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arXiv:0903.3167 · Physical Review A

Generation of two-dimensional cluster states by using high-finesse bimodal cavities

Denis Gonţa, Thomas Radtke, S. Fritzsche

Published Jun 18, 2009• 29 citations
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Abstract

We propose two schemes to generate the two-dimensional $2\ifmmode\times\else\texttimes\fi{}N$ and $3\ifmmode\times\else\texttimes\fi{}N$ cluster states by using a chain of (two-level) Rydberg atoms in the framework of cavity QED. These schemes work in a completely deterministic way and are based on the resonant interaction of the atoms in a chain with a bimodal cavity that supports two independent modes of the photon field. We demonstrate that a $2\ifmmode\times\else\texttimes\fi{}N$ cluster state can be generated efficiently with only a single bimodal cavity, while two such cavities are needed to produce a $3\ifmmode\times\else\texttimes\fi{}N$ cluster state. It is shown, moreover, how these schemes can be extended toward the generation of $M\ifmmode\times\else\texttimes\fi{}N$ two-dimensional cluster states.

DOI
10.1103/physreva.79.062319

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We propose two schemes to generate the two-dimensional 2\ifmmode×\else\texttimes\fiN2\ifmmode\times\else\texttimes\fi{}N2\ifmmode×\else\texttimes\fiN and 3\ifmmode×\else\texttimes\fiN3\ifmmode\times\else\texttimes\fi{}N3\ifmmode×\else\texttimes\fiN cluster states by using a chain of (two-level) Rydberg atoms in the framework of cavity QED. These schemes work in a completely deterministic way and are based on the resonant interaction of the atoms in a chain with a bimodal cavity that supports two independent modes of the photon field. We demonstrate that a 2\ifmmode×\else\texttimes\fiN2\ifmmode\times\else\texttimes\fi{}N2\ifmmode×\else\texttimes\fiN cluster state can be generated efficiently with only a single bimodal cavity, while two such cavities are needed to produce a 3\ifmmode×\else\texttimes\fiN3\ifmmode\times\else\texttimes\fi{}N3\ifmmode×\else\texttimes\fiN cluster state. It is shown, moreover, how these schemes can be extended toward the generation of M\ifmmode×\else\texttimes\fiNM\ifmmode\times\else\texttimes\fi{}NM\ifmmode×\else\texttimes\fiN two-dimensional cluster states.
We propose two schemes to engineer four-partite entangled Greenberger-Horne-Zeilinger (GHZ) and WWW states in a deterministic way by using chains of (two-level) Rydberg atoms within the framework of cavity QED. These schemes are based on the resonant interaction of the atoms with a bimodal cavity that simultaneously supports, in contrast to a single-mode cavity, two independent modes of the photon field. In addition, we suggest the schemes to reveal the nonclassical correlations for the engineered GHZ and WWW states. It is shown how these schemes can be extended in order to produce general NNN-partite entangled GHZ and WWW states.
We propose two schemes for the generation of cluster states in the context of cavity quantum electrodynamics (QED). In the first scheme, we prepare multi-cavity cluster states with information encoded in the coherent states. The second scheme is to generate multi-atom cluster states, where qubits are represented by the states of cascade Rydberg atoms. Both the schemes are based on the atom-cavity interaction and the atomic spontaneous radiation can be efficiently reduced since the cavity frequency is largely detuned from the atomic transition frequency.
We propose two experimental schemes to generate the cluster states in the context of microwave cavity quantum electrodynamics (QED). In the first scheme to prepare many cavities into the cluster states, we encode the vacuum state and one-photon state of the microwave cavity as the logic zero and one of the qubits. The second scheme is to prepare many atoms into the cluster states, where qubits are represented by the states of Rydberg atoms. Both schemes require the resonant atom-cavity interaction so that the quantum dynamics operates at a high speed, which is important in view of decoherence.
We propose a physical scheme for generating a two-atom cluster state through the simultaneous interaction of two two-level atoms with a single-mode cavity field prepared initially in an odd-coherent state under a large-detuned limit. The influence of the dissipation constant, the intensity of the field and the imperfect manipulation on the preparation scheme are investigated. It is shown that when the intensity of the cavity is large enough, the influence of the cavity decay is efficiently suppressed. The possible error in the implementation of the cluster state is negligible when the time difference between two atoms crossing the cavity axis is small. It is suggested that the scheme can be realized by current technologies.