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arXiv:0710.4980 · Laser Physics

Entangling the optical frequency comb: Simultaneous generation of multiple 2 × 2 and 2 × 3 continuous-variable cluster states in a single optical parametric oscillator

Hussain Zaidi, Nicolas C. Menicucci, Steven T. Flammia, Russell Bloomer, Matthew Pysher, Olivier Pfister

Published May 1, 2008• 38 citations

Abstract

We report on our research effort to generate large-scale multipartite optical-mode entanglement using as few physical resources as possible. We have previously shown that cluster-and GHZ-type N-partite continuous-variable entanglement can be obtained in an optical resonator that contains a suitably designed second-order nonlinear optical medium, pumped by at most $$ \mathcal{O} $$ (N 2) fields. In this paper, we show that the frequency comb of such a resonator can be entangled in an arbitrary number of independent 2 × 2 and 2 × 3 continuousvariable cluster states by a single optical parametric oscillator pumped by just a few optical modes.

DOI: 10.1134/s1054660x08050186

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\mathcal{O}

(N 2) fields. In this paper, we show that the frequency comb of such a resonator can be entangled in an arbitrary number of independent 2 × 2 and 2 × 3 continuousvariable cluster states by a single optical parametric oscillator pumped by just a few optical modes.

Cluster entangled states are often used as the fundamental resources for one-way quantum computation. In this paper, we put forward a scheme of generating the spatial cluster entangled states of Laguerre–Gaussian modes in a large-Fresnel-number degenerate optical parametric oscillator operating below threshold with type I phase matching, which is pumped by two spatial Laguerre–Gaussian modes with the same frequency. The nonlinear parametric process of each pump mode satisfies momentum, energy, and orbit angular momentum conservation. Eleven-partite spatial cluster entangled states of Laguerre–Gaussian modes can be produced in the optical mode comb under feasible experimental condition, which can be demonstrated by using the entanglement criterion proposed by van Loock and Furusawa.

We show theoretically that multipartite entanglement is generated on a massive scale in the spectrum, or optical frequency comb, of a single optical parametric oscillator (OPO) emitting well above threshold. In this system, the quantum dynamics of the strongly depleted pump field are responsible for the onset of the entanglement by correlating the two-mode squeezed, bipartite-entangled pairs of OPO signal fields. (Such pairs are independent of one another in the undepleted, classical pump approximation.) We verify the multipartite nature of the entanglement by evaluating the van Loock-Furusawa criterion for a particular set of entanglement witnesses deduced from physical considerations.

We show theoretically that multipartite entanglement is generated on a massive scale in the spectrum, or optical frequency comb, of a single optical parametric oscillator (OPO) emitting well above threshold. In this system, the quantum dynamics of the strongly depleted pump field are responsible for the onset of the entanglement by correlating the two-mode squeezed, bipartite-entangled pairs of OPO signal fields. (Such pairs are independent of one another in the undepleted, classical pump approximation.) We verify the multipartite nature of the entanglement by evaluating the van Loock-Furusawa criterion for a particular set of entanglement witnesses deduced from physical considerations.