Efficient Preparation of Entangled States in Cavity QED with Grover's Algorithm

We propose to employ the amplification mechanism of Grover's search algorithm to efficiently prepare entangled states of an ensemble of qubits. The conditional change of sign employed in the algorithm can be implemented by the phase shift of photons scattered on an optical cavity hosting an atomic ensemble. We show that collective Dicke states, Greenberger-Horne-Zeilinger states, and Schrödinger cat superpositions of N atoms may be prepared deterministically by few (∼N^{1/4}) photon scattering events without individual addressing of the atoms.