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arXiv:1310.4901 · Physical Review A

Making and identifying optical superpositions of high orbital angular momenta

Lixiang Chen, Wuhong Zhang, Qinghong Lu, Xinyang Lin

Published Nov 20, 2013• 57 citations
arXivHTMLPDF

Abstract

We report the experimental preparation of optical superpositions of high orbital angular momenta (OAM). Our method is based on the use of a spatial light modulator to modify the standard Laguerre-Gaussian beams to bear excessive phase helices. We demonstrate the surprising performance of a traditional Mach-Zehnder interferometer with one inserted Dove prism to identify these superposed twisted lights, where the high OAM numbers as well as their possible superpositions can be inferred directly from the interfered bright multiring lattices. The possibility of the present scheme working at the photon-count level is also shown using an electron multiplier CCD camera. Our results hold promise in high-dimensional quantum-information applications when high quanta are beneficial.

DOI
10.1103/physreva.88.053831

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We report the experimental preparation of optical superpositions of high orbital angular momenta (OAM). Our method is based on the use of a spatial light modulator to modify the standard Laguerre-Gaussian beams to bear excessive phase helices. We demonstrate the surprising performance of a traditional Mach-Zehnder interferometer with one inserted Dove prism to identify these superposed twisted lights, where the high OAM numbers as well as their possible superpositions can be inferred directly from the interfered bright multiring lattices. The possibility of the present scheme working at the photon-count level is also shown using an electron multiplier CCD camera. Our results hold promise in high-dimensional quantum-information applications when high quanta are beneficial.
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.
Orbital angular momentum (OAM) of single photons represents a new optical degree of freedom for the entanglement of photons [1,2]. One physical realization of OAM carrying light beams are the so called Laguerre-Gaussian modes of light with the required helical phase structure. One big advantage over the well known polarization degree of freedom is the possibility of realizing entanglement between two photons with very high quantum numbers. However, the creation of photonic OAM entanglement using the widely used spontaneous parametric downconversion process is limited by the strongly reduced efficiency for higher momenta [3]. We have realized a novel method to create entanglement between two photons with a very high difference in their OAM quantum number and momentum respectively. Furthermore we have explored hybrid entanglement of photons in the OAM and polarization degree of freedom.
Light carrying orbital angular momentum (OAM) has many applications ranging from optical manipulation, imaging and remote sensing, and optical communications, and can be used to perform fundamental studies in quantum mechanics and quantum information. Moreover, single photons with high-order OAM allow for increasing the amount of information carried per photon in quantum communication. This thesis describes the study of methods for the preparation and detection of OAM of light in high mode order by utilizing beam shaping techniques using spatial light modulators (SLMs). The quality of the generated high-order OAM mode is limited by optical aberrations which are induced by optical elements in realistic systems and propagation through realistic channels. In order to create and characterize the OAM modes with high quality, we investigate methods for aberration detection and correction using SLMs. These beam shaping techniques for the correction of optical aberrations allow us to generate and detect light carrying OAM with mode order ranging from l = 0 to l = 8 with good quality, and to generate high-quality superpositions of OAM modes with high mode order or in high dimensions. Furthermore, we observe low crosstalk and good levels of mode discrimination between different OAM modes of light. Our experimental setup can be applied in future studies to investigate and test different protocols in quantum information with high dimensional systems, such as high dimensional quantum state tomography.
Detection of photons in orbital angular momentum (OAM) superposition states is crucial to verification of OAM entanglement. In the past this has been realized by laterally shifting a hologram designed to remove a charge 1 phase singularity at its center. Such a laterally shifted hologram converts a beam with an off-center singularity (similar to that created by superposing an m = 0 beam and an m = 1 beam, where in is the OAM mode number) into a Gaussian beam, which is then filtered through a single mode fiber (SMF). However, it has been shown that a photon detected by this method is not a simple superposition of a photon in the m = 0 Gaussian mode and the m = 1 mode detected with an unshifted hologram, making it necessary to apply complicated analysis. One problem is that the radial distributions of the detected m = 0 and 1 components as determined by the SMF change as the hologram is shifted. Another, possibly more serious problem is the mixing of other OAM components. To overcome this problem we propose a new scheme for the detection of OAM superposition states consisting of a hologram and a path interferometer. The hologram is designed so that the output is equally distributed between the 0th and 1st order diffraction beams. The 0th order is the input beam itself, whose m = 0 Gaussian component is filtered through an SMF. In the 1st order beam the m = 1 component is converted to m = 0 and is filtered through a second SMF. The filtered beams now have the same spatial distribution, and can be superposed by a beam splitter. By inserting attenuators and phase modulators within the interferometer, superpositions with varying amplitude ratios and relative phases can be detected without shifting the hologram.