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Physical Review A

Conditional generation of the Greenberger-Horne-Zeilinger state of four distant atoms via cavity decay

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

Published Aug 6, 2003• 76 citations
Publisher

Abstract

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 $4m$ atoms.

DOI
10.1103/physreva.68.024302

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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.
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.
This paper presents a scheme for generating three-particle W state of remote atoms trapped in leaky cavities. The scheme uses cavity decay to inject photons into a setup of optical devices which consist of a series of beam splitters and photon detectors. Photon detection on the output mode projects the atomic state into the W state. In the condition of "weakly driven approach", it shows that the scheme is robust and has high fidelity. It also points out that the scheme is scalable to generate multi-atomic W state.
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.
A selective photon scheme is proposed to realize an N-qubit Greenberger–Horne–Zeilinger (GHZ) state with distant atoms trapped in spatially separated bimodal cavities coupled by optical fibres. The influence of deviations of some experimental parameters on our scheme is studied exactly and we prove that a highly reliable GHZ state is achievable. Moreover, we analyse the independence of fidelity on decoherence processes, such as atomic spontaneous emission, cavity decay and fibre losses. The results show that atomic spontaneous emission and fibre losses can be ignored in some special cases. With regards to the cavity decay, it indicates that a GHZ state with high fidelity may be realized in the current experiment.