Quadripartite entanglement from cascaded χ2 nonlinear interactions

We theoretically analyze the generation of quadripartite continuous-variable entanglement, with different frequency, by cascaded nonlinear process in a quadruply resonant optical cavity. This process is realized by one optical parametric down-conversion operated below threshold cascaded by two sum-frequency generations in a quasiperiodic optical supperlattice. It shows that the signal, idler and two sum frequency modes are entangled according to the sufficient inseparability criterion proposed by van Loock and Furusawa. The quantum correlation spectra among these four modes versus normalized analysis frequency and nonlinear coupling coefficients are discussed as well in detail.