  Coherent long-range interactions between atoms are a prerequisite for
numerous applications in the field of quantum information science, but they
usually decrease exponentially with the increase in atomic separation. Here we
present an appealing method to dramatically enhance the long-range atom-atom
interaction mediated by a coupled-cavity array that is subjected to two-photon
(parametric) drives. Our method allows one to greatly amplify both the
localization length of the single-photon bound-state wavefunction and the
effective atom-photon coupling strength, resulting in a significant improvement
of photon-mediated coherent interaction between two distant atoms.
Additionally, we illustrate this effect by analyzing how it facilitates the
transfer of information and the creation of entanglement between the atoms.
