Tripartite entanglement in a detuned non-degenerate optical parametric oscillator

Continuous variable multipartite entanglement is an important resource in quantum optics and quantum information. Non-degenerate optical parametric oscillator (NOPO), generally working in a resonant regime, can generate high quality tripartite entanglement. However, the detuning in a real experiment is inevitable and sometimes necessary, for instance, in an optomechanical system. We calculate the tripartite entanglement from a detuned triply quasi-resonant NOPO. Unlike the previous literature using inseparability criterion, we use the positivity of partial transpose, a sufficient and necessary criterion, to characterize the tripartite entanglement with full inseparability generated from a detuned NOPO. We also consider the influence of the pump and signal/idler losses on the tripartite entanglement. The results show that, the tripartite entanglement could exist even with a large detuning of several times cavity linewidth, and may be better for a detuned regime than for the resonant one under some conditions. With a fixed non-zero loss which always exists in a real experiment, an appropriate value of non-zero detuning could lead to the best entanglement. What’s more, unlike the bipartite entanglement, which exists both below and above threshold, the tripartite entanglement only occurs for a nonzero classical amplitude of signal/idler field. The jumping between the tripartite and bipartite entanglement could make the NOPO become a quantum state switch element, which promises a potential application on the multiparty quantum secret sharing.