Observation of Floquet rotational super-radiance.

Time-driven systems provide a framework for controlling waves through spatio-temporal modulation, which enables the synthesis of effective motion without mechanical displacement 1-7 . Within this framework, travelling-wave modulations can emulate moving media and give rise to phenomena such as Doppler-induced non-reciprocity 8-10 . 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 shifts 11-17 . Experimental access to this regime has remained limited due to the extreme rotation speeds required in mechanically rotating systems 18-21 . 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.