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Physical Review A

Scheme for optical implementation of orbital angular momentum beam splitter of a light beam and its application in quantum information processing

Xu‐Bo Zou, Wolfgang M. Mathis

Published Apr 14, 2005• 35 citations
Publisher

Abstract

Optical beams bearing orbital angular momentum have been recently recognized as potential candidates for realizing $D$-dimensional quantum systems (qudits). In this paper, we propose an optical scheme to implement an orbital angular momentum beam splitter, which changes the outgoing direction with respect to the incoming direction while leaving the qudit state unchanged. Furthermore we demonstrate that such a beam splitter can be used to sort different orbital angular states of a single photon, create arbitrary superpositions of orbital angular momentum states, and implement a high-dimensional Bennett-Brassard 1984 protocol for quantum key distribution.

DOI
10.1103/physreva.71.042324

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Optical beams bearing orbital angular momentum have been recently recognized as potential candidates for realizing DDD-dimensional quantum systems (qudits). In this paper, we propose an optical scheme to implement an orbital angular momentum beam splitter, which changes the outgoing direction with respect to the incoming direction while leaving the qudit state unchanged. Furthermore we demonstrate that such a beam splitter can be used to sort different orbital angular states of a single photon, create arbitrary superpositions of orbital angular momentum states, and implement a high-dimensional Bennett-Brassard 1984 protocol for quantum key distribution.
In recent years, the high-dimensional properties of the orbital angular momentum degree of freedom of light have attracted extensive attention. This degree of freedom has been studied and used in many scientific fields, especially in optical communication and quantum information. In order to fully utilize the high-dimensional properties of orbital angular momentum, non-destructive separation of different orbital angular momentum states has become a fundamental requirement. However, the existing orbital angular momentum beam-splitting systems either lack stability and cascade expansibility, or the properties of the separated orbital angular momentum states are seriously damaged, thus failing to participate in further interaction processes. In this work, we construct a miniature Mach-Zehnder interferometer based on the beam displacer, and design an orbital angular momentum beam splitter, thereby realizing the non-destructive beam splitting of orbital angular momentum mode. In the orbital angular momentum splitter, the theoretical energy loss is zero because there exists only total reflection of the beam. The beam in the miniature Mach-Zehnder interferometer passes through the same optical element, and the spatial deviation of the beam is small, so the orbital angular momentum beam splitter has good stability. In addition, because the separated orbital angular momentum state has the same propagation direction as the incident orbital angular momentum state, the beam splitter has good extensibility and is easy to use in cascade. Our research result is of great significance in using the orbital angular momentum as a high-dimensional degree of freedom in optical communication and other related fields.
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.
The beam with orbital angular momentum is a present domestic and foreign research key direction. Its application and development will bring the profound influence in the optical communications field. At the same time, light's orbital angular momentum promises potential applications in both classical and quantum optical communication. The research progress of the beam with orbital angular momentum and encoding information as light's OAM for free-space optical communication were reviewed in this article, the existing design method, mechanism and description methods of encoding information as light's OAM were discussed. In quantum communication, qudits can be encoded in photons using their OAM for creating high-dimensional entanglement based on entangled photon pairs from SPDC. In this paper, light's OAM is used as information carrier for classical and quantum communication, which is promising to ensures the security of atmospheric laser communication, improves the density and precision of information transmission. It is apparent that an efficient way to measure the orbital angular momentum of individual photons and light beams with good efficiency would be of potentially great importance for optical communications and quantum information. In view of the above, the measurements of orbital angular momentum of individual photons and light beams are analyzed and discussed in detail.
Single photons with orbital angular momentum (OAM) have attracted substantial attention from researchers. A single photon can carry infinite OAM values theoretically. Thus, OAM photon states have been widely used in quantum information and fundamental quantum mechanics. Although there have been many methods for sorting quantum states with different OAM values, the nondestructive and efficient sorter of high-dimensional OAM remains a fundamental challenge. Here, we propose a scalable OAM sorter which can categorize different OAM states simultaneously, meanwhile, preserving both OAM and spin angular momentum. Fundamental elements of the sorter are composed of symmetric multiport beam splitters (BSs) and Dove prisms with cascading structure, which in principle can be flexibly and effectively combined to sort arbitrarily high-dimensional OAM photons. The scalable structures proposed here greatly reduce the number of BSs required for sorting high-dimensional OAM states. In view of the nondestructive and extensible features, the sorters can be used as fundamental devices not only for high-dimensional quantum information processing, but also for traditional optics.
Among all degrees of freedom offered by single photons, the orbital angular momentum (OAM) has a great potential in the quantum information field, as it provides a natural choice for implementing single-photon qudits, the units of quantum information in a higher dimensional space. This can be an important practical advantage, as it enables higher security in quantum cryptographic protocols, as well as implications in fundamental quantum mechanics theory. Moreover, the combined use of different degrees of freedom of a photon, such as OAM and spin, enables the implementation of entirely new quantum tasks.
Measuring the state of a quantum system is a fundamental process in quantum mechanics and plays an essential role in quantum information and quantum technologies. One method to measure a quantum observable is to sort the system in different spatial modes according to the measured value, followed by single-particle detectors on each mode. Examples of quantum sorters are polarizing beam-splitters (PBS) - which direct photons according to their polarization - and Stern-Gerlach devices. Here we propose a general scheme to sort a quantum system according to the value of any d-dimensional degree of freedom, such as spin, orbital angular momentum (OAM), wavelength etc. Our scheme is universal, works at the single-particle level and has a theoretical efficiency of 100%. As an application we design an efficient OAM sorter consisting of a single multi-path interferometer which is suitable for a photonic chip implementation.