  In this paper we consider a honeycomb antiferromagnet subject to an external
laser field. Obtaining a time-independent effective Hamiltonian, we find that
the external laser renormalizes the exchange interaction between the in-plane
components of the spin-operators, and induces a synthetic Dzyaloshinskii-Moria
interaction (DMI) between second neighbors. The former allows the control of
the magnon dispersion's bandwidth and the latter breaks time-reversal symmetry
inducing non-reciprocity in momentum space. The eigen-excitations of the system
correspond to squeezed magnons whose squeezing parameters depend on the
properties of the laser. When studying how these spin excitations couple with
cavity photons, we obtain a coupling strength which can be enhanced by an order
of magnitude via careful tuning of the laser's intensity, when compared to the
case where the laser is absent. The transmission plots through the cavity are
presented, allowing the mapping of the magnons' dispersion relation.
