Efficient preparation of a four-photon cluster state with homodyne measurement via cross-Kerr nonlinearity

A scheme is proposed for generating a multiphoton entangled cluster state among four modes. The scheme only uses Kerr medium, beam splitter and homodyne measurements on coherent light fields, which can be efficiently made in quantum optical laboratories. The photon in the signal mode is prepared in a superposition state of the vacuum state and one-photon state while the probe beam is initially set in a coherent state superposition. The strong probe mode interacts successively with multiple signal-mode photons, each causing a conditional phase rotation in the probe mode. Subsequent momentum quadrature homodyne measurement of the probe mode will project the photons in the signal mode into the desired entangled states. It is shown that under certain conditions, the four-photon cluster state can be generated with high fidelity and high success probability, and the scheme is feasible by current experimental technology.