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arXiv:quant-ph/9907049 · Physical Review A

Position-momentum Einstein-Podolsky-Rosen state of distantly separated trapped atoms

A. S. Parkins, Harry J. Kimble

Published Apr 5, 2000• 50 citations
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Abstract

We propose a scheme for preparing an Einstein-Podolsky-Rosen state in position and momentum of a pair of distantly separated trapped atoms. The scheme utilizes the entangled light fields output from a nondegenerate optical parametric amplifier. Quantum-state exchange between these fields and the motional states of the trapped atoms is accomplished via interactions in cavity QED.

DOI
10.1103/physreva.61.052104

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We propose a scheme for preparing an Einstein-Podolsky-Rosen state in position and momentum of a pair of distantly separated trapped atoms. The scheme utilizes the entangled light fields output from a nondegenerate optical parametric amplifier. Quantum-state exchange between these fields and the motional states of the trapped atoms is accomplished via interactions in cavity QED.
We propose a scheme for entangling the motional mode of a trapped atom with a propagating light field via a cavity-mediated parametric interaction. We then show that if this light field is subsequently coupled to a second distant atom via a cavity-mediated linear-mixing interaction, it is possible to transfer the entanglement from the light beam to the motional mode of the second atom to create an Einstein-Podolsky-Rosen--type entangled state of the positions and momenta of two distantly separated atoms.
We describe and analyze numerically schemes (i) for entangling orthogonal motional modes of one or a few harmonically trapped atoms or ions and (ii) for transferring the entanglement from one of these local modes to a distant trapped atom (or atoms) via a light-mediated quantum-state transfer procedure proposed in previous work [A.S. Parkins and H.J. Kimble, J. Opt. B: Quantum Semiclass. Opt. 1,1,1, 496 (1999)]. Possibilities arising from these schemes include the generation of an Einstein-Podolsky-Rosen state in the positions and momenta of distantly separated trapped atoms and the preparation of delocalized mesoscopic vibrational states.
Pairs of atoms have been prepared in an entangled state of the Einstein-Podolsky-Rosen (EPR) type. They were produced by the exchange of a single photon between the atoms in a high QQQ cavity. The atoms, entangled in a superposition involving two different circular Rydberg states, were separated by a distance of the order of 1 cm. At variance with most previous EPR experiments, this one involves massive particles. It can be generalized to three or more atoms and opens the way to new tests of nonlocality in mesoscopic quantum systems.
A scheme for the output of an Einstein-Podolsky-Rosen entangled photon pair is proposed in a cavity QED system composed of two high QQQ cavities and a moving atom passing through them and with a final detection on the atomic ground states. The theoretical derivation shows that the production of multientangled photons can be achieved by passing the atom through additional cavities along the atom's path.