We harness orbital angular momentum (OAM) to discover a rich tapestry of topological maps in high dimensional spaces, moving beyond spin textured fields with mixed degrees of freedom to topologies using only the OAM of light. We confirm this experimentally using quantum states with an underlying topology of 48 dimensions and a topological spectrum spanning over 17000 maps, an encoding alphabet with enormous potential. We show that the topological spectrum allows the simultaneous ability to be robust to and probe for perturbation, the latter made possible by observing emergent signatures in the non-topological (trivial) spaces of the spectrum. We outline how our work opens exciting future possibilities for quantum sensing and communications.
We harness orbital angular momentum (OAM) to discover a rich tapestry of topological maps in high dimensional spaces, moving beyond spin textured fields with mixed degrees of freedom to topologies using only the OAM of light. We confirm this experimentally using quantum states with an underlying topology of 48 dimensions and a topological spectrum spanning over 17000 maps, an encoding alphabet with enormous potential. We show that the topological spectrum allows the simultaneous ability to be robust to and probe for perturbation, the latter made possible by observing emergent signatures in the non-topological (trivial) spaces of the spectrum. We outline how our work opens exciting future possibilities for quantum sensing and communications.
Orbital angular momentum (OAM) entanglement gives access to multiple qubit and high dimensional Hilbert spaces but is unfortunately susceptible to disturbance, decaying in real-world noisy channels. Here, we show that an underlying topology arising from OAM entanglement remains robust to such channels, which we demonstrate using atmospheric turbulence-exemplary of stochastic or chaotic media. Using a quantum channel with various turbulence strengths, we find that the OAM topological observable is preserved even though the OAM itself is shown to be highly sensitive to the turbulence. We show this is true for mixed states too, with the OAM topology intact even as the purity of the state decreases due to decoherence. Our Letter offers a new perspective on harnessing OAM entanglement in noisy channels, and may easily be extended to other spatial bases, degrees of freedom, and complex channels.
Orbital angular momentum (OAM) entanglement gives access to multiple qubit and high dimensional Hilbert spaces, but is unfortunately susceptible to disturbance, decaying in real-world noisy channels. Here, we show there is an underlying topology arising from OAM entanglement that is robust to such channels, which we demonstrate using atmospheric turbulence -- exemplary of stochastic or chaotic media. Using a quantum channel with various turbulence strengths, we find the OAM topological observable preserved even though the OAM itself is shown to be highly sensitive to the turbulence. We show this is true for mixed states too, with the OAM topology intact even as the purity of the state decreases due to decoherence. Our work offers a new perspective on OAM entanglement preservation, and may easily be extended to other spatial bases, degrees of freedom, as well as complex channels, whether static or dynamic.
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 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.
Quantum communication consists of the reliable transmission of quantum states among several parties and looks toward the long-term goal of a Quantum Internet. Quantum Internet could open up a whole universe of new applications, spanning from fundamental physics and secure communications to remote quantum computing. Multiple degrees of freedom can be used for the distribution of the quantum states, such as polarization, frequency, time and space. In particular, Orbital Angular Momentum (OAM) of light is one of the most promising thanks to its unbounded nature, albeit challenging to manipulate. OAM has been largely investigated both for classical and quantum communications, allowing for enhanced data rate in classical links and determining a high-dimensional basis for quantum communication. Here, we report our recent results related to quantum states encoded in the orbital angular momentum of light, proving the capability of preparing, manipulating, transmitting and measuring high-dimensional quantum states through a multimode fibre.
A recent result in quantum optics demonstrates that topology is not merely an ornament of a background space but an intrinsic, strictly immanent property of entangled orbital angular momentum (OAM) states. While two-dimensional cases exhibit skyrmion textures equivalent to the asymptotic structure of an ’t Hooft– Polyakov monopole, higher-dimensional cases (d > 2) reveal a structured multiplicity: a “topological spectrum” built from non-Abelian SU(d) gauge structures. This document provides a Possest–PQF reading of this phenomenon. We treat topology not as a static classification but as a stable signature of availability under a filtration regime. The core proposal defines the topological spectrum as a filtrational object, analyzing its consequences for robustness, diagnostics, and a geometry-first notion of novelty (emergence) that bypasses the “creation-fromnothing” narrative in favor of Simondonian transduction and Deleuzian multiplicity.