Periodic Reporting for period 1 - ONTOP (On-demand Non-hermitian TOPology) Reporting period: 2019-04-01 to 2021-03-31 Summary of the context and overall objectives of the project In photonics, topology represents a new approach for guiding light in a way that is robust against structural disorder. Light is confined along the edge of a corresponding material and this confinement remains for straight or zig-zag interfaces alike. Traditionally, the considered media consist of periodic photonic-crystal structures. In contrast, this action aimed to produce a topological confinement in random media through an external-control scheme that compensates for the effect of disorder. Therefore, with this approach topology can be externally “imprinted” on any device and be used to confine photons “on-demand”—i.e. confine at will photons on one edge of the system or the other. Technologically speaking, the conception of topological devices at optical wavelengths is currently hindered by tedious fabrication requirements (that reveal costly) and the need for high-level resolution. This action introduces a new approach where topology is “post-processed” onto low-quality architectures, which could lead to the conception of low-cost devices (e.g. sensors, waveguides) whose topological properties can be externally programmed. The overall objectives of this proposal were: (1) to theoretically develop external-control schemes that manipulate the topological properties of disordered systems “on-demand”; (2) to experimentally demonstrate such concept on an acoustic setup; (3) to transfer such control schemes to optical platforms and different properties. The conclusion that can be drawn from this action clearly emphasizes its positive delivery. Scientifically, a new control scheme was developed to form topological effects in random structures (objective (1)) and this approach was extended to the control of different optical properties (objective (3)). An acoustic experiment has been developed (objective (2)) but the envisioned demonstration has been postponed due to the current pandemic. Four different papers were written, one published in Nature Communications, two currently under review in Physical Review Letters and Optics Express and a last one that will be submitted to Physical Review Letters within a few weeks. For the fellow, this action represented an opportunity to develop both a scientific network and a research program that would help him secure a permanent research position in Europe. Throughout the course of this fellowship, the fellow attended multiple interviews for assistant-professor positions and received different offers. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far To deliver on objective (1), within the host team of Pr. Rotter, a theoretical model using external-control scheme to impose topological order in random media was investigated (and successfully developed). Then, through a collaboration with the team of Pr. Romain Fleury at “École Polytechnique Fédérale de Lausanne” (EPFL, Switzerland), an acoustic setup was designed to demonstrate experimentally this theoretical approach (objective (2)). Yet, owing to the international Covid pandemic in 2020 and the subsequent lock down of universities across Europe, the conception of this experimental setup was delayed. Currently a theoretical paper introducing the theoretical model of objective (1) is currently in preparation and will be submitted to Physics Review Letters within a few weeks. In parallel, the control approach of objective (1) was extended to different types of systems (objective (3)). In collaboration with Pr. Karl Unterrainer (TU Wien), the control of the spectral emission of a disordered source of light operating in the THz was demonstrated. The team of Pr. Unterrainer develops quantum cascade lasers that emit photons at a frequency of a few THz. At such frequencies the emitted light has a wavelength close to millimeters (visible light corresponds to sub-micrometer wavelengths) and thus offers different applications than traditional light sources. This project led to a publication in Nature Communications, while a second paper is currently under review in Optics Express. This approach was also replicated in a theoretical paper to cool-down a set of nanometer-size particles levitating in vacuum and this work is currently under review at Physics Review Letters. The dissemination of this scientific production was achieved through international conferences in Rome (PIERS 2019), London (Complex Nanophotonic Scientific Camp 2019) or San Francisco (Photonics West 2020) and workshops in places across Europe such as Vienna, Paris, Rennes or Bordeaux. Yet, the pandemic forced the cancellation of multiple events. To communicate about the different scientific achievements, a news coverage was written and broadcasted in media like “The Austrian Press Agency”, “Chemie.de” or “Analytica News” and a webpage was created to promote this action. All the scientific production associated with this fellowship has been made freely accessible via open-access journals or uploaded on Arxiv. 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) This fellowship aimed to introduce a new paradigm in photonics. Rather than relying on demanding and expensive fabrication processes, here it was demonstrated that the properties of disordered photonic structures (e.g. propagation of light, lasing emission) could be “post-processed” thanks to external-control schemes. In photonics, such an approach has never been envisioned to control the topology of a given architecture. As a result, this action could have an important impact in the field. Experimentally, it offers a new approach that greatly simplifies the formation of topological order and could facilitate the design and conception of topological devices. In the context of quantum cascade lasers, this approach offers the possibility of obtaining a large bandwidth tunability as well as an ability to tailor the emission spectrum of THz light sources. Being able to shape light emission in the THz is of remarkable importance because many molecules possess spectral signatures at these frequencies and, therefore, could be detected through such light fields. It was also shown for the first time that external-control schemes could cool down a gas of levitated particles, which could have important repercussions in the field. Levitated particles enable for the conception of sensors with extreme sensitivity, which could potentially sense gravitational waves or hypothetical types of dark matter. Over these past two years, for the fellow, the constant interactions with the host (Pr. Rotter) have been of great personal and professional benefit. His help was crucial to investigate the theory of topology and his guidance revealed precious for practicing for the job interviews obtained by the fellow. With the resources provided by this fellowship, to expand his knowledge on topology and complex systems, the fellow participated in different summer schools even though some of them got cancelled due to the pandemic. Imposing topology on a disordered system through an external-control scheme. Cooling down a multi-particle gas of nano-objects through an external-control scheme. Shaping the spectral emission of THz lasing sources through an external-control scheme.