Quantum Information Processing in An Array of Fiber Coupled Cavities

We consider a fiber coupled cavity array. Each cavity is doped with a single two-level atom. By treating the atom-cavity systems as combined polaritonic qubits, we can transform it into a polaritonic qubit-qubit array in the dispersive regime. We show that the four fiber coupled cavity open chain and ring can both generate the four qubit W state and cluster state, and can both transfer one and two qubit arbitrary states. We also discuss the dynamical behaviors of the four fiber coupled cavity array with unequal couplings. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)