The orbital angular momentum (OAM) of light is an infinite-dimensional degree of freedom of light with several applications in both classical and quantum optics. However, to fully take advantage of the potential of OAM states, reliable detection platforms to characterize generated states in experimental conditions are needed. Here, we present an approach to reconstruct input OAM states from measurements of the spatial intensity distributions they produce. To obviate issues arising from intrinsic symmetry of Laguerre-Gauss modes, we employ a pair of intensity profiles per state projecting it only on two distinct bases, showing how this allows to uniquely recover input states from the collected data. Our approach is based on a combined application of dimensionality reduction via principal component analysis, and linear regression, and thus has a low computational cost during both training and testing stages. We showcase our approach in a real photonic setup, generating up-to-four-dimensional OAM states through quantum walk dynamics. The high performance and versatility of the demonstrated approach make it an ideal tool to characterize high-dimensional states in quantum information protocols.
The orbital angular momentum (OAM) of light is an infinite-dimensional degree of freedom of light with several applications in both classical and quantum optics. However, to fully take advantage of the potential of OAM states, reliable detection platforms to characterize generated states in experimental conditions are needed. Here, we present an approach to reconstruct input OAM states from measurements of the spatial intensity distributions they produce. To obviate issues arising from intrinsic symmetry of Laguerre-Gauss modes, we employ a pair of intensity profiles per state projecting it only on two distinct bases, showing how this allows to uniquely recover input states from the collected data. Our approach is based on a combined application of dimensionality reduction via principal component analysis, and linear regression, and thus has a low computational cost during both training and testing stages. We showcase our approach in a real photonic setup, generating up-to-four-dimensional OAM states through quantum walk dynamics. The high performance and versatility of the demonstrated approach make it an ideal tool to characterize high-dimensional states in quantum information protocols.
Accurate reconstruction of the complex spectrum of orbital angular momentum (OAM) superposition states is crucial for their application in high-capacity optical communications and quantum information, yet existing methods are often constrained by system complexity, extensive data requirements, or incomplete information retrieval. Here, we propose and experimentally demonstrate an iterative algorithm that enables high-fidelity recovery of the complex OAM spectrum of high-dimensional superpositions from only a few sparsely sampled patterns. The method integrates the Laguerre-Gaussian (LG) modal basis as an a priori constraint, which enables the direct retrieval of spectral coefficients by circumventing intermediate field reconstruction. To validate its performance, we reconstructed a test field composed of a random superposition of 21 LG modes, achieving fidelities of 99.3% in simulation and 97.2% in experiment using only four sparse sampling patterns. This work provides an efficient and robust tool for characterizing high-dimensional structured light, with significant potential in optical communication and quantum science.
Orbital angular momentum (OAM) is one of the most recently discovered properties of light, and it is only in the past decade its quantum properties have been the subject of experimental investigations and have found applications. Unlike polarization, which is only bidimensional, orbital angular momentum provides, with relative ease, unprecedented access to a theoretically unbounded discrete state space. The process of spontaneous parametric down-conversion has long been used as a source of two-photon states that can be entangled in several degrees of freedom, including OAM. In this thesis, the properties of the natural OAM spectrum associated with the entangled states produced by parametric down-conversion were investigated. Chapters 2 and 3 describe the production and detection of tunable high-dimensional OAM entanglement in a down-conversion system. By tuning the phase-matching conditions and improving the detection stage, a substantial increase in the half-width of the OAM correlation spectrum was observed. The conjugate variable of OAM, angular position, was also considered when examining high-dimensional states entangled in OAM. In order to efficiently determine their dimension, high-dimensional entangled states were probed by implementing a technique based on phase masks composed of multiple angular sectors, as opposed to narrow single-sector analysers. Presented in chapter 4, this technique allows the measurements of tight angular correlations while maintaining high optical throughput. The states so produced were then used for a number of applications centred around the concept of mutually unbiased bases. One can define sets of mutually unbiased bases for arbitrary subspaces of the OAM state space. Two bases are mutually unbiased if the measurement of a state in one basis provides no information about the state as described in the other basis. Complete measurements in mutually unbiased bases of high-dimensional OAM spaces are presented in chapter 5. Measurements in sets of mutually unbiased bases are integral to quantum science and can be used in a variety of protocols that fully exploit the large size of the OAM state space; we describe their use in efficient quantum state tomography, quantum key distribution and entanglement detection. Caution is however necessary when dealing with state spaces embedded in higher-dimensional spaces, such as that provided by OAM. Experimental tests of Bell-type inequalities allow us to rule out local hidden variable theories in the description of quantum correlations. Correlations inconsistent with the states observed, or even with quantum mechanics, known as super-quantum correlations, have however been recorded previously in experiments that fail to comply with the fair-sampling conditions. Chapter 6 describes an experiment that uses a particular choice of transverse spatial modes for which super-quantum correlations persist even if the detection is made perfectly efficient. The sets of modes carrying OAM allow a complete description of the transverse field. The ability to control and combine additional degrees of freedom provides the possibility for richer varieties of entanglement and can make quantum protocols more powerful and versatile. One such property of light, associated with transverse modes possessing radial nodes in the field distribution, can be accessed within the same type of experimental apparatus used for OAM. In chapter 7, the radial degree of freedom is explored, together with OAM, in the context of Hong-Ou-Mandel interference.
The capability to engineer and characterize high dimensional states has become a crucial request in the quantum information field. The quantum walk dynamics proved to be a suitable resource for developing general quantumstate engineering protocols. Here, we experimentally verified the flexibility of an engineering protocol based on a one-dimensional quantum walk in the Orbital Angular Momentum (OAM). Although this degree of freedom has found several applications in the quantum information field, extract the information stored in them appears to be difficult. Therefore, we employ machine learning protocols to classify and characterize particularly structured beams endowed with a not uniform distribution of the polarization on the transverse plane. Moreover, we prove that by modeling the engineering process through a refined model it is possible to improve the performances of measurement techniques such as holographic projection and machine-learning based classification. These results represent a further investigation in the manipulation and detection of OAM modes coupling the photonics platforms with machine-learning protocols.
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.
Experimental engineering of high-dimensional quantum states is a crucial task for several quantum information protocols. However, a high degree of precision in the characterization of the noisy experimental apparatus is required to apply existing quantum-state engineering protocols. This is often lacking in practical scenarios, affecting the quality of the engineered states. We implement, experimentally, an automated adaptive optimization protocol to engineer photonic orbital angular momentum (OAM) states. The protocol, given a target output state, performs an online estimation of the quality of the currently produced states, relying on output measurement statistics, and determines how to tune the experimental parameters to optimize the state generation. To achieve this, the algorithm does not need to be imbued with a description of the generation apparatus itself. Rather, it operates in a fully black-box scenario, making the scheme applicable in a wide variety of circumstances. The handles controlled by the algorithm are the rotation angles of a series of waveplates and can be used to probabilistically generate arbitrary four-dimensional OAM states. We showcase our scheme on different target states both in classical and quantum regimes and prove its robustness to external perturbations on the control parameters. This approach represents a powerful tool for automated optimizations of noisy experimental tasks for quantum information protocols and technologies.
Abstract The orbital angular momentum (OAM) of light has been at the center of several classical and quantum applications for imaging, information processing and communication. However, the complex structure inherent in OAM states makes their detection and classification nontrivial in many circumstances. Most of the current detection schemes are based on models of the OAM states built upon the use of Laguerre–Gauss (LG) modes. However, this may not in general be sufficient to capture full information on the generated states. In this paper, we go beyond the LG assumption, and employ hypergeometric-Gaussian (HyGG) modes as the basis states of a refined model that can be used—in certain scenarios—to better tailor OAM detection techniques. We show that enhanced performances in OAM detection are obtained for holographic projection via spatial light modulators in combination with single-mode fibers (SMFs), and for classification techniques based on a machine learning approach. Furthermore, a three-fold enhancement in the SMF coupling efficiency is obtained for the holographic technique, when using the HyGG model with respect to the LG one. This improvement provides a significant boost in the overall efficiency of OAM-encoded single-photon detection systems. Given that most of the experimental works using OAM states are effectively based on the generation of HyGG modes, our findings thus represent a relevant addition to experimental toolboxes for OAM-based protocols in quantum communication, cryptography and simulation.