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Robust and adjustable C-shaped electron vortex beams

Mousley, Michael Gordon, Thirunavukkarasu, Gnanavel, M. Babiker, Yuan, Jun

Published Apr 20, 2017• 10 citations
OpenAlex

Abstract

Wavefront engineering is an important quantum technology, often applied to the production of states carrying orbital angular momentum (OAM). Here, we demonstrate the design and production of robust C-shaped beam states carrying OAM, in which the usual doughnut shaped transverse intensity structure of the vortex beam contains an adjustable gap. We find that the presence of the vortex lines in the core of the beam is crucial for maintaining the stability of the C-shape structure during beam propagation. The topological charge of the vortex core controls mainly the size of the C-shape, while its opening angle is related to the presence of vortex-anti-vortex loops. We demonstrate the generation and characterisation of C-shaped electron vortex beams, although the result is equally applicable to other quantum waves. C-shaped electron vortex beams have potential applications in nanoscale fabrication of planar split ring structures and three dimensional chiral structures as well as depth sensing and magnetic field determination through rotation of the gap in the C-shape.

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Robust and adjustable C-shaped electron vortex beams

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Wavefront engineering is an important quantum technology, often applied to the production of states carrying orbital angular momentum (OAM). Here, we demonstrate the design and production of robust C-shaped beam states carrying OAM, in which the usual doughnut-shaped transverse intensity structure of the vortex beam contains an adjustable gap. We find that the presence of the vortex lines in the core of the beam is crucial for maintaining the stability of the C-shape structure during beam propagation. The topological charge of the vortex core controls mainly the size of the C-shape, while its opening angle is related to the presence of vortex–anti-vortex loops. We demonstrate the generation and characterisation of C-shaped electron vortex beams, although the result is equally applicable to other quantum waves. C-shaped electron vortex beams have potential applications in nanoscale fabrication of planar split-ring structures and three-dimensional chiral structures as well as depth sensing and magnetic field determination through rotation of the gap in the C-shape.

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Wavefront engineering is an important quantum technology, often applied to the production of states carrying orbital angular momentum (OAM). Here, we demonstrate the design and production of robust C-shaped beam states carrying OAM, in which the usual doughnut shaped transverse intensity structure of the vortex beam contains an adjustable gap. We find that the presence of the vortex lines in the core of the beam is crucial for maintaining the stability of the C-shape structure during beam propagation. The topological charge of the vortex core controls mainly the size of the C-shape, while its opening angle is related to the presence of vortex-anti-vortex loops. We demonstrate the generation and characterisation of C-shaped electron vortex beams, although the result is equally applicable to other quantum waves. C-shaped electron vortex beams have potential applications in nanoscale fabrication of planar split ring structures and three dimensional chiral structures as well as depth sensing and magnetic field determination through rotation of the gap in the C-shape.
Wavefront engineering is an important quantum technology, often applied to the production of states carrying orbital angular momentum (OAM). Here, we demonstrate the design and production of robust C-shaped beam states carrying OAM, in which the usual doughnut-shaped transverse intensity structure of the vortex beam contains an adjustable gap. We find that the presence of the vortex lines in the core of the beam is crucial for maintaining the stability of the C-shape structure during beam propagation. The topological charge of the vortex core controls mainly the size of the C-shape, while its opening angle is related to the presence of vortex–anti-vortex loops. We demonstrate the generation and characterisation of C-shaped electron vortex beams, although the result is equally applicable to other quantum waves. C-shaped electron vortex beams have potential applications in nanoscale fabrication of planar split-ring structures and three-dimensional chiral structures as well as depth sensing and magnetic field determination through rotation of the gap in the C-shape.
We conduct theoretical investigations into a fundamental closed-loop Λ-type atomic system using 87 Rb atoms, aiming to efficiently generate and manipulate structured light beams. A phase-singular microwave (MW) beam with a topological charge l μ and a phase-singular optical probe beam with a topological charge l p collectively induce phase-dependent atomic coherence, resulting in periodic oscillations of probe absorption in the transverse plane. The number of absorption or transparency windows in the transverse plane is determined by the resultant topological charge of the system, denoted as l = l μ − l p . We investigate the propagation of a paraxial doughnut-shaped probe beam through the phase-dependent atomic medium and showcase the generation of petal-like structured beams for various combinations of l μ and l p . We provide a detailed theoretical explanation of these results using the analytical expression of probe susceptibility. We outline how this scheme effectively serves as a sensor adept at discerning particular OAM modes. This selective detection capability is valuable in scenarios where only certain OAM states carry relevant information. The relative phase between the interacting fields can be used to rotate the structured probe beam by 360 deg in the clockwise or counterclockwise direction. This manipulation of spatial position of different OAM modes can be employed in implementing OAM-based logical operations.
Abstract Spatially structured optical reflection and phase modulation in cavity quantum electrodynamics present a pathway to programmable control of structured light and topological photonic states. This study examines the spatial response of a three-level atom–assisted single-sided cavity, driven by a composite vortex control field, by analyzing the transverse distributions of the reflection coefficient and reflected-phase shift as influenced by variations in cavity decay rate, external coupling strength, and the orbital angular momentum (OAM) content of the driving fields. The control Rabi frequency Ω l ( r , ϕ ) , which inherits the doughnut-shaped amplitude and helical phase of vortex beams, results in position-dependent atomic coherence and effective cavity susceptibility, imprinting ring-like or petal-like textures onto both reflectivity and phase. For symmetric counter-rotating vortices with l 1 = − l 2 = 1 − 4 , the reflection forms 2 l -petal patterns, and the phase exhibits complementary 2 l -fold lobes with sharp phase-gradient boundaries dictated by cos ⁡ ( 2 l ϕ ) interference, while central singular features intensify with OAM order. In the case of asymmetric OAM pairs, rotational symmetry is disrupted, and the spatial spectra are primarily determined by Δ l = 3 and 5, respectively, resulting in distorted threefold and fivefold modulations with localized singular defects and star-like phase topology.
Vortex beams with different topological charge usually have different profiles and radii of peak intensity. This introduces a degree of complexity the fair study of the nature of optical OAM (orbital angular momentum). To avoid this, we introduced a new approach by creating a perfect vortex beam using an annular illuminating beam with a fixed intensity profile on an SLM that imposes a chosen topological charge. The radial intensity profile of such an experimentally created perfect vortex beam is independent to any given integer value of its topological charge. The well-defined OAM density in such a perfect vortex beam is probed by trapping microscope particles. The rotation rate of a trapped necklace of particles is measured for both integer and non-integer topological charge. Experimental results agree with the theoretical prediction. With the flexibility of our approach, local OAM density can be corrected in situ to overcome the problem of trapping the particle in the intensity hotspots. The correction of local OAM density in the perfect vortex beam therefore enables a single trapped particle to move along the vortex ring at a constant angular velocity that is independent of the azimuthal position. Due to its particular nature, the perfect vortex beam may be applied to other studies in optical trapping of particles, atoms or quantum gases.
Optical vortex beams are profiled as helical wavefronts with a phase singularity carrying an orbital angular momentum (OAM) associated with their spatial distribution. The transverse intensity distribution of a conventional optical vortex has a strong dependence on the carried topological charge. However, perfect optical vortex (POV) beams have their transverse intensity distribution independent of their charge. Such “size-invariant” POV beams have found exciting applications in optical manipulation, imaging, and communication. In this paper, we investigate the use of POV modes in the efficient generation of high-dimensional quantum states of light. We generate heralded single photons carrying OAM using spontaneous parametric downconversion (SPDC) of POV beams. We show that the heralding efficiency of the SPDC single photons generated with a POV pump is greater than that with normal optical vortex beams. The dimensionality of the two-photon OAM states is increased with POV modes in the pump and projective measurements using Bessel–Gaussian vortex modes that give POV, instead of Laguerre–Gaussian modes.
Chiral electron-vortex beams, carrying a well-defined orbital angular momentum (OAM) about the propagation axis, are potentially useful as probes of magnetic and other chiral materials. We present an effective operator, expressible in a multipolar form, describing the inelastic processes in which electron-vortex beams interact with atoms, including those present in Bose-Einstein condensates, involving exchange of OAM. We show clearly that the key properties of the processes are dependent on the dynamical state and location of the atoms involved as well as the vortex-beam characteristics. Our results can be used to identify scenarios in which chiral-specific electron-vortex spectroscopy can probe magnetic sublevel transitions normally studied using circularly polarized photon beams with the advantage of atomic-scale spatial resolution.