Reduction to the Fock state via a degenerate four-wave mixing

A scheme to generate the Fock state via a degenerate four-wave mixing and partial measurement is proposed. A conditional state of the signal mode of a degenerate four-wave mixer will be shown to reduce to the Fock state when the outcome of the measurement on the reference mode satisfies a certain condition. The photon number of the Fock state is distributed when the measurement is repeated many times. Conditioning for the quantum state of the signal mode is carried out by the photon counting measurement on the reference mode whose input state is assumed to be the vacuum. The phase coherence of the conditional signal state is also considered. Furthermore conditioning for the signal mode by means of heterodyne and homodyne detections are briefly considered.