Continuous-variable multimode entanglement in multi-wave mixing

We present a scheme to obtain continuous-variable multimode entanglement via multi-wave mixing. For a four-level atomic system in a diamond configuration, four strong coherence fields are applied to the four dipole-allowed transitions to amplify eight sidebands as cavity fields, respectively. Due to the atomic coherence, the eight side modes constitute a pair of double quantum-beats and combine into two quantum-beat collective modes, which are in a four-wave mixing parametric interaction. As a result, the entanglement occurs between these two collective modes. Correspondingly, any two individual modes from two different collective modes are entangled with each other. This gives rise to continuous-variable eight-mode entanglement with different frequencies, which has extensively application in quantum communication and quantum network.