Preparation of Greenberger-Horne-Zeilinger and W states of three atoms trapped in one cavity through cavity output process

We propose a protocol to generate Greenberger-Horne-Zeilinger (GHZ) and W states of three atoms trapped in only one cavity. The setup involves one cavity and linear optical elements. The quantum information of each qubit is skillfully encoded on the degenerate ground states of the three different atoms, hence the entanglement between them is relatively stable against spontaneous emission. The advantages of the protocol are their robustness against detection inefficiency and asynchronous emission of the photons. We discuss the issue related to the practical implementation and show that the protocol is accessible within the current cavity QED technology and linear optical technology.