OAM) excitation pump-probe (Pp) spectroscopy and perform experiments on a Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+δ} (Bi2212) superconductor. The OAM modulation for the pump is realized by using a transverse mode conversion technique which allows to modulate the chirality of the optical OAM with a fixed polarization. The result reveals a difference of the OAM-dependent transient reflectivity changes below T{sub c}, indicating that the pump OAM can break the chiral symmetry of the superconducting (SC) state. The OAM dependences of the transient signal imply that the quasi-particle (QP) excitation with OAM enhances the SC with opposite chirality and/or suppress the SC with equal chirality. The temperature dependence of the OAM dynamics shows virtually no pairing fluctuation that usually appears in the QP dynamics observed by conventional Pp, suggesting that the nonequilibrium OAM dynamics is sensitive to the delocalized OAM associated with long range order.
Generation of extreme-ultraviolet beams with time-varying orbital angular momentum
Light fields carrying orbital angular momentum (OAM) provide powerful capabilities for applications in optical communications, microscopy, quantum optics, and microparticle manipulation. We introduce a property of light beams, manifested as a temporal OAM variation along a pulse: the self-torque of light. Although self-torque is found in diverse physical systems (i.e., electrodynamics and general relativity), it was not realized that light could possess such a property. We demonstrate that extreme-ultraviolet self-torqued beams arise in high-harmonic generation driven by time-delayed pulses with different OAM. We monitor the self-torque of extreme-ultraviolet beams through their azimuthal frequency chirp. Lastly, this class of dynamic-OAM beams provides the ability for controlling magnetic, topological, and quantum excitations and for manipulating molecules and nanostructures on their natural time and length scales.
ORBITAL ANGULAR MOMENTUM BEAMS RESEARCH USING A FREE-ELECTRON LASER OSCILLATOR
Orbital angular momentum (OAM) photon beams are excellent tools for non-contact optical manipulation of mat- ter in a broad photon energy range. A free-electron laser (FEL) oscillator is well-suited for studying OAM beams with various features including a wide spectral coverage, wavelength tunability, two-color lasing, polarization control, etc. Here, we report the first experimental demonstration of superposed OAM beams from an oscillator FEL. Lasing at around 458 nm, we have generated superposed OAM beams up to the fourth order as a superposition of two pure OAM modes with opposite helicities. These generated beams have a good beam quality, a high degree of circular polarization, and high power. Using external rf modulation with frequen- cies from 1 to 30 Hz, we also developed a pulsed mode operation of the OAM beams with a highly reproducible temporal structure. FEL operation showcased in this work can be extended to higher photon energies, e.g. using a future x-ray FEL oscillator. The operation of such an OAM FEL also paves the way for the generation of OAM gamma-ray beams via Compton scattering.
Photons, phonons, and plasmons with orbital angular momentum in plasmas
Exact eigen modes with orbital angular momentum (OAM) in the complex media of unmagnetized homogeneous plasmas are studied. Three exact eigen modes with OAM are derived, i.e., photons, phonons, and plasmons. The OAM of different plasma components are closely related to the charge polarities. For photons, the OAM of electrons and ions are of the same magnitude but opposite direction, and the total OAM is carried by the field. For the phonons and plasmons, their OAM are carried by the electrons and ions. Lastly, the OAM modes in plasmas and their characteristics can be explored for potential applications in plasma physics and accelerator physics.
Parametric amplification of orbital angular momentum beams based on light-acoustic interaction
A high fidelity amplification of beams carrying orbital angular momentum (OAM) is very crucial for OAM multiplexing and other OAM-based applications. Here, we report a demonstration of stimulated Brillouin amplification for OAM beams, and the energy conversion efficiency of photon-phonon coupling and the phase structure of amplified signals are investigated in collinear and noncollinear frame systems, respectively. Our results demonstrate that the OAM signals can be efficiently amplified without obvious noise introduced, and the modes of output signal are independent of the pump modes or the geometrical frames. Meanwhile, an OAM state depending on the optical modes and the geometrical frames is loaded into phonons by coherent light-acoustic interaction, which reveals more fundamental significance and a great application potential in OAM-multiplexing.
Scattering of twisted particles: Extension to wave packets and orbital helicity
High-energy photons and other particles carrying nonzero orbital angular momentum (OAM) emerge as a new tool in high-energy physics. Recently, it was suggested to generate high-energy photons with nonzero OAM (twisted photons) by the Compton backscattering of twisted optical photons on relativistic electron beams. Twisted electrons in the intermediate energy range have also been demonstrated experimentally; twisted protons and other particles can, in principle, be created in a similar way. Collisions of energetic twisted states can offer a new look at particle properties and interactions. A theoretical description of twisted particle scattering developed previously treated them as pure Bessel states and ran into difficulty when describing the OAM of the final twisted particle at nonzero scattering angles. Here we develop further this formalism by incorporating two additional important features. First, we treat the initial OAM state as a wave packet of a finite transverse size rather than a pure Bessel state. This realistic assumption allows us to resolve the existing controversy between two theoretical analyses for nonforward scattering. Second, we describe the final twisted particle in terms of the orbital helicity: the OAM projection on its average direction of propagation rather than on the fixed reaction axis. Using this formalism, we determine to what extent the twisted state is transferred from the initial to final OAM particle in a generic scattering kinematics. As a particular application, we prove that in the Compton backscattering the orbital helicity of the final photon stays close to the OAM projection of the initial photon.
Orbital angular momenta of quarks and gluons in the nucleon -model-dependent versus model-independent extractions-
We demonstrate that there exist two kinds of gauge-invariant decompositions of the nucleon spin, which are physically inequivalent. The quark and gluon orbital angular momenta (OAMs) appearing in one decomposition are basically the canonical OAMs, while the quark and gluon OAMs appearing in another decomposition are called the dynamical OAMs. It is shown that the dynamical OAMs of quarks and gluons in the nucleon can be related to definite high-energy deep-inelastic-scattering observables. On the other hand, we conjecture that the canonical OAMs of quarks and gluon in the nucleon are model-dependent quantities, which is meaningful only within a specific theoretical model of the nucleon.
Antiferromagnetic real-space configuration probed by dichroism in scattered x-ray beams with orbital angular momentum
X-ray beams with orbital angular momentum (OAM) are a promising tool for x-ray characterization techniques. Beams with OAM have a helicity - an azimuthally varying phase - which leads to a gradient of the light field. New material properties can be probed by utilizing the helicity of an OAM beam. Here, we demonstrate a dichroic effect in resonant diffraction from an artificial antiferromagnet with a topological defect. We found that the scattered OAM beam has circular dichroism at the antiferromagnetic Bragg peak whose sign is coupled to its helicity, which reveals the real-space configuration of the antiferromagnetic ground state. Thermal cycling of the artificial antiferromagnet can change the ground state, as indicated by reversal of the sign of circular dichroism. This result is one of the first demonstrations of a soft x-ray spectroscopy characterization technique utilizing the OAM of x rays. In conclusion, this helicity-dependent circular dichroism exemplifies the potential to utilize OAM beams to probe matter in a way that is inaccessible using currently available x-ray techniques.
Orbital angular momentum at small $x$ revisited
We revisit the problem of the small Bjorken-x asymptotics of the quark and gluon orbital angular momentum (OAM) distributions in the proton utilizing the revised small-x helicity evolution derived recently in [1]. We relate the quark and gluon OAM distributions at small x to the polarized dipole amplitudes and their (first) impact-parameter moments. To obtain the OAM distributions, we derive novel small-x evolution equations for the impact-parameter moments of the polarized dipole amplitudes in the double-logarithmic approximation (summing powers of α s ln 2 (1/x) with α s the strong coupling constant). We solve these evolution equations numerically and extract the leading large-N c , small-x asymptotics of the quark and gluon OAM distributions, which we determine to be ${L}_{q+\overline{q}}\left(x,{Q}^2\right)\sim {L}_G\left(x,{Q}^2\right)\sim \Delta \Sigma \left(x,{Q}^2\right)\sim \Delta G\left(x,{Q}^2\right)\sim {\left(\frac{1}{2}\right)}^{3.66\sqrt{\frac{\alpha_s{N}_c}{2_π}}}$in agreement with [2] within the precision of our numerical evaluation. (Here N c is the number of quark colors.) We also investigate the ratios of the quark and gluon OAM distributions to their helicity distribution counterparts in the small-x region.
Multiple copies of orbital angular momentum states through second-harmonic generation in a two-dimensional periodically poled LiTaO{sub 3} crystal
We experimentally demonstrate multiple copies of optical orbital angular momentum (OAM) states through quasi-phase-matched (QPM) second-harmonic (SH) generation in a 2D periodically poled LiTaO{sub 3} (PPLT) crystal. Since the QPM condition is satisfied by involving different reciprocal vectors in the 2D PPLT crystal, collinear and noncollinear SH beams carrying OAMs of l{sub 2} are simultaneously generated by the input fundamental beam with an OAM of l{sub 1}. The OAM conservation law (i.e., l{sub 2} = 2l{sub 1}) holds well in the experiment, which can tolerate certain phase-mismatch between the interacting waves. Our results provide an efficient way to obtain multiple copies of the wavelength-converted OAM states, which can be used to enhance the capacity in optical communications.
Conversion of the optical orbital angular momentum in a plasmon-assisted second-harmonic generation
We experimentally demonstrate the plasmon-assisted second-harmonic generation of an optical orbital angular momentum (OAM) beam. Because of the shape resonance, the plasmons in a periodic array of rectangular metal holes greatly enhance the nonlinear optical conversion of an OAM state. The OAM conservation (i.e., 2l{sub 1} = l{sub 2} with l{sub 1} and l{sub 2} being the OAM numbers of the fundamental and second-harmonic waves, respectively) holds well under our experimental configuration. Our results provide a potential way to realize nonlinear optical manipulation of an OAM mode in a nano-photonic device.
Modeling of high intensity orbital angular momentum beams for laser–plasma interactions
In this work, we explore the field of high intensity orbital angular momentum (OAM) beams, their generation with spiral phase mirrors, and the theory behind modeling both ideal and realistic beams. We explore OAM beam asymmetries introduced by aberrations in the beam, manufacturing defects, and bandwidth. A full three-dimensional description of the paraxial Laguerre–Gaussian (LG) modes suitable for modeling beams down to f/2 focal geometries is derived. A perturbative approach to modeling asymmetric OAM beams is introduced showing that only three LG modes are sufficient to model a wide variety of OAM asymmetries. The models are compared with experimental results followed by a discussion on the future of high intensity OAM beams in plasma physics.
Hybrid entanglement swapping of photons: Creating the orbital angular momentum Bell states and Greenberger-Horne-Zeilinger states
Twisted photons offer a high-dimensional Hilbert space with the degree of freedom of orbital angular momentum (OAM). Entanglement swapping allows entangling photons that never interact. We report in this paper the hybrid entanglement swapping from multiphoton spin-entangled states to multiphoton OAM entangled states with the aid of N-pair hybrid spin-OAM entangled photons. Our scheme provides a feasible method for creating the two-photon OAM Bell states (N=2) or multiphoton multidimensional OAM Greenberger-Horne-Zeilinger states (N{>=}3). We highlight the advantage of multiparticle, multidimensional entangled states in some applications of quantum information protocols.
Spin-textured neutron beams with orbital angular momentum
In this work, we present a rigorous theoretical framework underpinning the technique of spin-echo modulated small-angle neutron scattering (SEMSANS), and show how the technique can be extended in order to generate spin-textured neutron beams with orbital angular momentum (OAM) via birefringent neutron spin-polarization devices known as magnetic Wollaston prisms. Neutron OAM beams are mathematically characterized by a “cork-screw” phase singularity e iℓΦ about the propagation axis where ℓ is the OAM quantum number. To understand the precise relationship between the emergent OAM state and the variety of spin textures realized by various setups, we have developed a path-integral approach that in the interferometric limit makes a judicious use of magnetic Snell's law. We show that our proposed technique produces a complex two-dimensional pattern of spin-OAM entangled states which may be useful as a probe of quantum magnetic materials. We compare our path-integral approach to the well-known single-path Larmor precession model and present a pedagogical derivation of magnetic Snell's law of refraction for both massive and massless particles based on Maupertuis's action principle.
Elastic dijet production in electron scattering on a longitudinally polarized proton at small x : A portal to orbital angular momentum distributions
We calculate the elastic production of dijets from electron collisions with a longitudinally polarized proton target at small values of the Bjorken x variable. Building on the pioneering proposals of Hatta [Gluon orbital angular momentum at small- x , .] and Bhattacharya [Signature of the gluon orbital angular momentum, ., Probing the quark orbital angular momentum at electron-ion colliders using exclusive π 0 production, ., and Exploring orbital angular momentum and spin-orbit correlation for gluons at the Electron-Ion Collider, .] for measuring the quark and gluon orbital angular momentum (OAM) distributions, our focus is on both the longitudinal double spin asymmetry (DSA) and longitudinal single spin asymmetry (SSA). We compute the numerators of these asymmetries in the small- x formalism of the light-cone operator treatment. Utilizing the small- x expressions for the OAM distributions derived earlier in Kovchegov and Manley [Orbital angular momentum at small x revisited, .], we demonstrate that the DSA provides a robust probe for both the quark and gluon OAM distributions within the proton. In contrast, we find that while the SSA is also sensitive to the OAM distributions, extraction of the latter from the SSA would require new developments in small- x theory and phenomenology, and is probably not feasible at this point in time. These findings highlight the potential of DSA measurements in elastic dijet production at the future Electron-Ion Collider to provide the first-ever direct access to the quark and gluon OAM distributions at small x , paving the way for new insights into the proton spin puzzle. Published by the American Physical Society 2025
X-ray pulse generation with ultra-fast flipping of its orbital angular momentum
A method to temporally tailor the properties of X-ray radiation carrying Orbital Angular Momentum (OAM) is presented. In simulations, an electron beam is prepared with a temporally modulated micro-bunching structure which, when radiating at the second harmonic in a helical undulator, generates OAM light with a corresponding temporally modulated intensity. This method is shown to generate attosecond pulse trains of OAM light without the need for any additional external optics, making the wavelength range tunable. In addition to the OAM pulse train, the method can be adapted to generate radiation where the handedness of the OAM mode may also be temporally modulated (flipped).