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arXiv:0812.4631 · Physical Review A

Generation of pure continuous-variable entangled cluster states of four separate atomic ensembles in a ring cavity

Gao‐xiang Li, Sha‐Sha Ke, Z. Ficek

Published Mar 17, 2009• 53 citations

Abstract

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.

DOI: 10.1103/physreva.79.033827

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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.

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.

Four-mode continuous-variable (CV) cluster states are an important and necessary resource in continuous-variable quantum computation. In this paper, we present a simple and efficient scheme to realize an unequally weighted four-mode square CV cluster state using atomic ensembles driven by seven strong classical laser fields. The scheme requires just a single selection of the appropriate squeezing parameters and pump laser parameters. With the unique squeezing operator and a new unitary transformation, we show that seven laser fields drive four atomic ensembles into a stationary four-mode squeezed vacuum state via the cavity dissipation.

We propose a scheme to generate four-mode cluster states with four atomic ensembles trapped in single-mode cavities connected by short fibers. With the aid of the cavity dissipation, we find that a four-mode cluster state can be unconditionally created by the simultaneous driving of the ensembles with laser pulses of suitably chosen Rabi frequencies and phases. The scheme could be easily extended to the case of

N

-mode cluster states.

We investigate the generation of continuous-variable (CV) entanglement of two separated atomic ensembles in coupled cavities. We find that under certain conditions, the entanglement between the two ensembles is gained periodically when the three-level $\ensuremath{\Lambda}$-type atoms in each ensemble dispersively interact with one classical field and one cavity mode. Generation of the entangled state does not completely depend on the cavity photon number. In addition, the effect of decoherence can be suppressed effectively.

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.