On Small Beams with Large Topological Charge II: Photons, Electrons and Gravitational Waves

Beams of light with a large topological charge significantly change their spatial structure when they are focused strongly. Physically, it can be explained by an emerging electromagnetic field component in the direction of propagation, which is neglected in the simplified scalar wave picture in optics. Here we ask: Is this a specific photonic behavior, or can similar phenomena also be predicted for other species of particles? We show that the same modification of the spatial structure exists for relativistic electrons as well as for focused gravitational waves. However, this is for different physical reasons: For electrons, which are described by the Dirac equation, the spatial structure changes due to a Spin-Orbit coupling in the relativistic regime. In gravitational waves described with linearized general relativity, the curvature of space-time between the transverse and propagation direction leads to the modification of the spatial structure. Thus, this universal phenomenon exists for both massive and massless elementary particles with Spin 1/2, 1 and 2. It would be very interesting whether other types of particles such as composite systems (neutrons or C$_{60}$) or neutrinos show a similar behaviour and how this phenomenon can be explained in a unified physical way.Comment: 8 pages, 3 figure

Quantum gate description for induced coherence without induced emission and related phenomena

We introduce unitary quantum gates for photon pair creation in spontaneous parametric down-conversion nonlinear crystals (NLs) and for photon path alignment. These are the two key ingredients for the method of "induced coherence without induced emission" and many ensuing variations thereof. The difficulty in doing so stems from an apparent mixing of the mode picture (such as the polarization of photons) and the Fock picture (such as the existence of the photons). We illustrate utility of these gates by obtaining quantum circuits for the experimental setups of the frustrated generation of photon pairs, identification of a point-like object with undetected photons, and creation of a Bell state. We also introduce an effective nonunitary description for the action of NLs in experiments where all the NLs are pumped coherently. As an example, by using this simplifying picture, we show how NLs can be used to create superposition of given quantum states in a modular fashion.Comment: 4+3 page

Quantum Experiments and Graphs: Multiparty States as coherent superpositions of Perfect Matchings

We show a surprising link between experimental setups to realize high-dimensional multipartite quantum states and Graph Theory. In these setups, the paths of photons are identified such that the photon-source information is never created. We find that each of these setups corresponds to an undirected graph, and every undirected graph corresponds to an experimental setup. Every term in the emerging quantum superposition corresponds to a perfect matching in the graph. Calculating the final quantum state is in the complexity class #P-complete, thus cannot be done efficiently. To strengthen the link further, theorems from Graph Theory -- such as Hall's marriage problem -- are rephrased in the language of pair creation in quantum experiments. We show explicitly how this link allows to answer questions about quantum experiments (such as which classes of entangled states can be created) with graph theoretical methods, and potentially simulate properties of Graphs and Networks with quantum experiments (such as critical exponents and phase transitions).Comment: 6+5 pages, 4+7 figure

On Small Beams with Large Topological Charge

Light beams can carry a discrete, in principle unbounded amount of angular momentum. Examples of such beams, the Laguerre-Gauss modes, are frequently expressed as solutions of the paraxial wave equation. There, they are eigenstates of the orbital angular momentum (OAM) operator. The paraxial solutions predict that beams with large OAM could be used to resolve arbitrarily small distances - a dubious situation. Here we show how to solve that situation by calculating the properties of beams free from the paraxial approximation. We find the surprising result that indeed one can resolve smaller distances with larger OAM, although with decreased visibility. If the visibility is kept constant (for instance at the Rayleigh criterion, the limit where two points are reasonably distinguishable), larger OAM does not provide an advantage. The drop in visibility is due to a field in the direction of propagation, which is neglected within the paraxial limit.Comment: 6 pages, 2 figures; + supplementary informatio

Quantum Experiments and Graphs III: High-Dimensional and Multi-Particle Entanglement

Quantum entanglement plays an important role in quantum information processes, such as quantum computation and quantum communication. Experiments in laboratories are unquestionably crucial to increase our understanding of quantum systems and inspire new insights into future applications. However, there are no general recipes for the creation of arbitrary quantum states with many particles entangled in high dimensions. Here, we exploit a recent connection between quantum experiments and graph theory and answer this question for a plethora of classes of entangled states. We find experimental setups for Greenberger-Horne-Zeilinger states, W states, general Dicke states, and asymmetrically high-dimensional multipartite entangled states. This result sheds light on the producibility of arbitrary quantum states using photonic technology with probabilistic pair sources and allows us to understand the underlying technological and fundamental properties of entanglement.Comment: 7 pages, 7 figures; Appendix 3 pages, 5 figure

Gouy Phase Radial Mode Sorter for Light: Concepts and Experiments

We present an in principle lossless sorter for radial modes of light, using accumulated Gouy phases. The experimental setups have been found by a computer algorithm, and can be intuitively understood in a geometric way. Together with the ability to sort angular-momentum modes, we now have access to the complete 2-dimensional transverse plane of light. The device can readily be used in multiplexing classical information. On a quantum level, it is an analog of the Stern-Gerlach experiment -- significant for the discussion of fundamental concepts in quantum physics. As such, it can be applied in high-dimensional and multi-photonic quantum experiments.Comment: main text: 7 pages, 5 figures. Supplementary Information: 5 pages, 4 figure

Orbital angular momentum of photons and the entanglement of Laguerre-Gaussian modes

The identification of orbital angular momentum (OAM) as a fundamental property of a beam of light nearly twenty-five years ago has led to an extensive body of research around this topic. The possibility that single photons can carry OAM has made this degree of freedom an ideal candidate for the investigation of complex quantum phenomena and their applications. Research in this direction has ranged from experiments on complex forms of quantum entanglement to the interaction between light and quantum states of matter. Furthermore, the use of OAM in quantum information has generated a lot of excitement, as it allows for encoding large amounts of information on a single photon. Here we explain the intuition that led to the first quantum experiment with OAM fifteen years ago. We continue by reviewing some key experiments investigating fundamental questions on photonic OAM and the first steps into applying these properties in novel quantum protocols. In the end, we identify several interesting open questions that could form the subject of future investigations with OAM.Comment: 17 pages, 7 figures; close to accepted versio

Twisted Photons: New Quantum Perspectives in High Dimensions

Quantum information science and quantum information technology have seen a virtual explosion world-wide. It is all based on the observation that fundamental quantum phenomena on the individual particle or system-level lead to completely novel ways of encoding, processing and transmitting information. Quantum mechanics, a child of the first third of the 20th century, has found numerous realizations and technical applications, much more than was thought at the beginning. Decades later, it became possible to do experiments with individual quantum particles and quantum systems. This was due to technological progress, and for light in particular, the development of the laser. Hitherto, nearly all experiments and also nearly all realizations in the fields have been performed with qubits, which are two-level quantum systems. We suggest that this limitation is again mainly a technological one, because it is very difficult to create, manipulate and measure more complex quantum systems. Here, we provide a specific overview of some recent developments with higher-dimensional quantum systems. We mainly focus on Orbital Angular Momentum (OAM) states of photons and possible applications in quantum information protocols. Such states form discrete higher-dimensional quantum systems, also called qudits. Specifically, we will first address the question what kind of new fundamental properties exist and the quantum information applications which are opened up by such novel systems. Then we give an overview of recent developments in the field by discussing several notable experiments over the past 2-3 years. Finally, we conclude with several important open questions which will be interesting for investigations in the future.Comment: 15 pages, 7 figure

Predicting Research Trends with Semantic and Neural Networks with an application in Quantum Physics

The vast and growing number of publications in all disciplines of science cannot be comprehended by a single human researcher. As a consequence, researchers have to specialize in narrow sub-disciplines, which makes it challenging to uncover scientific connections beyond the own field of research. Thus access to structured knowledge from a large corpus of publications could help pushing the frontiers of science. Here we demonstrate a method to build a semantic network from published scientific literature, which we call SemNet. We use SemNet to predict future trends in research and to inspire new, personalized and surprising seeds of ideas in science. We apply it in the discipline of quantum physics, which has seen an unprecedented growth of activity in recent years. In SemNet, scientific knowledge is represented as an evolving network using the content of 750,000 scientific papers published since 1919. The nodes of the network correspond to physical concepts, and links between two nodes are drawn when two physical concepts are concurrently studied in research articles. We identify influential and prize-winning research topics from the past inside SemNet thus confirm that it stores useful semantic knowledge. We train a deep neural network using states of SemNet of the past, to predict future developments in quantum physics research, and confirm high quality predictions using historic data. With the neural network and theoretical network tools we are able to suggest new, personalized, out-of-the-box ideas, by identifying pairs of concepts which have unique and extremal semantic network properties. Finally, we consider possible future developments and implications of our findings.Comment: 9+6 pages, 6 figure

Automated Search for new Quantum Experiments

Quantum mechanics predicts a number of at first sight counterintuitive phenomena. It is therefore a question whether our intuition is the best way to find new experiments. Here we report the development of the computer algorithm Melvin which is able to find new experimental implementations for the creation and manipulation of complex quantum states. And indeed, the discovered experiments extensively use unfamiliar and asymmetric techniques which are challenging to understand intuitively. The results range from the first implementation of a high-dimensional Greenberger-Horne-Zeilinger (GHZ) state, to a vast variety of experiments for asymmetrically entangled quantum states -- a feature that can only exist when both the number of involved parties and dimensions is larger than 2. Additionally, new types of high-dimensional transformations are found that perform cyclic operations. Melvin autonomously learns from solutions for simpler systems, which significantly speeds up the discovery rate of more complex experiments. The ability to automate the design of a quantum experiment can be applied to many quantum systems and allows the physical realization of quantum states previously thought of only on paper.Comment: 5+8 pages, 4+1 figures (main text + supplementary