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Journal of Optics B Quantum and Semiclassical Optics

Proposal for preparing delocalized mesoscopic states of material oscillators

A. S. Parkins

Published Jan 25, 2001• 3 citations
Publisher

Abstract

A scheme is proposed for preparing delocalized mesoscopic states of the motion of two or more atoms trapped at distantly separated locations. Generation of entanglement is achieved using interactions in cavity quantum electrodynamics which facilitate motional quantum state transmission, via light, between separate nodes of a quantum network. Possible applications of the scheme are discussed.

DOI
10.1088/1464-4266/3/1/354

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A scheme is proposed for preparing delocalized mesoscopic states of the motion of two or more atoms trapped at distantly separated locations. Generation of entanglement is achieved using interactions in cavity quantum electrodynamics which facilitate motional quantum state transmission, via light, between separate nodes of a quantum network. Possible applications of the scheme are discussed.
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.
We propose a scheme to generate superposition and entanglement between the mesoscopic squeezed vacuum states by considering the two-photon interaction of NNN two-level atoms in a cavity with high quality factor, assisted by a strong driving field. By virtue of specific choices of the cavity detuning, a number of multiparty entangled states can be prepared, including the entanglement between the atomic and the squeezed vacuum cavity states and between the squeezed vacuum states and the coherent states of the cavities. We also present how to prepare entangled states and ``Schr\"odinger cats'' states regarding the squeezed vacuum states of the cavity modes. The possible extension and application of our scheme are discussed. Our scheme is close to the reach with current cavity QED techniques.
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.
In a recent publication [K. Hammerer, M. Wallquist, C. Genes, M. Ludwig, F. Marquardt, P. Treutlein, P. Zoller, J. Ye, and H. J. Kimble, Phys. Rev. Lett. 103, 063005 (2009)] we have shown the possibility to achieve strong coupling of the quantized motion of a micron-sized mechanical system to the motion of a single trapped atom. In the proposed setup the coherent coupling between a SiN membrane and a single atom is mediated by the field of a high finesse cavity and can be much larger than the relevant decoherence rates. This makes the well-developed tools of cavity quantum electrodynamics with single atoms available in the realm of cavity optomechanics. In this article we elaborate on this scheme and provide detailed derivations and technical comments. Moreover, we give numerical as well as analytical results for a number of possible applications for transfer of squeezed or Fock states from atom to membrane as well as entanglement generation, taking full account of dissipation. In the limit of strong-coupling the preparation and verification of nonclassical states of a mesoscopic mechanical system is within reach.