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arXiv:1009.3349 · Physical Review A

Analysis of a continuous-variable quadripartite cluster state from a single optical parametric oscillator

S. L. W. Midgley, M. K. Olsen, Ashton S. Bradley, Olivier Pfister

Published Nov 24, 2010• 13 citations

Abstract

We examine the feasibility of generating continuous-variable multipartite entanglement in an intracavity concurrent downconversion scheme that has been proposed for the generation of cluster states by Menicucci et al. [Phys. Rev. Lett. 101, 130501 (2008)]. By calculating optimized versions of the van Loock-Furusawa correlations we demonstrate genuine quadripartite entanglement and investigate the degree of entanglement present. Above the oscillation threshold the basic cluster state geometry under consideration suffers from phase diffusion. We alleviate this problem by incorporating a small injected signal into our analysis. Finally, we investigate squeezed joint operators. While the squeezed joint operators approach zero in the undepleted regime, we find that this is not the case when we consider the full interaction Hamiltonian and the presence of a cavity. In fact, we find that the decay of these operators is minimal in a cavity, and even depletion alone inhibits cluster state formation.

DOI: 10.1103/physreva.82.053826

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We examine the feasibility of generating continuous-variable multipartite entanglement in an intracavity concurrent downconversion scheme that has been proposed for the generation of cluster states by Menicucci et al. [Phys. Rev. Lett. 101, 130501 (2008)]. By calculating optimized versions of the van Loock-Furusawa correlations we demonstrate genuine quadripartite entanglement and investigate the degree of entanglement present. Above the oscillation threshold the basic cluster state geometry under consideration suffers from phase diffusion. We alleviate this problem by incorporating a small injected signal into our analysis. Finally, we investigate squeezed joint operators. While the squeezed joint operators approach zero in the undepleted regime, we find that this is not the case when we consider the full interaction Hamiltonian and the presence of a cavity. In fact, we find that the decay of these operators is minimal in a cavity, and even depletion alone inhibits cluster state formation.

We investigate an experimentally feasible intracavity coupled down-conversion scheme to generate quadripartite entanglement using concurrent nonlinearities. We verify that quadripartite entanglement is present in this system by calculating the output fluctuation spectra and then considering violations of optimized inequalities of the van Loock--Furusawa type. The entanglement characteristics both above and below the oscillation threshold are considered. We also present analytic solutions for the quadrature operators and the van Loock--Furusawa correlations in the undepleted pump approximation.

We theoretically show that continuous-variable genuine quadripartite entanglement can be generated by intracavity cascaded nonlinear optical interactions. The process consists of a parametric down-conversion, a sum-frequency generation of pump and signal and a sum-frequency generation of pump and idler. The characteristics of the quadripartite entanglement among the signal, the idler, and two sum-frequency modes are analyzed by applying a sufficient inseparability criterion for multipartite continuous-variable entanglement proposed by Van Loock and Furusawa. The threshold properties of the system are also discussed.

We designed the experimental generation system of the optical GHZ-like and cluster-like quadripartite entangled states for continuous variables.We theoretically demonstrated that the two different types of quadripartite entangled states can be obtained by the linearly optical transformation of four amplitude-quadrature and phase-quadrature squeezed states produced from a pair of nondegenerate optical parametric amplifiers under appropriate phase relations.The criteria for full inseparability of quadripartite cluster-like state were deduced,and the dependency of the quadripartite entanglement on the initial squeezing degree,the transmission efficiencies of the system and the detection efficiency of homodyne detection were numerically calculated.

The quantum correlations between the output signal, the output idler and the reflected pump fields generated by non-degenerate optical parametric oscillator operating above the oscillation threshold are theoretically calculated with the semi-classical formulae. According to the multipartite entanglement criteria for the continuous variables, proposed by P. van Loock and A. Furusawa, the calculated results prove the existence of the quantum correlations between the amplitude and the phase quadrature for the three optical fields, i. e. they form a tripartite entangled state. We numerically calculate the dependence of the entanglement on the physical parameters of the optical oscillator and find the optimum operating conditions of the oscillator to produce the three-color tripartite entangled state, which provide the direct references for the design of the continuous variable multipartite entanglement generation systems.