  Hybrid magnonics has recently attracted intensive attentions as a promising
platform for coherent information processing. In spite of its rapid
development, on-demand control over the interaction of magnons with other
information carriers, in particular microwave photons in electromagnonic
systems, has been long missing, significantly limiting the broad applications
of hybrid magnonics. Here, we show that by introducing Floquet engineering into
cavity electromagnonics, coherent control on the magnon-microwave photon
coupling can be realized. Leveraging the periodic temporal modulation from a
Floquet drive, our first-of-its-kind Floquet cavity electromagnonic system can
manipulate the interaction between hybridized cavity electromagnonic modes on
demand. Moreover, we demonstrate a new coupling regime in such systems: the
Floquet ultrastrong coupling, where the Floquet splitting is comparable with or
even larger than the level spacing of the two interacting modes, resulting in
the breakdown of the rotating wave approximation. Our findings open up new
directions for magnon-based coherent signal processing.
