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

Enhancing strength and range of atom-atom interaction in a coupled-cavity array via parametric drives