  The ground state of quantum chromodynamics in sufficiently strong external
magnetic fields and at moderate baryon chemical potential is a chiral soliton
lattice (CSL) of neutral pions. We investigate the interplay between the CSL
structure and dynamical electromagnetic fields. Our main result is that in
presence of the CSL background, the two physical photon polarizations and the
neutral pion mix, giving rise to two gapped excitations and one gapless mode
with a nonrelativistic dispersion relation. The nature of this mode depends on
the direction of its propagation, interpolating between a circularly polarized
electromagnetic wave and a neutral pion surface wave, which in turn arises from
the spontaneously broken translation invariance. Quite remarkably, there is a
neutral-pion-like mode that remains gapped even in the chiral limit, in seeming
contradiction to the Goldstone theorem. Finally, we have a first look at the
effect of thermal fluctuations of the CSL, showing that even the soft
nonrelativistic excitation does not lead to the Landau-Peierls instability.
However, it leads to an anomalous contribution to pressure that scales with
temperature and magnetic field as $T^{5/2}(B/f_\pi)^{3/2}$.
