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Journal of Atomic and Molecular Physics

Generation of Greenberger-Horne-Zeilinger-type States of n Atoms

Rui Shao

Published Dec 25, 2008• 0 citations
OpenAlex

Abstract

We propose a scheme for generating Greenberger-Horne-Zeilinger-type states of n atoms trapped in the distant cavities by using interference of polarized photons. In our scheme, the atom-cavity coupling strength is smaller than the cavity decay rate. Thus, the requirement on the quality factor of the cavities is greatly relaxed. Furthermore, thefidelity of our scheme is not affected by the detection ineffciency and atomic decay.

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We propose a scheme for generating Greenberger-Horne-Zeilinger-type states of n atoms trapped in the distant cavities by using interference of polarized photons. In our scheme, the atom-cavity coupling strength is smaller than the cavity decay rate. Thus, the requirement on the quality factor of the cavities is greatly relaxed. Furthermore, thefidelity of our scheme is not affected by the detection ineffciency and atomic decay.
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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 present a scheme for generation of two-atomic entangled state by using the interference of polarized photons. The scheme does not require complete mapping between the atomic state and the photonic state, nor does it require the establishment of maximal entanglement between the atom and the cavity. And the atom-cavity coupling strength is smaller than the cavity decay rate. This greatly relaxes the requirement on the cavity quality. The scheme is for non-post-selection results and all the steps of the scheme are within the current technologies.
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.
A scheme is proposed for the generation of W entangled states for several atoms trapped in a cavity by detecting photon decay. The scheme works in the regime, where the cavity decay rate is larger than the atom-cavity coupling strength. Thus, the requirement for the quality factor of the cavity is greatly loosened, which is of importance in view of experiment. Another advantage of this scheme is that the atoms are always populated in two ground states coupled by Raman transitions, thus the spontaneous emission can also be suppressed.