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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., Comment: 11 pages, 7 figures

The collective modes of two-dimensional ordered atomic arrays can modify the radiative environment of embedded atomic impurities. We analyze the role of the lattice geometry on the impurity's emission linewidth by comparing the effective impurity decay rate obtained for all non-centered Bravais lattices and an additional honeycomb lattice. We demonstrate that the lattice geometry plays a crucial role in determining the effective decay rate for the impurity. In particular, we find that the minimal effective decay rate appears in lattices where the number of the impurity's nearest neighbours is maximal and the number of distinct distances among nearest neighbours is minimal. We further show that, in the choice between interstitial and substitutional placement of the impurity, the former always wins by exhibiting a lower decay rate and longer photon storage. For interstitial placements, we determine the optimal impurity position in the lattice plane, which is not necessarily found in the center of the lattice plaquette., Comment: 10 pages, 6 figures; increased figure label sizes, added references, corrected typos