Quadripartite entanglement from a double three-level Λ -type-atom model

We present a theoretical scheme for the generation of four quantized modes in a three-level double-Λ atomic system driven by two counterpropagating far-detuned pump beams and find the entanglement between the four modes. By using the second-order perturbation method and the phase-matching condition for the four-wave mixing processes, the effective Hamiltonian is derived, which clearly illustrates the generation of four light beams and their entanglement. The dependence of the four-mode entanglement on interaction time, pump detuning, strength of interaction force, and the ratio of Rabi frequency of two pump beams is analyzed with inseparability. The result presented here provides a method for the experimental generation of multipartite entanglement in an atomic system.