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arXiv:quant-ph/0505131 · Physical Review A

Bright tripartite entanglement in triply concurrent parametric oscillation

Ashton S. Bradley, M. K. Olsen, Olivier Pfister, Raphael C. Pooser

Published Nov 4, 2005• 77 citations
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Abstract

We show that an optical parametric oscillator based on three concurrent ${\ensuremath{\chi}}^{(2)}$ nonlinearities can produce, above threshold, bright output beams of macroscopic intensities which exhibit strong tripartite continuous-variable entanglement. We also show that there are two ways that the system can exhibit a three-mode form of the Einstein-Podolsky-Rosen paradox, and calculate the extracavity fluctuation spectra that may be measured to verify our predictions.

DOI
10.1103/physreva.72.053805

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We show that an optical parametric oscillator based on three concurrent \ensuremathχ(2){\ensuremath{\chi}}^{(2)}\ensuremathχ(2) nonlinearities can produce, above threshold, bright output beams of macroscopic intensities which exhibit strong tripartite continuous-variable entanglement. We also show that there are two ways that the system can exhibit a three-mode form of the Einstein-Podolsky-Rosen paradox, and calculate the extracavity fluctuation spectra that may be measured to verify our predictions.
We show that an intracavity optical device which utilises concurrent chi(2)\\chi^{(2)}chi(2) nonlinearities can produce output beams which exhibit strong tripartite entanglement. Above threshold a significant degree of entanglement is predicted for beams with macroscopic intensities. We also demonstrate two independent ways that the system can exhibit a three mode form of the Einstein-Podolsky-Rosen paradox.
We calculate the quantum correlations existing among the three output fields (pump, signal, and idler) of a triply resonant nondegenerate optical parametric oscillator operating above threshold. By applying the standard criteria [P. van Loock and A. Furusawa, Phys. Rev. A 67, 052315 (2003)], we show that strong tripartite continuous-variable entanglement is present in this well-known and simple system. Furthermore, since the entanglement is generated directly from a nonlinear process, the three entangled fields can have very different frequencies, opening the way for multicolored quantum information networks.
We develop three-mode generalizations of the Einstein-Podolsky-Rosen paradox, allowing us to define inequalities which may be used to indicate continuous-variable tripartite entanglement. We use these inequalities and an appropriate version of the previously developed van Loock-Furusawa inequalities to theoretically compare the continuous-variable tripartite entanglement available from the use of three concurrent x (2) nonlinearities and from three independent squeezed states mixed on beamsplitters.
We consider an optical parametric oscillator above threshold; under appropriate conditions and in the far-field, the emitted signal is composed by two spatially separate beams, highly correlated on the quantum level. We show that this system can realize the Einstein–Podolsky–Rosen paradox for continuous and macroscopic observables. The pair of non-commuting obserables considered are the intensity and the phase of the two separate beams; the spectral variances of the fluctuation in the intensity difference and in the phase sum of the two beams are calculated. The conditions for which the product of the spectral variances is below the limit settled by the Heisenberg uncertainty principle are studied.
We compare theoretically the tripartite entanglement available from the use of three concurrent χ(2)χ^{(2)}χ(2) nonlinearities and three independent squeezed states mixed on beamsplitters, using the van Loock-Furusawa inequalities. We also define three-mode generalisations of the Einstein-Podolsky-Rosen paradox which are an alternative for demonstrating the inseparability of the density matrix.