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Communications in Theoretical Physics

Generation of Four-Photon Cluster State with Coherent Light via Cross-Kerr Nonlinearity

Du Qian-Hua, Ye Ming-Yong, Zhihua Chen, Xinghua Li, Xiu‐Min Lin

Published Sep 1, 2008• 3 citations
Publisher

Abstract

We propose two schemes for preparing four-photon cluster state through cross-Kerr nonlinearity. Two coherent fields interact when they enter a nonlinear Kerr medium. If the interaction time is chosen appropriately in each Kerr medium, four-photon cluster state can be generated based on the results of two homodyne detectors in the first scheme. These schemes only use Kerr medium and homodyne measurements on coherent light fields, which can be efficiently made in quantum optical laboratories. In addition, weak cross-Kerr nonlinearity is sufficient. All of the properties make these schemes feasible in experiments.

DOI
10.1088/0253-6102/50/3/18

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We propose two schemes for preparing four-photon cluster state through cross-Kerr nonlinearity. Two coherent fields interact when they enter a nonlinear Kerr medium. If the interaction time is chosen appropriately in each Kerr medium, four-photon cluster state can be generated based on the results of two homodyne detectors in the first scheme. These schemes only use Kerr medium and homodyne measurements on coherent light fields, which can be efficiently made in quantum optical laboratories. In addition, weak cross-Kerr nonlinearity is sufficient. All of the properties make these schemes feasible in experiments.
We show how to prepare three different types of four-photon polarization entangled states among four modes. The scheme only use cross-Kerr medium, polarization beam splitters and X homodyne measurements on coherent light fields, which can be efficiently implemented in quantum optical laboratories. GHZ states and symmetric Dick states can be generated in deterministic way based on the scheme. With the possible availability of suitable strong Kerr nonlinearity, another type of entangled state called genuine four-photon entangled state can be realized as well.
A scheme is proposed for generating a polarization four-photon cluster state based on weak cross-Kerr nonlinearity. Compared with the existing schemes, the distinct feature of the present scheme would be its preparation with near-perfect fidelity due to homodyne measurement on the probe mode. After the probe mode interacts successively with multiple signal-mode photons, sixteen terms about the signal modes can be divided into four groups with the help of homodyne measurement. Each group can be transformed into the cluster state through the appropriate local operations. Thus the present scheme has a high success probability. Because it is difficult to obtain deterministic single-photon sources for current experimental technology, the realistic success probability is rather low but is preponderant in contrast to the existing schemes.