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Physical Review A

Separated atomic ensembles: Multimode squeezed states and multipartite entangled states

Qing Yang Xu, Xiangming Hu

Published Sep 26, 2012• 9 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.86.032337

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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 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.
Two schemes for the preparation of weighted continuous variable cluster states with four atomic ensembles are proposed. In the first scheme, the four separated atomic ensembles inside a two-mode ring cavity are driven by pulse laser fields. The basic idea of the scheme is to transfer the ensemble bosonic modes into suitable linear combinations that can be prepared in a pure cluster state by a sequential application of the laser pulses with the aid of the cavity dissipation. In the second one, we take two separate two-mode cavities, each containing two atomic ensembles. The distant cavities are coupled by dissipation in a cascade way. It has been found that the mixed cluster state can be produced. These schemes may contribute towards implementing continuous variable quantum computation, quantum communication and networking based on atomic ensembles.
We describe the effects of Raman interactions on the quantum correlations of multimode optical fields. It is shown that both quantum beats and four-wave mixing processes exist in the Raman interactions of multimode fields with atomic reservoirs. These two mechanisms combine to lead to emission in pairs into multiple cavity modes. For four fields taken as examples, we find that the four-mode squeezed state can be created at steady state. From this we can obtain the Greenberger–Horne–Zeilinger entangled state, and the linear and square cluster entangled states. This scheme does not need the preparation of the initial states of atoms and cavity modes, and is robust against atomic spontaneous decay.
A practical scheme is proposed for the creation of continuous-variable entangled cluster states of four distinct atomic ensembles located inside a high-finesse ring cavity. The scheme does not require a set of external input squeezed fields, a network of beam splitters, and measurements. It is based on nothing else than the dispersive interaction between the atomic ensembles and the cavity mode and a sequential application of laser pulses of a suitably adjusted amplitudes and phases. We show that the sequential laser pulses drive the atomic ``field modes'' into pure squeezed vacuum states. The state is then examined against the requirement to belong to the class of cluster states. We illustrate the method on three examples of the entangled cluster states: the so-called continuous-variable linear, square, and T-type cluster states.