  Long-range dipole-dipole interactions in subwavelength arrays of quantum
emitters involve virtual photon exchange processes that impart forces on the
emitters due to the imposed photon recoil. We perform a semi-classical analysis
of the dynamics of an impurity allowed to freely move through a subwavelength
array of atoms in different parameter regimes. We numerically solve the coupled
set of equations between motional and spin degrees of freedom to elucidate the
possible impurity trajectories realizable in this system. We find that the
impurity can maintain quasi-stable orbits within the plaquette for long times.
The regions through which these orbits pass are strongly dependent on the
chosen atomic transition dipole moment. We further provide intuition for our
findings based on a simplified model, where the lattice dynamics is
adiabatically eliminated. As a final point of analysis, we also take the
motional degrees of freedom of the lattice atoms into account, and study the
polaron-like excitation induced in the kinetic state of the lattice by the
impurity.
