Generation of the quadripartite Greenberger-Horne-Zeilinger entangled state in quantum beat lasers

In this letter, a scheme is presented to obtain quadripartite Greenberger-Horne-Zeilinger (GHZ) entanglement via quantum beats in a four-level diamond configuration atomic system. When the top and the ground states are initially prepared in a coherent superposition, the four quantized fields coupling with four dipole-allowed transitions can be correlated with each other by using a strong microwave field to drive the dipole-forbidden transition. It is the combined effect of atomic coherence-controlled correlated-spontaneous emission and double quantum beats that results in the quadripartite GHZ-type entanglement. Our numerical results show that the quadripartite entanglement, which can be controlled effectively by varying the amplitude and phase of the microwave field, occurs in a very wide parameter range. In addition, using input-output theory, we find that the output quadripartite entanglement is robust against thermal fluctuations, which may be useful for long-distance quantum communications.