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This seminar presents a comprehensive overview of the research initiatives in Quantum Technologies and Metrology led by the Universidad Nacional de Colombia, together with a detailed analysis of recent advancements in the engineering of Photonic Crystals (PhCs) for nanoscale light manipulation. The first part of the seminar outlines the strategic initiatives developed under a nationally funded project on Quantum Metrology and Technologies. It presents the experimental milestones enabled by advanced instrumentation acquired through this grant, covering key research pillars such as quantum metrology, high-resolution spectroscopy, quantum information and computing, and quantum materials. Furthermore, the socio-economic and scientific impact of these developments is highlighted, emphasizing their role in fostering technological sovereignty and innovation within the Colombian scientific landscape. The second part of the presentation provides a technical review of fundamental developments in PhC research, including: All-optical logic gates and waveguides: Design and optimization of PhC-based architectures for optical signal processing. Cavity–emitter interactions: Analysis of the coupling between quantum emitters and localized modes in PhC cavities to enhance light–matter interactions. Topological and chiral photonics: Exploration of symmetry-protected states and non-reciprocal light propagation in periodic dielectric structures. Coupled cavity systems: Study of modal coupling and energy transfer in multicavity arrays. Finally, specific contributions from the research group are showcased, including original designs for high-sensitivity sensors, optimized waveguides, and structured environments for emitters in PhC slabs. These results illustrate the potential for synergy and collaborative research between Colombian institutions and international partners, particularly with the Instituto de Física Fundamental (IFF-CSIC).

We study the directed transport of bosons along a one dimensional lattice in a dissipative setting, where the hopping is only facilitated by coupling to a Markovian reservoir. By combining numerical simulations with a field-theoretic analysis, we investigate the current fluctuations for this process and determine its asymptotic behavior. These findings demonstrate that dissipative bosonic transport belongs to the Kardar-Parisi-Zhang universality class and therefore, in spite of the drastic difference in the underlying particle statistics, it features the same coarse-grained behavior as the corresponding asymmetric simple exclusion process for fermions. However, crucial differences between the two processes emerge when focusing on the full counting statistics of current fluctuations. By mapping both models to the physics of fluctuating interfaces, we find that dissipative transport of bosons and fermions can be understood as surface growth and erosion processes, respectively. Within this unified description, both the similarities and discrepancies between the full counting statistics of the transport are reconciled. Beyond purely theoretical interest, these findings are relevant for experiments with cold atoms or long-lived quasiparticles in nanophotonic lattices, where such transport scenarios can be realized.

Lattice gauge theories are very complicated models, capturing a variety of interesting physics, but like most quantum many-body models, their study involves several challenges, both analytical and numerical. In my talk I will discuss an analogy between them and PEPS (projected entangled pair states), a high dimensional tensor network construction, and show how it can be used for studying such models while overcoming long standing bottlenecks.