Periodic Reporting for period 4 - PHOSPhOR (Photonics of Spin–Orbit Optical Phenomena) Reporting period: 2020-12-01 to 2021-11-30 Summary of the context and overall objectives of the project Light, or more generally the optical electromagnetic field, has two important properties, phase and polarization, both not visible to the naked eye. The phase structure in space determines the light subsequent propagation, while the polarization is mainly important in the interaction with matter. For a single quantum particle of light – the photon – the phase spatial structure is sometimes defined as the “orbital” degree of freedom, as it defines the photon trajectories, while the polarization is related to the “spin” degree of freedom, which could be visualized as an intrinsic rotation of the photon. In most optical phenomena, these two degrees of freedom are rather independent, but recently, a growing number of systems is being discovered, or artificially engineered, in which the photon spin-orbit interactions are important. PHOSPhOR is aimed at investigating these interactions and exploiting them for enhancing our control of the light spatial and temporal structure, with possible benefits for many applications, including optical communication, quantum information technology, photo lithography, etc. PHOSPhOR vision is to promote the development of a full-fledged spin-orbit photonic science and technology, in which the vector states of structured light beams, optical pulses and even quantum states of individual photons can be precisely tailored and manipulated in all their aspects and used, in combination with suitable material systems, to obtain new classical- or quantum-optical functionalities; or they can be exploited as scientific tools to investigate new physical phenomena. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far During the project, we obtained several important results in different directions. We demonstrated the generation and measurement of light fields having a complex spatial vector structure by exploiting novel techniques we introduced to this purpose. We explored various possible applications of spin-orbit interactions in quantum information protocols and quantum simulations of material systems, in particular topological quantum phases and phase transitions. These new technologies may find application in future photonic-based quantum computation systems. We demonstrated spin-orbit photonic media and spin-orbit effects occurring in photosensitive materials. Overall, we have made strong progress towards fully exploiting spin-orbit optical phenomena science and technology.Let us now briefly mention some of our most important specific results.We introduced a new fundamental principle for light lateral confinement and guiding, entirely based on spin-orbit interactions. This new concept, which we proposed and demonstrated experimentally, relies on using polarization manipulations to introduce the optical phases needed to achieve waveguiding.We ideated and developed a new photonic platform for quantum simulations based on a suitable sequence of optical elements that exploit spin-orbit interactions to control the internal spatial structure of a single optical beam. The evolution of the light beam in such system can be proved to be equivalent to that of a particle performing a “quantum walk” in a suitable lattice. This concept can be applied in various directions. We focused our quantum-simulation work on investigating topological physics and demonstrated new methods for measuring the underlying topological invariants by observing the time evolution of the particle in the system bulk. Our platform was initially limited to one-dimensional (1D) lattices, then we upgraded it to two-dimensional (2D) systems which are associated with a much richer physics. We are applying this platform both to classical light simulations and few-photon ones. The latter may be suitable for future applications in quantum computing.We demonstrated several very promising applications of structured light. Among them, perhaps the most interesting one for possible commercial exploitation is a new non-contact optical method for measuring nanometric displacements of a mechanical stage.All our scientific results were widely disseminated in the scientific community via peer-review publications and communications in conferences. Over 30 articles in prestigious international journals were published based on the project ideas and results, including several in very high-ranked journals such as Nature Photonics, Nature Communications, Physical Review Letters, Optica, etc. Several other publications are expected to appear in the next months, as the more recent work we completed becomes finalized. In addition, some of the results were presented to the general public in various ways (e.g. on the project website and in non-technical publications and presentations). A patent and a patent application were also generated from work carried out in the project and we will explore their possible commercial exploitation in the future. Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) Not applicable Structured vortex light generated by q-plate sequence
