  We demonstrate and characterize the extraction of genuine tripartite
entanglement from the vacuum of a periodic cavity field. That is, three probe
quantum systems (detectors) can become both bipartitely and tripartitely
entangled without coming into causal contact, by means of interaction with a
common quantum field. We do this by using an oscillator-detector model that
forgoes the need for perturbation theory and which instead is solved exactly.
We find that the extraction of tripartite entanglement is considerably easier
than that of bipartite. As a secondary result, we also compare a periodic
cavity with one that has Dirichlet boundary conditions. We find that the
extraction of both bipartite and tripartite entanglement is more easily
achieved using the former case.
