Three-color continuous-variable (CV) entangled beams can be produced by single-pass cascaded sum-frequency processes of third-harmonic generation by quasi-phase-matching technique in only one optical superlattice. Firstly, second-harmonic field is generated by the first double-frequency process of the fundamental field. Then, the third-harmonic field can be generated by the second cascaded sum-frequency process between the second-harmonic and the fundamental fields by quasi-phase-matching technique in the same optical superlattice. By using the quantum stochastic method, we investigated the conversion dynamics of the cascaded sum-frequency processes and the quantum correlation nature among the fundamental, second-harmonic, and third-harmonic fields. The results show that the higher conversion efficiency of third-harmonic generation can be achieved with the larger nonlinear coupling parameter of the second cascaded sum-frequency process. We also show that the fundamental, second-, and third-harmonic beams are CV entangled with each other according to the necessary and sufficient CV entanglement criterion. This scheme of three-color entanglement generation without involving optical cavity is easy to realize in experiment. Moreover, the three-color entangled beams are separated by an octave in frequency which has potential applications in quantum communication and computation networks.

Continuous-variable (CV) entanglement frequency comb can be produced by enhanced Raman scattering in an above-threshold optical oscillator cavity in which a hexagonally-poled LiTaO3 crystal resides as a Raman gain medium. The Stokes and anti-Stokes Raman signals are enhanced by a coupled quasi-phase-matching optical parametric process and the entanglement natures among these Raman signals and pump are demonstrated by applying a sufficient inseparability criterion for CV entanglement. Such entanglement frequency comb source with different frequencies and continuously tunable frequency interval may be very significant for the applications in quantum communication and networks.

Three-colour continuous-variable entanglement produced by single-pass cascaded quasi-phase-matching fourth harmonic generation is investigated. The fourth harmonic can be generated through cascaded double-frequency processes in a quasiperiodic optical superlattice by using quasi-phase-matching technology. The conversion dynamics of the cascaded double-frequency processes is studied using quantum stochastic methods. The nature of the entanglement is discussed by applying a necessary and sufficient criterion for continuous-variable entanglement. Strong three-colour entanglement among the fundamental, second-, and fourth-harmonic beams with a double frequency interval can be produced without an optical oscillator cavity. This is experimentally feasible and has potential applications in quantum communication and computation networks.

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Quadripartite continuous-variable (CV) entanglement with different optical frequencies can be generated by nondegenerate optical parametric amplification cascaded with a sum-frequency process in only one optical superlattice. Firstly, the idler beam is generated by a different frequency process between pump and signal beams. Then, the sum-frequency beam will be generated by a cascaded sum-frequency process between pump and idler beams in the same optical superlattice. The conversion dynamics of the cascaded nonlinear processes is investigated by using a quantum stochastic method. The quantum correlations among pump, signal, idler and sum-frequency beams are calculated by applying a sufficient inseparability criteria for quadripartite CV entanglement. The results show that quadripartite CV entangled beams can be produced by this single-pass cascaded nonlinear process in one optical superlattice.