PIF2025 - From atom transport to Quantum Hydrodynamics in a Rydberg quantum simulator - (PID2024-162669NB-I00)

This project aims to uncover the mechanisms driving the emergence of diffusion at late times in the transport of conserved quantities in closed quantum many-body systems. To achieve this, we will use a quantum simulator based on two-dimensional arrays of atoms coupled to Rydberg states. Our work builds on an experimental setup currently under construction at CINN-CSIC, which we will enhance with key upgrades. These include a defect-free array generation system, advanced cooling techniques, machine-learning-assisted assembly methods, precise control of electric and microwave fields, and an addressing setup for preparing initial quantum states to study their time evolution. Once fully operational, our upgraded apparatus will enable quantum simulation experiments on the dipolar XY model allowing us to observe hydrodynamics at infinite temperature in real-time dynamics. Starting from one-dimensional chains, we will measure diffusion coefficients and investigate energy transport in the system. Furthermore, we will extend our studies to two-dimensional systems, an unexplored regime for which no general or analytic numerical methods currently exist. Our results are expected to have a significant impact on the condensed matter community, where this topic remains an area of intense research, and has the potential for practical applications.