Bipartite and tripartite steering by a nonlinear medium in a cavity

Abstract

Nonlocal quantum correlations are important for potential applications in quantum optics and quantum information. Multipartite quantum correlations are relevant to access to high-dimensional systems such as qudits. There are also different proposals for the generation of quantum steering based on nonlinear systems and cavities. Here, we consider the Hamiltonian of a triple photon parametric down-conversion process to investigate the regions where bipartite and tripartite steering are generated. In this model, three beams interact with a nonlinear medium inside a cavity through the process of parametric down-conversion, creating three output fields. The positive P representation is used to analyze this system and steady-state solutions are obtained. We calculated the intracavity fluctuation spectra to analyze steering in the frequency domain and used different criteria to certify this quantum correlation. We certified bipartite steering for the three output fields from the cavity. In the case of full tripartite two-way steering inseparability, it is also present for all the bipartitions under consideration. Our results show regimes where bipartite and tripartite steering is certified for this model.