On-demand generation of entanglement of atomic qubits via optical interferometry

The problem of on-demand generation of entanglement between single-atom qubits via a common photonic channel is examined within the framework of optical interferometry. As expected, for a Mach-Zehnder interferometer with coherent laser beam as input, a high-finesse optical cavity is required to overcome sensitivity to spontaneous emission. We show, however, that with a twin-Fock input, useful entanglement can in principle be created without cavity-enhancement. Both approaches require single-photon resolving detectors, and best results would be obtained by combining both cavity-feedback and twin-Fock inputs. Such an approach may allow a fidelity of $.99$ using a two-photon input and currently available mirror and detector technology. In addition, we study interferometers based on NOON states and show that they perform similarly to the twin-Fock states, yet without the need for high-precision photo-detectors. The present interferometrical approach can serve as a universal, scalable circuit element for quantum information processing, from which fast quantum gates, deterministic teleportation, entanglement swapping $etc.$, can be realized with the aid of single-qubit operations.