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Journal of Physics B Atomic Molecular and Optical Physics

Quadripartite cluster and Greenberger–Horne–Zeilinger entangled light via cascade interactions with separated atomic ensembles

Xing Li, Xiangming Hu

Published Jun 19, 2012• 4 citations
Publisher

Abstract

It has been known that two-mode entangled light can possibly be generated by employing near-resonant interaction with an ensemble of two-level atoms. The responsible mechanism is the absorption of two photons from the strong driving field and the emission of two new photons into the cavity field. Here, we generalize such a mechanism to three separated atomic ensembles and establish cascade interactions for four nondegenerate fields. It is shown that the quadripartite cluster and Greenberger–Horne–Zeilinger entangled states occur for continuous variables. The advantage of the present scheme for the multipartite entanglement lies in that the coupling strengths are much larger due to the near resonances than for far-off-resonance-based parametric processes.

DOI
10.1088/0953-4075/45/13/135503

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It has been known that two-mode entangled light can possibly be generated by employing near-resonant interaction with an ensemble of two-level atoms. The responsible mechanism is the absorption of two photons from the strong driving field and the emission of two new photons into the cavity field. Here, we generalize such a mechanism to three separated atomic ensembles and establish cascade interactions for four nondegenerate fields. It is shown that the quadripartite cluster and Greenberger–Horne–Zeilinger entangled states occur for continuous variables. The advantage of the present scheme for the multipartite entanglement lies in that the coupling strengths are much larger due to the near resonances than for far-off-resonance-based parametric processes.
It has been known that one reservoir of driven two-level atoms can establish two-mode interactions and generate bipartite continuous-variable entangled light. Here we show that three-mode interactions can be created by combining two such reservoirs, each of which interacts with two adjacent fields in frequency. It is shown that the van Loock--Furusawa criteria [Phys. Rev. A 67, 052315 (2003)] are well satisfied for a wide range of the relevant parameters. This determines that tripartite continuous-variable Greenberger-Horne-Zeilinger entanglement is obtainable. The scalability to more fields is straightforward, allowing an alternative implementation of a multipartite quantum networks with continuous variables.
We show that, in analogy to light fields, effective bosonic modes of atomic ensembles in the Holstein-Primakoff representation can be prepared in multimode squeezed states, and multipartite continuous-variable cluster and Greenberger-Horne-Zeilinger (GHZ) entangled states. Our scheme uses a cascade of optical cavities, in each of which one atomic ensemble is placed. Through Raman transitions between stable atomic ground states, the atomic ensembles are in the interactions with the cavity and laser fields. Because of the long-lived ground states, the atomic ensembles act as quantum network nodes, whose cluster entangled states are applicable in the one-way quantum computer, and whose GHZ entangled states have potential for quantum communication.
The cluster states and Greenberger-Horne-Zeilinger (GHZ) states are two different types of multipartite quantum entangled states. We present the first experimental results generating continuous variable quadripartite cluster and GHZ entangled states of electromagnetic fields. Utilizing two amplitude-quadrature and two phase-quadrature squeezed states of light and linearly optical transformations, the two types of entangled states for amplitude and phase quadratures of light are experimentally produced. The combinations of the measured quadrature variances prove the full inseparability of the generated four subsystems. The presented experimental schemes show that the multipartite entanglement of continuous variables can be deterministically generated with the relatively simple implementation.
We show that it is possible to generate a quadripartite square graph-state entanglement in two-photon resonant systems. Every vertex of the square represents an optical field and every side stands for the entanglement of the two vertices. Four optical fields of different frequencies are coupled to coherently driven three-level ladder atoms. Through such a system, quantum beats and two-photon resonant interactions combine to cause the collective-mode parametric interactions. This results in the collective-mode entanglement, which corresponds to the square graph-state entanglement of the four individual fields.
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.