  The interaction between light and matter in condensed matter excitations and
electromagnetic resonators serves as a rich playground for fundamental research
and lies at the core of photonic and quantum technologies. Herein, we present
comprehensive experimental and theoretical studies of the photon-mediated
hybridization of magnons and phonons in the terahertz (THz) range. We
demonstrate the intriguing concept of composite states formed by distinct
electric and magnetic quasiparticles strongly coupled to the same optical
cavity modes. Specifically, we explore magnons excited in a slab of an
antiferromagnetic crystal and phonons excited in a distinct specimen of an
insulating material. The crystal slabs form an optical cavity with
Fabry-P\'erot oscillations in the THz range. We demonstrate hybridized
phonon-magnon polariton modes and their tunability by adjusting the distance
between the slabs, showing that hybridization persists even at separations up
to several millimeters. The experimental results are interpreted using both
classical and quantum electrodynamical models. The quantum description allows
us to quantify the degree of hybridization that is linked to a topological
behavior of the electric field phasor, in agreement with the classical
electrodynamics expectations. Importantly, the presented results refer to
temperature conditions and cavities of millimeter size, paving the way for
engineering realistic, frequency-tunable THz devices through the hybridization
of electric (phononics) and magnetic (spintronics) elementary excitations of
matter.
