Photon-Mediated Interactions: A Scalable Tool to Create and Sustain Entangled States of N Atoms

We propose and study the use of photon-mediated interactions for the generation of long-range steady-state entanglement between N atoms. Through the judicious use of coherent drives and the placement of the atoms in a network of cavity QED systems, a balance between their unitary and dissipative dynamics can be precisely engineered to stabilize a long-range correlated state of qubits in the steady state. We discuss the general theory behind such a scheme and present an example of how it can be used to drive a register of N atoms to a generalized W state and how the entanglement can be sustained indefinitely. The achievable steady-state fidelities for entanglement and its scaling with the number of qubits are discussed for presently existing superconducting quantum circuits. While the protocol is primarily discussed for a superconducting circuit architecture, it is ideally realized in any cavity QED platform that permits controllable delivery of coherent electromagnetic radiation to specified locations.