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Physical Review A

Creating multimode squeezed states and Greenberger-Horne-Zeilinger entangled states using atomic coherent effects

Xiao Liang, Xiangming Hu, Chang He

Published Mar 26, 2012• 18 citations
Publisher

Abstract

We propose a scalable scheme for a unitary multimode operator using an optical cavity with an atomic ensemble. We exemplify three-mode and four-mode cases and engineer the squeeze operators that are decoupled from the atomic degrees of freedom. The squeeze parameters can be large since they are proportional to the number of atoms. Using the input-output theory we show that ideal squeezed states and perfect squeezing could be approached at the output. At the same time, we show that it is possible to obtain tripartite and quadripartite Greenberger-Horne-Zeilinger entangled states for continuous variables. The responsible mechanism for both the multimode squeezing and the genuine multipartite entanglement is based on the atomic coherence controlled parametric interactions. The scalability of the scheme is simply obtained by including more transitions in the atomic system.

DOI
10.1103/physreva.85.032329

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We propose a scalable scheme for a unitary multimode operator using an optical cavity with an atomic ensemble. We exemplify three-mode and four-mode cases and engineer the squeeze operators that are decoupled from the atomic degrees of freedom. The squeeze parameters can be large since they are proportional to the number of atoms. Using the input-output theory we show that ideal squeezed states and perfect squeezing could be approached at the output. At the same time, we show that it is possible to obtain tripartite and quadripartite Greenberger-Horne-Zeilinger entangled states for continuous variables. The responsible mechanism for both the multimode squeezing and the genuine multipartite entanglement is based on the atomic coherence controlled parametric interactions. The scalability of the scheme is simply obtained by including more transitions in the atomic system.
A scheme is presented for generating unitarily multimode field squeezing, cluster entanglement, and Greenberger-Horne-Zeilinger (GHZ) entanglement via cavity quantum electrodynamics. Through a suitable laser system, we are able to engineer a squeeze field operator decoupled from the atomic degrees of freedom, yielding a large squeeze parameter proportional to the number of atoms. The physical mechanism is attributed to the multiple four-photon processes and the dispersive atom-cavity-field interaction in large detuning systems.
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.
We propose a method of generating unitarily single and two-mode field squeezing in an optical cavity with an atomic cloud. Through a suitable laser system, we are able to engineer a squeeze field operator decoupled from the atomic degrees of freedom, yielding a large squeeze parameter that is scaled up by the number of atoms, and realizing degenerate and nondegenerate parametric amplification. By means of the input-output theory we show that ideal squeezed states and perfect squeezing could be approached at the output. The scheme is robust to decoherence processes.
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.
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.