  Long-distance strong coupling between short-wavelength magnons remains an
outstanding challenge in quantum magnonics, an emerging interdiscipline between
magnonics and quantum information science. Recently, altermagnets are
identified as the third elementary class of magnets that break the
time-reversal symmetry without magnetization and thus combine characteristics
of conventional collinear ferromagnets and antiferromagnets. In this work, we
show that cavity photons can mediate the long-distance strong coupling of
exchange magnons with opposite chiralities in altermagnets, manifesting as an
anticrossing of the magnon-polariton spectrum in the extremely dispersive
regime. The predicted effective magnon-magnon coupling strongly depends on the
magnon propagation direction, and is thus highly anisotropic. Our findings are
intimately connected to the intrinsic nature of altermagnetic magnons, i.e.,
chirality-splitting-induced crossing of exchange magnons, which has no
counterpart in conventional ferromagnets or antiferromagnets, and may open a
new path way for magnon-based quantum information processing in altermagnets.
