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Physical Review A

Quantum entanglement of four distant atoms trapped in different optical cavities

Xu‐Bo Zou, K. Pahlke, Wolfgang M. Mathis

Published May 14, 2004• 52 citations
Publisher

Abstract

We propose a unified scheme to generate $W$ states, Greenberger-Horne-Zeilinger (GHZ) states, and cluster states of four distant atoms, which are trapped separately in leaky cavities. The proposed schemes require linear optical elements and photon detectors with single-photon sensitivity. The quantum noise influences the fidelity of the generated states. Further, based on the four-photon coincidence detection, we propose another scheme to generate the $W$ states and GHZ states of four distant atoms. The scheme is insensitive to the quantum noise, but cannot be used to generate the cluster states.

DOI
10.1103/physreva.69.052314

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We propose a unified scheme to generate WWW states, Greenberger-Horne-Zeilinger (GHZ) states, and cluster states of four distant atoms, which are trapped separately in leaky cavities. The proposed schemes require linear optical elements and photon detectors with single-photon sensitivity. The quantum noise influences the fidelity of the generated states. Further, based on the four-photon coincidence detection, we propose another scheme to generate the WWW states and GHZ states of four distant atoms. The scheme is insensitive to the quantum noise, but cannot be used to generate the cluster states.
It has been shown that there exist two inequivalent classes of three-qubit entangled states, namely, the Greenberger-Horne-Zeilinger (GHZ) class and the W class. In this paper, we propose conditional schemes to generate GHZ states and W states of three distant atoms, which are trapped separately in three leaky cavities. More generally, the schemes can be modified to generate any superposition of the Dicke states of three distant atoms. The proposed schemes require linear optical elements and a multifold coincidence detection and are insensitive to the quantum noise. It is briefly pointed out that these schemes can be extended to generate GHZ states and W states of N distant atoms.
We propose a scheme to generate a four-particle Greenberger-Horne-Zeilinger (GHZ) state of distant atoms that are trapped separately in leaky cavities. This scheme uses cavity decay to inject photons into a setup of optical devices that consist of a symmetric series of beam splitters and photon detectors. Photon detection on the output modes of the beam splitters projects the atom-cavity-system state onto the GHZ state. It is briefly pointed out that this scheme can be extended to generate GHZ states of 4m4m4m atoms.
We show a way to use an optical device set-up to generate the four-particle Greenberger–Horne–Zeilinger (GHZ) state of atoms, which are trapped separately in leaky cavities. Based on cavity decay, photons are transferred from the atom–cavity systems to a symmetric series of beam splitters and photon detectors. The events of photon detection on the output modes of the beam splitters project the state of the atom–cavity systems onto the GHZ state. It is briefly pointed out how this scheme can be extended to generate GHZ states of 4 m atoms.
Based on the interference effect of polarized photons leaking out of separate cavities, we propose schemes for the generation of the N -atom Greenberger–Horne–Zeilinger (GHZ) state, three-atom W state and a genuine four-atom entangled state |χ⟩. In these schemes, each of the atoms is trapped separately in a remote optical cavity, and the possible spontaneous channels induced by the excited atoms lead to the coherent superposition of the states of the atoms. The desired multipartite entangled states can be generated with a certain success probability by the subsequent detection of the polarized photons in different modes. The schemes would be useful steps towards long-distance quantum communication, distributed quantum computation and constructing remote quantum information processing networks.
Schemes to generate Greenberger-Horne-Zeilinger (GHZ) and WWW states of three distant atoms are proposed in this paper. The schemes use the effects of quantum statistics of indistinguishable photons emitted by the atoms inside optical cavities. The advantages of the schemes are their robustness against detection inefficiency and asynchronous emission of the photons. Moreover, in Lamb-Dicke limit, the schemes do not require the simultaneous click of the detectors. This makes the schemes more realizable in experiments.