The competition between turbulent convection and global rotation in planetary and stellar interiors governs the transport of heat and tracers, as well as magnetic-field generation. These objects operate in dynamical regimes ranging from weakly rotating convection to the diffusivity-free (or 'ultimate') regime of rapidly rotating convection. However, the latter regime has remained elusive in the laboratory, despite a worldwide effort to design ever-taller rotating convection cells over the last decade. Building on a recent experimental approach where convection is driven radiatively, I will report measurements in quantitative agreement with this diffusivity-free scaling regime, the experimental scaling-laws being validated against direct numerical simulations (DNS) of the idealized setup.