This internship focuses on the realization of topological quantum phases in a dynamical system based on a Bose–Einstein condensate (BEC) of potassium atoms. Topology provides robust properties in quantum states, often revealed through protected states or invariants, and can emerge in periodically driven ("Floquet") systems. Building on the group’s recent advances in implementing effective spin–orbit coupling with spin-dependent optical potentials and modulated Raman coupling, the project will combine experimental and numerical approaches. The intern will contribute to ongoing experiments on BEC preparation of optical driving sequences, experimentation and data analysis, as well as develop numerical simulations, aimed at identifying signatures of topological phases, such as topological invariants. The project offers the opportunity to collaborate with theorists and is intended as a precursor to a PhD, extending toward many-body topological systems. The position is hosted at the PhLAM laboratory (University of Lille, CNRS) within the “Quantum Systems” team, which provides strong experimental and theoretical support. Candidates should have a background in quantum/atomic physics, interest in both theory and experiment, and prior lab experience is highly valued.