Multipartite continuous-variable entanglement in a multi-mode period pumping non-degenerate optical parametric amplifier

The multipartite continuous-variable (CV) entanglement characteristic of a multi-mode phased-locked period pumping non-degenerate optical parametric amplification system was investigated for the case when finite bandwidth is considered. A continuously modulated pumping with a sinusoidal envelope can produce an improvement in the minimum values of the multipartite CV entanglement. The minimum variances can be described approximately by the linear theory formula 1/(1 + mu). We should take a proper bandwidth Delta omega in order to obtain a long-term entanglement. The larger values of pump parameter mu and particle number N result in long-term entanglement.