Generation of multi-atom W states via Raman transitionin an optical cavity

A simple scheme is proposed to generate the $W$ state of $N$ $\Lambda$-type neutral atoms trapped in an optical cavity via Raman transition. Conditional on no photon leakage from the cavity, the $N$-qubit $W$ state can be prepared perfectly by turning on a classical coupling field for an appropriate time. Compared with the previous ones, our scheme requires neither individual laser addressing of the atoms, nor demand for controlling $N$ atoms to go through an optical cavity simultaneously with a constant velocity. We investigate the influence of cavity decay using the quantum jump approach and show that the preparation time decreases and the success probability increases with atom number because of a collective enhancement of the coupling.