Time-driven systems provide a framework for controlling waves through spatio-temporal modulation, which enables the synthesis of effective motion without mechanical displacement1–7. Within this framework, travelling-wave modulations can emulate moving media and give rise to phenomena such as Doppler-induced non-reciprocity8–10. A related effect is the extraction of energy from rotating media, which has been theoretically predicted to occur when waves experience sufficiently large rotational Doppler shifts11–17. Experimental access to this regime has remained limited due to the extreme rotation speeds required in mechanically rotating systems18–21. Here we show that Floquet-induced rotation enables access to such ultrafast rotational regimes using purely spatio-temporal modulation. When spinning at effective superluminal speeds, angular-momentum bandgaps emerge in the band structure of the underlying space–time crystal. These gaps host parametric processes that efficiently extract energy from the Floquet-rotating medium, resulting in angular-momentum-selective amplification of orbital waves within a dissipation-shaped spectral bandwidth. We realize this effect experimentally in a ring network of time-modulated resonators, where we observe a Floquet regime of rotational super-radiance mediated by non-Hermitian and parametric dynamics in space–time structured media. These results demonstrate a controllable platform for studying rotational energy transfer and angular-momentum-dependent wave amplification in space–time-modulated media.
