Quantum SWAP gate with atomic ensembles in two distant cavities

A scheme is presented to realize remote quantum SWAP gate with atomic ensembles. During the process, the fiber mode is only virtually excited. The quantum information is encoded in two degenerate ground states, so the atoms' spontaneous emission can be omitted approximately. Moreover, the time needed to complete the gate is proportional to the inverse of the number of atoms and thus the gate is greatly speeded up as the number of atoms increases.