We point out a link between orbital angular momentum (OAM) carrying light beams and number theory. The established link makes it possible to formulate and implement a simple and ultrafast protocol for prime number factorization by employing OAM endowed beams that are modulated by a prime number sieve. We are able to differentiate factors from non-factors of a number by simply measuring the on-axis intensity of light in the rear focal plane of a thin lens focusing on a source beam. The proposed protocol solely relies on the periodicity of the OAM phase distribution, and hence, it is applicable to fully as well as partially coherent fields of any frequency and physical nature—from optical or x-ray to matter waves—endowed with OAM. Our experimental results are in excellent agreement with our theory. We anticipate that our protocol will trigger new developments in optical cryptography and information processing with OAM beams.
We point out a link between orbital angular momentum (OAM) carrying light beams and number theory. The established link makes it possible to formulate and implement a simple and ultrafast protocol for prime number factorization by employing OAM endowed beams that are modulated by a prime number sieve. We are able to differentiate factors from non-factors of a number by simply measuring the on-axis intensity of light in the rear focal plane of a thin lens focusing on a source beam. The proposed protocol solely relies on the periodicity of the OAM phase distribution, and hence, it is applicable to fully as well as partially coherent fields of any frequency and physical nature—from optical or x-ray to matter waves—endowed with OAM. Our experimental results are in excellent agreement with our theory. We anticipate that our protocol will trigger new developments in optical cryptography and information processing with OAM beams.
The study of optical beams with orbital angular momentum (OAM) has gained the interest of researchers since the seminal work of the Woerdman group in Leiden in 1992. These beams have been used as optical tweezers, as a tool for high-resolution nanoscopy, as a new instrument for increased angular resolution measurement, and as a resource for increased channel capacity in optical communications and high-dimensional information carrier for diverse applications in quantum information science among others. In this presentation, I will introduce beams with OAM, their properties and peculiarities. I will talk about how these beams are generated with a focus on the coherent generation of these kinds of beams using sum-frequency generation. I will discuss the applications of these beams in detecting spinning object, and as pointer states to probe joint weak value in weak measurements. I will end my talk with possible directions for this field of research.
The orbital angular momentum (OAM) carried by optical beams is a useful quantity for encoding information. This form of encoding has been incorporated into various works ranging from telecommunications to quantum cryptography, most of which require methods that can rapidly process the OAM content of a beam. Among current state-of-the-art schemes that can readily acquire this information are so-called OAM sorters, which consist of devices that spatially separate the OAM components of a beam. Such devices have found numerous applications in optical communications, a field that is in constant demand for additional degrees of freedom, such as polarization and wavelength, into which information can also be encoded. Here, we report the implementation of a device capable of sorting a beam based on its OAM and polarization content, which could be of use in works employing both of these degrees of freedom as information channels. After characterizing our fabricated device, we demonstrate how it can be used for quantum communications via a quantum key distribution protocol.
We study theoretically the orbital angular momentum (OAM) density in arbitrary scalar optical fields, and outline a simple approach using only a spatial light modulator to measure this density. We demonstrate the theory in the laboratory by creating superpositions of non-diffracting Bessel beams with digital holograms, and find that the OAM distribution in the superposition field matches the predicted values. Knowledge of the OAM distribution has relevance in optical trapping and tweezing, and quantum information processing.
This Chapter presents a review of the quantum mechanical properties of spatially structured light fields, specifically those fields carrying orbital angular momentum (OAM). This review is concerned both with the conceptual understanding of the quantum features of these light fields and with the use of these features for applications. We describe how to produce spatially entangled light fields by means of the nonlinear optical process of parametric downconversion. We ask and provide a tentative answer to the question of how much information can be encoded into a single photon. As an example, we review a recent experiment that demonstrated the ability to discriminate among four target objects using only one photon for illumination. We also present a description of the concept of the OAM of light, and we describe means to generate and detect OAM. We then present a brief survey of some recent studies of the fundamental quantum properties of structured light beams. Much of this work is aimed at studying the nature of entanglement for the complementary variables of angular position and OAM. Finally, as a realworld application, we describe a secure communication system based on quantum key distribution (QKD). This key distribution system makes use of encoding information in the OAM modes of light and hence is able to transmit more than one bit of information per photon. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Photons are an ideal candidate for encoding both classical and quantum information. Besides spin angular momentum associated with circular polarization, single photon can also carry other fundamentally new degree of freedom of orbital angular momentum related to the spiral phase structure of light. The key significance of orbital angular momentum lies in its potential in realizing a high-dimensional Hilbert space and in encoding a high-dimensional quantum information. Since Allen et al. [Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185] recognized the physical reality of photon orbital angular momentum in 1992, rapidly growing interest has been aroused in orbital angular momentum (OAM) from both classical and quantum points of view. Here we present an overall review on the high-order orbital angular momentum of photon, including its preparation and manipulation based on some specific techniques and also its applications. The spatial light modulator is a commercial device that has been widely employed to generate the OAM beams. We make and identify the optical OAM superposition with very high quantum numbers up to l=360. Recently, the metallic spiral phase mirrors were also developed to produce high-order OAM beams up to l=5050. In addition, the Q-plates made of anisotropic and inhomogeneous liquid crystals were invented to generate high-order OAM beams in a polarization-controllable manner, and the OAM superposition of l=± 50 were achieved. Owing to high rotational symmetry, these high OAM beams have been found to have more and more important applications in the fields of high-sensitivity sensing and high-precision measurements. Two fascinating examples are discussed in detail. The first example is that the research group led by Prof. Zeilinger has prepared and observed the quantum entanglement of high orbital angular momenta up to l=±300 by the technique of polarization-OAM entanglement swapping, and they demonstrated that the angular resolution could be significantly improved by a factor of l. Their result was the first step for entangling and twisting even macroscopic, spatially separated objects in two different directions. The second example is that the research group led by Prof. Padgett has demonstrated an elegant experiment of rotational Doppler effects for visible light with l=±20 OAM superposition. They showed that a spinning object with an optically rough surface might induce a Doppler effect in light reflected from the direction parallel to the rotation axis, and the frequency shift was proportional to both the disk's angular speed and the optical OAM. The potential applications in noncontact measurement of angular speed and in significant improvement of angular resolution for remote sensing will be particularly fascinating.
High-dimensional quantum computing has emerged as a recent alternative to conventional qubit-based approaches, offering advantages such as an increased information density and enhanced robustness against noise. In this work, we explore the use of the orbital angular momentum (OAM) of light as a degree of freedom in which high-dimensional quantum gates can be implemented. We present a theoretical and experimental study of structured light beams carrying OAM, with emphasis on Laguerre–Gauss modes, as a natural basis for high-dimensional quantum computing. We then describe the generation of OAM beams using computer-generated holograms and spatial light modulators, detailing practical methods for encoding arbitrary phase profiles. Building on this framework, we analyze the implementation of high-dimensional quantum logic gates, focusing on the generalized Pauli Z_d and X_d operations. Optical setups based on Dove prisms, Sagnac interferometers, spiral phase plates, and parity sorters are proposed and theoretically validated. Finally, we report experimental results demonstrating the generation of Laguerre–Gauss beams, the transformation properties of Dove prisms, and the operation of a parity sorter, which constitutes a building block for realizing high-dimensional quantum gates. These results establish a solid foundation for future implementations of high-dimensional quantum information processing using the orbital angular momentum of light.