  We study the laser control of magnon topological phases induced by the
Aharonov-Casher effect in insulating antiferromagnets (AFs). Since the laser
electric field can be considered as a time-periodic perturbation, we apply the
Floquet theory and perform the inverse frequency expansion by focusing on the
high frequency region. Using the obtained effective Floquet Hamiltonian, we
study nonequilibrium magnon dynamics away from the adiabatic limit and its
effect on topological phenomena. We show that a linearly polarized laser can
generate helical edge magnon states and induce the magnonic spin Nernst effect,
whereas a circularly polarized laser can generate chiral edge magnon states and
induce the magnonic thermal Hall effect. In particular, in the latter, we find
that the direction of the magnon chiral edge modes and the resulting thermal
Hall effect can be controlled by the chirality of the circularly polarized
laser through the change from the left-circular to the right-circular
polarization. Our results thus provide a handle to control and design magnon
topological properties in the insulating AF.
