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arXiv:1712.01756 · Physical Review Letters

Hexapartite Entanglement in an above-Threshold Optical Parametric Oscillator

F. A. S. Barbosa, A. S. Coelho, Luis F. Muñoz-Martínez, Luis Ortiz-Gutiérrez, Alessandro S. Villar, P. Nussenzveig, M. Martinelli

Published Aug 13, 2018• 50 citations

Abstract

We demonstrate, theoretically and experimentally, the generation of hexapartite modal entanglement by the optical parametric oscillator (OPO) operating above the oscillation threshold. We show that the OPO generates a rich structure of entanglement among sets of six optical sideband modes interacting through the nonlinear crystal. The class of quantum states thus produced can be controlled by a single parameter, the power of the external laser that pumps the system. Our platform allows for the generation of massive entanglement among many optical modes with well defined but vastly different frequencies, potentially bridging nodes of a multicolor quantum network.

DOI: 10.1103/physrevlett.121.073601

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The optical parametric oscillator (OPO) is a non-linear optical device capable of producing an effective interaction among optical modes with different colors. Up to now, it was believed that only three modes would be involved in the interaction. By developing a new theoretical model to analyze the sideband structure of entanglement, we show that in fact six modes are involved in the stimulated parametric interaction. We experimentally investigate how those modes are entangled to one another, in particular showing that the hexapartite entanglement can be thought of as being generated by a combination of two-mode squeezers and beam splitter Hamiltonians acting on six different colors of light.

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.

We measure the complete quantum state for six modes of the electromagnetic field produced by an optical parametric oscillator. The investigation involves the sideband of the intense pump, signal, and idler fields generated by stimulated parametric downconversion inside a triply resonant optical resonator. We develop a theoretical model to successfully interpret the experimental results. The model takes into account the coupling of the field modes to the phonon bath of the nonlinear crystal, clearly showing the roles of different physical effects in shaping the structure of the quantum correlations between the six optical modes.