Cavity loss induced generation of W states

The existence of decoherence-free subspace (DFS) has been discussed widely. In this paper, we propose an alternative scheme for generating the four-atom $W$ states by manipulating DF qubits. The atoms are divided into two pairs and trapped in two separate optical cavities. Manipulation of atoms within DFS may generate a two-atom maximally entangled state in an individual cavity, which is a stable state. After driving the system out of DFS, the atoms will interact resonantly with the cavity field. The photons leaking from the cavities interfere at the beamsplitter, which destroys which-path information, and are finally detected by one of the detectors, leading to the generation of a $W$ state. In addition, the numerical simulation indicates that the fidelity of the prepared state can, for a very wide parameter regime, be very close to unity.