  Currently, there is a growing interest in studying the coherent interaction
between magnetic systems and electromagnetic radiation in a cavity, prompted
partly by possible applications in hybrid quantum systems. We propose a
multimode cavity optomagnonic system based on antiferromagnetic insulators,
where optical photons couple coherently to the two homogeneous magnon modes of
the antiferromagnet. These have frequencies typically in the THz range, a
regime so far mostly unexplored in the realm of coherent interactions, and
which makes antiferromagnets attractive for quantum transduction from THz to
optical frequencies. We derive the theoretical model for the coupled system,
and show that it presents unique characteristics. In particular, if the
antiferromagnet presents hard-axis magnetic anisotropy, the optomagnonic
coupling can be tuned by a magnetic field applied along the easy axis. This
allows to bring a selected magnon mode into and out of a dark mode, providing
an alternative for a quantum memory protocol. The dynamical features of the
driven system present unusual behavior due to optically induced magnon-magnon
interactions, including regions of magnon heating for a red detuned driving
laser. The multimode character of the system is evident in a substructure of
the optomagnonically induced transparency window.
