  Magnon-photon coupling in antiferromagnets has many attractive features that
do not exist in ferro- or ferrimagnets. We show quantum-mechanically that, in
the absence of an external field, one of the two degenerated spin wave bands
couples with photons while the other does not. The photon mode anticrosses with
the coupled spin waves when their frequencies are close to each other. Similar
to its ferromagnetic counterpart, the magnon-photon coupling strength is
proportional to the square root of number of spins $\sqrt{N}$ in
antiferromagnets. An external field removes the spin wave degeneracy and both
spin wave bands couple to the photons, resulting in two anticrossings between
the magnons and photons. Two transmission peaks were observed near the
anticrossing frequency. The maximum damping that allows clear discrimination of
the two transmission peaks is proportional to $\sqrt{N}$ and it's well below
the damping of antiferromagnetic insulators. Therefore the strong magnon-photon
coupling can be realized in antiferromagnets and the coherent information
transfer between the photons and magnons is possible.
