  W state is a key resource in quantum communication. Fusion technology has
been proven to be a good candidate for preparing a large-size W state from two
or more small-size W states in linear optical system. It is of great importance
to study how to fuse W states via light-matter interface. Here we show that it
is possible to prepare large-size W-state networks using a fusion mechanism in
cavity QED system. The detuned interaction between three atoms and a vacuum
cavity mode constitute the main fusion mechanism, based on which two or three
small-size atomic W states can be fused into a larger-size W state. If no
excitation is detected from those three atoms, the remaining atoms are still in
the product of two or three new W states, which can be re-fused. The
complicated Fredkin gate used in the previous fusion schemes is avoided here. W
states of size 2 can be fused as well. The feasibility analysis shows that our
fusion processes maybe implementable with the current technology. Our results
demonstrate how the light-matter interaction based fusion mechanism can be
realized, and may become the starting point for the fusion of multipartite
entanglement in cavity QED system.
