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

TL;DR

This paper explores the generation and properties of a continuous-variable quadripartite cluster state using a single optical parametric oscillator, analyzing entanglement, phase diffusion, and the effects of cavity dynamics.

Contribution

It demonstrates the feasibility of creating a quadripartite cluster state in a cavity, addressing phase diffusion issues and analyzing the impact of cavity and depletion effects on entanglement.

Findings

Genuine quadripartite entanglement is demonstrated.

Phase diffusion can be mitigated with an injected signal.

Cavity effects inhibit perfect cluster state formation.

Abstract

We examine the feasibility of generating continuous-variable multipartite entanglement in an intra-cavity quadruply concurrent downconversion scheme that has been proposed for the generation of cluster states by Menicucci \textit{et al.} [Physical Review Letters \textbf{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.