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arXiv:2112.06277

Efficient full state tomography of the orbital angular momentum states of light using Helicity sorter

Joel M. Sunil, Goyal, Sandeep K.

Published Dec 12, 2021• 0 citations
arXivHTMLPDF

Abstract

Orbital angular momentum (OAM) of light is a promising degree of freedom for quantum communication and quantum computation. However, efficient methods to transform and measure OAM modes are still not available readily. Here, we propose a method for full quantum state tomography for arbitrary OAM states of light. The key component in our scheme is the helicity sorter, a device that can sort OAM modes of a light beam based on their Helicity. We present two setups to implement the Helicity sorted, one requires $\mathcal{O}(N)$ number of optical elements for $2^N$ OAM modes, and the other uses spatial light modulators and is independent of the number of OAM modes. Ours is the first method to provide the efficient and scalable full quantum state tomography of the OAM modes and can be extremely important for quantum communication and quantum computation.

DOI
10.48550/arxiv.2112.06277

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Orbital angular momentum (OAM) of light is a promising degree of freedom for quantum communication and quantum computation. However, efficient methods to transform and measure OAM modes are still not available readily. Here, we propose a method for full quantum state tomography for arbitrary OAM states of light. The key component in our scheme is the helicity sorter, a device that can sort OAM modes of a light beam based on their Helicity. We present two setups to implement the Helicity sorted, one requires O(N)\mathcal{O}(N)O(N) number of optical elements for 2N2^N2N OAM modes, and the other uses spatial light modulators and is independent of the number of OAM modes. Ours is the first method to provide the efficient and scalable full quantum state tomography of the OAM modes and can be extremely important for quantum communication and quantum computation.
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.
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.
While measuring the orbital angular momentum state of bright light beams can be performed using imaging techniques, a full characterization at the single-photon level is challenging. For applications to quantum optics and quantum information science, such characterization is an essential capability. Here, we present a setup to perform the quantum state tomography of photonic qubits encoded in this degree of freedom. The method is based on a projective technique using spatial mode projection via fork holograms and single-mode fibers inserted into an interferometer. The alignment and calibration of the device is detailed as well as the measurement sequence to reconstruct the associated density matrix. Possible extensions to higher-dimensional spaces are discussed.
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.
The orbital angular momentum of light (OAM) is a fundamental property of light. Beams with OAM have a helical wave front that carries quantized orbital angular momentum L hbar per photon, where L is any integer. This unbounded Hilbert space can increase information capacity of both classical and quantum communications and also improve and extend qubit and qudit quantum algorithms. Additionally, the use of the OAM modes allows for novel imaging techniques to directly observe and measure various topological properties of objects ranging from defects in semiconductors to rotating black holes and extrasolar planets. However, measuring such higher dimensional OAM states is fundamentally important, albeit challenging, in order to use this rich degree of freedom. In the work that follows, I present two novel OAM to time mapping schemes and an application using the higher dimensionality of OAM to non-destructively probe quantum states. These are the first OAM measuring schemes to use the temporal degree of freedom to measure OAM. The use of the novel loop nature allows for high fidelity and high speed measurements of a large number of OAM states without significant increase in experimental resources. The first scheme experimentally demonstrates a compact and practical device to measure the OAM spectrum. I report a fidelity of -21.3 dB for 5 different OAM states. The second scheme extends the first, but uses non-demolition measurements to iteratively test for specific OAM values. While this increases experimental complexity, it allows for the detection of an arbitrarily large OAM value from a single photon. I also discuss details of each technique investigate the affects of misalignment on the OAM spectrum. In the remaining part, I discuss my novel generalized quantum Zeno interrogation. The original quantum Zeno interrogation is limited to the two-dimensional state of a single object; while the generalized version has the ability to non-destructively probe the quantum state a set of objects, and deterministically imprint that information onto a single photon using the OAM degree of freedom.
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 ddd-dimensional degree of freedom, such as spin, orbital angular momentum (OAM), wavelength etc. Our scheme is universal, works at 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.